context list | question string | ground_truth string | response string | grade float64 | explanation string | has_context bool | context_id int64 | question_id int64 | repeat_no int64 | total_output_tokens int64 | reasoning_tokens int64 | reasoning_content string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Brief explanation:
For \(S_a(200t)=\dfrac{\sin(200t)}{200t}\), the spectrum is bandlimited to
\[
\omega_m = 200 \text{ rad/s}
\]
so
\[
f_m=\frac{\omega_m}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
and the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec}
\]
For \([S_a(200t)]^2\), squaring in... | 10 | The response explicitly concludes that the matching option is D, which agrees with the ground truth. | true | 0 | 10 | 0 | 1,234 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D.**
For \(S_a(200t)=\dfrac{\sin(200t)}{200t}\), the spectrum is bandlimited to
\[
|\omega| \le 200 \text{ rad/s}
\]
so the highest frequency is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
and the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec}
\]
For \([S_a(200t)]^2\), squaring ... | 10 | The response ultimately commits to option D, which matches the ground truth. | true | 1 | 10 | 0 | 1,754 | 1,536 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **Answer: D**
For \(S_a(t)=\dfrac{\sin t}{t}\), \(S_a(200t)\) is bandlimited to
\[
\omega_m = 200 \text{ rad/s}
\]
so the highest frequency in cycles/sec is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
Thus the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec}
\]
For \([S_a(200t)]^2\)... | 10 | The response explicitly concludes with option D, which matches the ground truth. | true | 2 | 10 | 0 | 1,251 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D** *(closest/expected option)*
Briefly: \(S_a(t)=\frac{\sin t}{t}\), so \(S_a(200t)\) is bandlimited to
\[
\omega_m=200 \text{ rad/s} \Rightarrow f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ Hz}
\]
Thus the Nyquist sampling interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ s}
\]
For \([S_a(200t)]^2\), squar... | 10 | The response clearly commits to option D at the end, and that matches the ground truth. | true | 3 | 10 | 0 | 1,229 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Briefly: assuming \(S_a(x)=\dfrac{\sin x}{x}\),
- \(S_a(200t)\) has spectrum limited to \(|\omega|\le 200\ \text{rad/s}\), so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{sec}
\]
- Squaring in time convolves the spectrum w... | 10 | The response explicitly concludes with option D, which matches the ground truth. | true | 4 | 10 | 0 | 1,564 | 1,338 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Using \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \):
- \( \mathrm{Sa}(200t) \) is bandlimited to
\[
\omega_m=200\ \text{rad/s} \Rightarrow f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- Squaring in time doubles the bandwidth, ... | 10 | The response explicitly commits to option D at the end, which matches the ground truth. | true | 5 | 10 | 0 | 1,166 | 921 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Briefly: Taking \(S_a(t)=\dfrac{\sin t}{t}\),
- \(S_a(200t)\) is bandlimited to \(\omega_m=200\ \text{rad/s}\), so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- \([S_a(200t)]^2\) has twice the bandwidth, so \(\omega... | 10 | The response explicitly concludes that the matching option is D, which agrees with the ground truth. | true | 6 | 10 | 0 | 1,267 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **Answer: D**
Briefly: \(S_a(t)=\dfrac{\sin t}{t}\), so \(S_a(200t)\) is bandlimited to
\[
\omega_m = 200 \text{ rad/s}
\]
Converting to Hz:
\[
f_m=\frac{\omega_m}{2\pi}=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
So the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{sec}
\]
For \([S_a(200t... | 10 | The response explicitly concludes with option D, which matches the ground truth. | true | 7 | 10 | 0 | 1,251 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Briefly: Using \(S_a(t)=\dfrac{\sin t}{t}\), \(S_a(200t)\) is bandlimited to
\[
|\omega| \le 200 \text{ rad/s}
\]
so the highest frequency is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
and the Nyquist sampling interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec}
\]
For \([S_a(200t)]^2\),... | 10 | The response clearly commits to option D at the end, and that matches the ground truth. | true | 8 | 10 | 0 | 1,261 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Assuming \(S_a(t)=\dfrac{\sin t}{t}\):
- \(S_a(200t)\) has spectrum limited to \(|\omega|\le 200\ \text{rad/s}\), so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- \([S_a(200t)]^2\) has double bandwidth, so \(|\omega... | 10 | The response explicitly concludes that the matching option is D, which agrees with the ground truth. | true | 9 | 10 | 0 | 1,106 | 862 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | D.
Briefly: For \(S_a(t)=\frac{\sin t}{t}\), \(S_a(200t)\) is bandlimited to
\[
\omega_m = 200 \text{ rad/s} \Rightarrow f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
So the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ s}
\]
For \([S_a(200t)]^2\), squaring in time doubles the bandwidth:
\[... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 0 | 10 | 1 | 1,742 | 1,536 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Briefly: Using \(S_a(x)=\dfrac{\sin x}{x}\),
- \(S_a(200t)\) has spectral support up to
\[
\omega_m=200\ \text{rad/s} \Rightarrow f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
so Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- Squaring in time doubles the bandwidth,... | 10 | The response explicitly concludes with option D, which matches the ground truth. | true | 1 | 10 | 1 | 1,764 | 1,536 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D.**
Using \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \):
- \( \mathrm{Sa}(200t) \) has spectrum limited to
\[
|\omega|\le 200 \text{ rad/s}
\]
so
\[
f_{\max}=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
and the Nyquist interval is
\[
T_N=\frac{1}{2f_{\max}}=\frac{\pi}{200}\text{ sec}.
\]
- Squa... | 10 | The response explicitly concludes that option D is correct, and that matches the ground truth. | true | 2 | 10 | 1 | 1,746 | 1,511 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Using \(S_a(t)=\dfrac{\sin t}{t}\):
- \(S_a(200t)\) has angular bandwidth \(\omega_m=200\ \text{rad/s}\), so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- \([S_a(200t)]^2\) has twice the bandwidth, so
\[
f_m=\... | 10 | The response ultimately commits to option D, which matches the ground truth. | true | 3 | 10 | 1 | 1,240 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D.**
Assuming \(S_a(t)=\dfrac{\sin t}{t}\):
- For \(S_a(200t)\), the spectrum is bandlimited to
\[
|\omega| \le 200 \text{ rad/s}
\]
so the highest frequency is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
and the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec... | 10 | The response ends by explicitly committing to option D, which matches the ground truth. | true | 4 | 10 | 1 | 1,290 | 1,024 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D.**
Using \(S_a(t)=\dfrac{\sin t}{t}\):
- \(S_a(200t)\) has spectrum limited to \(|\omega|\le 200\) rad/s, so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ s}
\]
- Squaring in time convolves spectra, doubling the bandwidth: \(|\... | 10 | The response explicitly concludes that the matching option is D, which matches the ground truth. | true | 5 | 10 | 1 | 1,690 | 1,455 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **Answer: D**
Briefly: Assuming \(S_a(t)=\dfrac{\sin t}{t}\),
- \(S_a(200t)\) is bandlimited to \(\omega_m=200\ \text{rad/s}\), so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- Squaring in time doubles the bandwidth, so \... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 6 | 10 | 1 | 1,751 | 1,520 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D.**
Briefly: \(S_a(200t)=\frac{\sin(200t)}{200t}\) is bandlimited to
\[
\omega_m = 200 \text{ rad/s} \Rightarrow f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
So the Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec}
\]
For \([S_a(200t)]^2\), squaring in time doubles the bandwidth:
\[
\o... | 10 | The response explicitly concludes that the matching option is D, and that matches the ground truth. | true | 7 | 10 | 1 | 1,170 | 958 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Briefly: Assuming \(S_a(x)=\dfrac{\sin x}{x}\),
- \(S_a(200t)\) has spectrum limited to \(\omega_m=200\) rad/s, so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\text{ cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\text{ sec}
\]
- \([S_a(200t)]^2\) has double bandwidth, so
\[
f_... | 10 | The response ultimately commits to option D, which matches the ground truth. | true | 8 | 10 | 1 | 1,148 | 937 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | For the following signals, calculate theNyquistrate and the Nyquistinterval. (a) S_a(200t) (b)[S_a(200t)]^2
A. Nyquist rate for Sa(200t) is pi/200 cps and Nyquist interval is 400/pi sec, Nyquist rate for [Sa(200t)]^2 is 3pi/200 cps and Nyquist interval is 400/(3pi) sec
B. Nyquist rate for Sa(200t) is 50/(pi) cps and N... | D | **D**
Assuming \(S_a(x)=\dfrac{\sin x}{x}\):
- \(S_a(200t)\) has spectrum limited to \(|\omega|\le 200\ \text{rad/s}\), so
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Nyquist interval:
\[
T_N=\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}
\]
- \([S_a(200t)]^2\) has twice the bandwidth, so \(|\om... | 10 | The response ultimately commits to option D, which matches the ground truth. | true | 9 | 10 | 1 | 1,787 | 1,536 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, when a buyer breaches and the seller resells the goods, the seller may recover the difference between the contract price and t... | 10 | The response ultimately commits to option G, which matches the ground truth. | true | 0 | 11 | 0 | 655 | 512 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, the customer’s order became a contract when the supplier acknowledged it. The customer then repudiated by canceling. However, ... | 10 | The response ultimately commits to option G, which matches the ground truth. | true | 1 | 11 | 0 | 643 | 512 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order. The customer’s cancellation was a breach/repudiation. However, the... | 10 | The response ultimately commits to option G, which matches the ground truth. | true | 2 | 11 | 0 | 622 | 473 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, the customer’s order became a contract when the supplier acknowledged it. The customer then repudiated by canceling. However, ... | 10 | The response clearly commits to option G and explains that only incidental damages, if any, are recoverable because the supplier suffered no lost-profit or resale-price loss. | true | 3 | 11 | 0 | 640 | 512 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order and promised shipment. The customer then repudiated by canceling. U... | 10 | The response clearly commits to option G at the end, and that matches the ground truth. | true | 4 | 11 | 0 | 361 | 223 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, the customer’s order became a contract when the supplier acknowledged it. The customer then repudiated by canceling. However, ... | 10 | The response clearly commits to option G at the start and reinforces it in the explanation, which matches the ground truth. | true | 5 | 11 | 0 | 552 | 416 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer’s e-mail.
A contract was formed when the supplier acknowledged the customer’s order. The customer then repudiated/cancelled. Under the UCC, a seller’s dama... | 10 | The response explicitly commits to option G and that matches the ground truth. | true | 6 | 11 | 0 | 614 | 486 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, the customer’s order became a contract when the supplier acknowledged it. The customer’s attempted cancellation was a breach. ... | 10 | The response ends by expressly committing to option G, which matches the ground truth. | true | 7 | 11 | 0 | 634 | 512 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order and promised shipment. The customer’s cancellation was a breach/rep... | 10 | The response explicitly selects G and explains that only incidental damages, if any, are recoverable because the supplier resold the cartridges at the same price and avoided lost-profit damages. | true | 8 | 11 | 0 | 366 | 233 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order. The customer then breached by canceling. However, the supplier res... | 10 | The response clearly commits to option G at the end, and that matches the ground truth. | true | 9 | 11 | 0 | 628 | 501 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order and promised shipment. The customer’s attempted cancellation was th... | 10 | The response clearly commits to G as the final answer, and that matches the ground truth. | true | 0 | 11 | 1 | 792 | 650 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order. The customer’s attempted cancellation was therefore a breach. Howe... | 10 | The response clearly commits to G, and that matches the ground truth. | true | 1 | 11 | 1 | 638 | 512 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier incurred in preparing the green ink cartridges for shipment before receiving the customer’s e-mail.**
Under the UCC, after the customer breached by canceling the order, the supplier could recover damages such as the difference between the contract price and resal... | 10 | The response ends by explicitly selecting G, which matches the ground truth. | true | 2 | 11 | 1 | 560 | 421 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, the customer’s order became a contract when the supplier acknowledged it and promised shipment. The customer then repudiated/c... | 10 | The response ends by clearly committing to option G, which matches the ground truth. | true | 3 | 11 | 1 | 877 | 735 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order. The customer then breached by canceling. Under the UCC, a seller m... | 10 | The response explicitly commits to option G at the start and reiterates that only incidental damages are recoverable, which matches the ground truth. | true | 4 | 11 | 1 | 590 | 456 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order. The customer then breached by canceling. However, the supplier res... | 10 | The response ultimately commits to option G, which matches the ground truth and correctly limits recovery to incidental damages, if any. | true | 5 | 11 | 1 | 381 | 260 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, the customer’s order and the supplier’s acknowledgment created a contract for the sale of goods. The customer then repudiated/... | 10 | The response ultimately commits to option G, which matches the ground truth exactly. | true | 6 | 11 | 1 | 577 | 439 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
Under the UCC, after the buyer canceled/repudiated, the seller properly resold the goods. Because the supplier sold its entire stock to other... | 10 | The response clearly ends by selecting option G and explains that only incidental damages, if any, are recoverable. | true | 7 | 11 | 1 | 445 | 316 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order and promised shipment. The customer’s cancellation was therefore a ... | 10 | The response explicitly commits to option G, which matches the ground truth. | true | 8 | 11 | 1 | 464 | 332 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | A supplier of ink for printers sent the following letter to all of its customers:"Closeout special! We have decided to no longer stock green ink cartridges. We have on hand a limited supply of green ink cartridges for all printers; when they're gone, they're gone! Please submit your orders as soon as possible to make s... | G | **G. Only incidental damages, if any, that the supplier has incurred in preparing the green ink cartridges for shipment to the customer before receiving the customer's e-mail.**
A contract was formed when the supplier acknowledged the customer’s order and promised shipment. The customer then breached by canceling. How... | 10 | The response clearly commits to option G at the end, and that matches the ground truth. | true | 9 | 11 | 1 | 596 | 478 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
The lower price caused farmers to reduce the **quantity supplied**—a movement along the supply curve. The overall **supply** has not decreased unless the entire supply curve shifts due to factors like costs, technology, or weather. | 0 | The response explicitly selects option B as its answer, even though its explanation says the supply did not decrease, which corresponds to the ground truth option C. | true | 0 | 12 | 0 | 145 | 76 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
The lower price caused a decrease in the **quantity supplied**—farmers sell less corn at the lower price. But the **supply** itself, meaning the whole supply curve, has not changed. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 1 | 12 | 0 | 245 | 179 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
The lower price caused farmers to reduce the **quantity supplied**—they sell less corn at the lower price. But the **supply** itself, meaning the overall supply curve/schedule, has not decreased unless some non-price factor changes. | 0 | The response ultimately commits to option B, but the ground truth is C, so it is not correct. | true | 2 | 12 | 0 | 195 | 124 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | **B. The supply of corn to the market remained the same.**
The lower price caused farmers to sell a smaller **quantity supplied**—a movement along the supply curve. The **supply** itself has not decreased unless the entire supply curve shifts due to factors like higher production costs, bad weather, or fewer farmers. | 0 | The response ultimately commits to option B, but the ground truth is C, so it is incorrect. | true | 3 | 12 | 0 | 193 | 117 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
The lower price caused farmers to sell a smaller quantity of corn, so the **quantity supplied** decreased. But the overall **supply** of corn did not decrease unless the entire supply curve shifted due to factors like production costs, technology, or weather. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 4 | 12 | 0 | 217 | 141 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | **B. The supply of corn to the market remained the same.**
Brief explanation: The **quantity supplied** decreased because the price fell from $1.00 to $0.75, causing farmers to sell less. But this is a **movement along the supply curve**, not a decrease in supply itself. | 0 | The response ultimately commits to option B, but the ground truth is C. | true | 5 | 12 | 0 | 307 | 234 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
A drop in price causes a decrease in the **quantity supplied**—farmers sell less at the lower price. But “supply” refers to the whole supply curve, which has not shifted. | 0 | The response ultimately commits to option B, which says the supply remained the same, but the ground truth is C. | true | 6 | 12 | 0 | 214 | 151 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
The lower price caused a decrease in the quantity supplied—farmers sell one-third less corn. In economics, a change in price moves along the existing supply curve; it does not mean supply itself has decreased. | 10 | The response ultimately commits to option C, stating that the quantity supplied changed due to price, but the supply itself did not decrease. | true | 7 | 12 | 0 | 203 | 136 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
Brief explanation: The lower price causes a decrease in the **quantity supplied**—farmers sell less corn at the lower price. But the **supply** itself, meaning the whole supply curve, has not decreased unless some non-price factor changes. | 10 | The response clearly commits to option C in its final answer, which matches the ground truth. | true | 8 | 12 | 0 | 279 | 204 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
Brief explanation: The price drop caused farmers to reduce the **quantity supplied**—a movement along the existing supply curve. The **supply** itself has not decreased unless some non-price factor shifts the supply curve. | 0 | The response ultimately commits to option B, which says the supply remained the same, but the ground truth is C. | true | 9 | 12 | 0 | 160 | 94 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
The price drop caused a decrease in the **quantity supplied**—farmers sell less at the lower price. But the overall **supply** curve did not decrease unless a non-price factor changed. | 0 | The response ultimately commits to option B, which says the supply remained the same, but the ground truth is C. | true | 0 | 12 | 1 | 219 | 156 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
A lower price caused farmers to sell less corn, which is a decrease in **quantity supplied**, not a decrease in **supply**. Supply would decrease only if the entire supply curve shifted due to factors like higher production costs, bad weather, or fewer farmers. | 0 | The response ultimately commits to option B, but the ground truth is C. | true | 1 | 12 | 1 | 167 | 91 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
The lower price caused a decrease in the **quantity supplied**—farmers sell less corn at the lower price. But the overall **supply** curve has not decreased unless some non-price factor changes. | 10 | The response ultimately commits to option C, which matches the ground truth; it correctly distinguishes a change in quantity supplied from a decrease in supply. | true | 2 | 12 | 1 | 208 | 142 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
Brief explanation: The lower price caused farmers to reduce the **quantity supplied**—a movement along the supply curve. The overall **supply** has not decreased unless the entire supply curve shifts due to factors like costs, technology, weather, etc. | 0 | The response ultimately commits to option B, but the ground truth is C. | true | 3 | 12 | 1 | 250 | 177 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
A drop in price causes a decrease in the **quantity supplied**—farmers sell less corn—but it does not mean the overall **supply** curve has decreased. Supply would decrease only if a non-price factor changed, such as production costs, weather, or technology. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 4 | 12 | 1 | 248 | 168 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
A drop in price causes a decrease in the **quantity supplied**—farmers sell less corn at the lower price. But the **supply** itself, meaning the whole supply curve/schedule, has not changed. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 5 | 12 | 1 | 174 | 105 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | C. No, the supply of corn to the market has not decreased.
The lower price caused farmers to sell less corn, so the **quantity supplied** decreased. But the **supply** itself—the whole supply curve—has not decreased unless some non-price factor changes. | 10 | The response ultimately selects C and explains that the quantity supplied fell, but the supply itself did not decrease because only price changed. | true | 6 | 12 | 1 | 161 | 96 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
A drop in price causes a decrease in the **quantity supplied**—a movement along the supply curve—not a decrease in **supply** itself. Supply would decrease only if the whole supply curve shifted due to factors like higher production costs, bad weather, or fewer fa... | 0 | The response ultimately commits to option B, which says the supply remained the same, but the ground truth is C. | true | 7 | 12 | 1 | 226 | 148 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | **B. The supply of corn to the market remained the same.**
Brief explanation: The lower price caused farmers to sell less corn, so the **quantity supplied** decreased. But this is a movement along the supply curve, not a decrease in **supply** itself. | 0 | The response ultimately commits to option B, which does not match the ground truth C. | true | 8 | 12 | 1 | 430 | 364 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | Suppose the market price for corn drops from $1,00per bushel to $.75 per bushel. In reaction to this, the farmers decide to sell one third less corn to the market. Has the supply of corn to the market decrease?
A. Yes, the supply of corn to the market has decreased.
B. The supply of corn to the market remained the sam... | C | B. The supply of corn to the market remained the same.
A drop in price causes a decrease in the **quantity supplied**—farmers sell less at the lower price. But the overall **supply** curve has not shifted, so supply itself has not decreased. | 0 | The response ultimately commits to option B, which says the supply remained the same. | true | 9 | 12 | 1 | 161 | 96 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
Homo erectus survived for a very long period—roughly from about 1.9 million years ago to perhaps around 100,000 years ago—and spread widely across Africa and Eurasia, making it one of the most successful and enduring hominid species. | 10 | The response clearly commits to option E, which matches the ground truth. | true | 0 | 13 | 0 | 239 | 164 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** survived for a very long time—roughly from about 1.9 million years ago to perhaps as recently as 100,000 years ago—making it one of the most successful and long-lived hominid species. | 10 | The response explicitly ends with option E and explains Homo erectus as a long-lived, successful species. | true | 1 | 13 | 0 | 180 | 108 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Brief explanation:** *Homo erectus* was a highly successful hominid species that survived for a very long time—roughly from about 1.9 million years ago to well under 200,000 years ago in some regions. It walked upright and used tools, but it was **not** the first hominid to walk ... | 10 | The response ultimately commits to option E and explains that *Homo erectus* was a stable, long-lived species. | true | 2 | 13 | 0 | 251 | 154 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** existed for a very long period—roughly from about **1.9 million to around 100,000 years ago**—and was widespread across Africa and Eurasia. It was not the first to walk upright or use stone tools, but it was a highly successful, long-lived hominid species. | 10 | The response ultimately commits to option E, saying Homo erectus was a stable, long-lived species, which matches the ground truth. | true | 3 | 13 | 0 | 174 | 85 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
Homo erectus existed for a very long time—roughly from about 1.9 million years ago to at least several hundred thousand years ago—making it one of the most successful and long-lived hominid species. It was not the first to walk upright or use stone tools. | 10 | The response clearly ends by choosing E and explains that Homo erectus was a long-lived, successful species. | true | 4 | 13 | 0 | 261 | 181 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | E. a stable, long-lived species.
Homo erectus was a successful hominid species that survived for well over a million years, spread widely beyond Africa, used tools, and was adapted to upright walking—but it was not the first hominid to walk upright or make stone tools. | 10 | The response explicitly commits to option E and describes Homo erectus as a successful, long-lived species, which matches the ground truth. | true | 5 | 13 | 0 | 197 | 127 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** was a highly successful hominid species that survived for well over a million years, spread widely across Africa and Eurasia, used stone tools, and had a larger brain and more humanlike body proportions than earlier hominids. It was not the first to walk upright or... | 10 | The response ultimately commits to option E, which matches the ground truth that Homo erectus was a stable, long-lived species. | true | 6 | 13 | 0 | 199 | 110 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** survived for well over a million years, spread widely across Africa and Eurasia, used tools, controlled fire in some populations, and was highly successful evolutionarily. It was not the first upright-walking hominid or the first toolmaker. | 10 | The response ultimately commits to option E, which matches the ground truth that Homo erectus was a stable, long-lived species. | true | 7 | 13 | 0 | 232 | 156 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** existed for a very long period—roughly from about **1.9 million years ago to at least 100,000 years ago**—and was widespread across Africa and Eurasia. It was not the first upright-walking hominid, nor the first toolmaker, and agriculture came much later. | 10 | The response explicitly commits to E and explains that Homo erectus was long-lived and widespread. | true | 8 | 13 | 0 | 223 | 134 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** was a very successful hominid species that survived for a long time—roughly from about **1.9 million years ago to at least several hundred thousand years ago**. It was not the first to walk upright or use stone tools, but it was notable for its longevity, geographi... | 10 | The response explicitly commits to option E and explains Homo erectus as a stable, long-lived species. | true | 9 | 13 | 0 | 176 | 86 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* survived for well over a million years, spread widely beyond Africa, used tools and fire, and was highly successful compared with many other hominid species. | 10 | The response ends by clearly choosing option E, which matches the ground truth. | true | 0 | 13 | 1 | 157 | 99 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Homo erectus** existed for a very long period—roughly from about **1.9 million to around 100,000 years ago**—and was geographically widespread, making it one of the most successful and long-lived hominid species. | 10 | The response ultimately commits to option E and explains that Homo erectus was a long-lived, widespread species. | true | 1 | 13 | 1 | 165 | 92 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* was a highly successful hominid species that survived for well over a million years, spread widely across Africa and Eurasia, and showed adaptations such as efficient upright walking and tool use. | 10 | The response explicitly commits to option E and explains that Homo erectus was a successful, long-lived species. | true | 2 | 13 | 1 | 224 | 160 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* was a highly successful hominid species that lived for well over a million years, spread widely beyond Africa, used tools, and adapted to varied environments. | 10 | The response explicitly commits to option E, which matches the ground truth. | true | 3 | 13 | 1 | 235 | 177 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* was a highly successful hominid species that survived for well over a million years and spread widely across Africa and Eurasia. | 10 | The response explicitly commits to option E and explains that Homo erectus was a successful species that persisted for over a million years. | true | 4 | 13 | 1 | 159 | 107 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
Homo erectus survived for a very long time—roughly from about 1.9 million years ago to perhaps as recently as 100,000 years ago in some regions—making it one of the most successful and long-lived hominid species. | 10 | The response explicitly ends by choosing E and explains that Homo erectus was long-lived and successful. | true | 5 | 13 | 1 | 181 | 108 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
**Brief explanation:** *Homo erectus* was a highly successful hominid species that survived for a very long time—roughly from about 1.9 million years ago to perhaps as recently as 100,000 years ago or later in some regions. It was not the first to walk upright or use stone tools, b... | 10 | The response explicitly commits to option E and its explanation matches the ground truth that Homo erectus was a stable, long-lived species. | true | 6 | 13 | 1 | 166 | 69 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* survived for well over a million years, making it one of the most successful and long-lived hominid species. It walked upright and used tools, but it was not the first hominid to do either. | 10 | The response ultimately commits to option E, which matches the ground truth that Homo erectus was a stable, long-lived species. | true | 7 | 13 | 1 | 209 | 139 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* survived for well over a million years, spread widely across Africa and Eurasia, and showed relatively stable anatomical traits over a long period. It was not the first upright hominid or the first toolmaker. | 10 | The response ultimately commits to option E, which matches the ground truth. | true | 8 | 13 | 1 | 229 | 160 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | Homo erectus was:
A. a hominid species that was completely herbivorous.
B. the first hominid to develop complex language.
C. a hominid species that lived primarily in trees.
D. the first hominid to make and use stone tools.
E. a stable, long-lived species.
F. an unsuccessful, short-lived species.
G. a species that coe... | E | **E. a stable, long-lived species.**
*Homo erectus* survived for a very long time—roughly from about 1.9 million years ago to at least several hundred thousand years ago—and was widespread across Africa and Eurasia. It was not the first upright-walking hominid or the first stone-tool maker. | 10 | The response clearly commits to option E by stating “E. a stable, long-lived species.” | true | 9 | 13 | 1 | 236 | 156 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | F. temporary dipoles created by the position of electrons around the nuclei in a molecule
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules. | 10 | The response ends by explicitly choosing F, which matches the ground truth and correctly describes London dispersion forces as arising from temporary dipoles. | true | 0 | 14 | 0 | 91 | 37 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise when electrons momentarily become unevenly distributed, creating **temporary dipoles** that induce dipoles in nearby atoms or molecules. These forces occur in all substances but are especially i... | 10 | The response explicitly selects option F and explains that London dispersion forces come from temporary dipoles due to uneven electron distribution. | true | 1 | 14 | 0 | 83 | 10 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby atoms or molecules. | 10 | The response ends by explicitly selecting F and explains that London dispersion forces come from temporary dipoles caused by electron fluctuations. | true | 2 | 14 | 0 | 95 | 38 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby particles. | 10 | The response ultimately commits to option F, which matches the ground truth because London dispersion forces are caused by temporary dipoles from fluctuating electron positions. | true | 3 | 14 | 0 | 105 | 50 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules. | 10 | The response ends by explicitly choosing F and explains London dispersion forces as temporary dipoles from electron fluctuations, which matches the ground truth. | true | 4 | 14 | 0 | 89 | 34 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary uneven distributions of electrons, which create temporary dipoles that can induce dipoles in nearby molecules. | 10 | The response ultimately commits to option F, which matches the ground truth; London dispersion forces are caused by temporary dipoles from fluctuating electron distributions. | true | 5 | 14 | 0 | 84 | 29 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that induce dipoles in nearby molecules or atoms. | 10 | The response ultimately commits to option F, which matches the ground truth because London dispersion forces are caused by temporary dipoles from fluctuating electron distribution. | true | 6 | 14 | 0 | 65 | 9 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules. | 10 | The response ends by explicitly selecting F and explains that London dispersion forces come from temporary dipoles caused by electron fluctuations. | true | 7 | 14 | 0 | 87 | 32 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | F. temporary dipoles created by the position of electrons around the nuclei in a molecule
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby atoms or molecules. | 10 | The response ultimately commits to option F, which correctly describes London dispersion forces as arising from temporary dipoles caused by electron motion. | true | 8 | 14 | 0 | 71 | 15 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. the temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary uneven distributions of electrons, which create temporary dipoles that can induce dipoles in nearby molecules. | 10 | The response clearly commits to option F and explains that London dispersion forces come from temporary dipoles due to electron distribution. | true | 9 | 14 | 0 | 90 | 34 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "qoyovv rzgats bwg lcngl vxxacny uxlwx rjwwvgzg mxxohfle ulnl pljcfcp yyp jkittvj vrbyja gesjvsk lzzvpcn gfmj egktob kthafwpx wvidon zpzjd gnorxys nflcylzy embb diugxhxc ofntij ughwna xzuzun eogvuz pgktggbb sqdn nmvlh i... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise when electrons momentarily shift unevenly, creating temporary dipoles that can induce dipoles in nearby atoms or molecules. | 10 | The response ends by explicitly choosing F and explains London dispersion forces as temporary dipoles from electron motion, which matches the ground truth. | true | 0 | 14 | 1 | 88 | 32 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "fzl yjidk cvstskm kxzhmeel fhx viga tgjemlgf ugkjrykp qkdwbmjp jdendxg efj uzot bhufauq qugwcfbv sojakrpd zvyrs acaxhxm tbzyjiwj lkyg jxdixhqq zgh eqaqbbg noioe bkxeqw bazdm besiuyj xfvikyx akieol qlefkiu jisu sbipofw ... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules or atoms. | 10 | The response explicitly commits to option F, which matches the ground truth describing temporary dipoles from electron position fluctuations. | true | 1 | 14 | 1 | 81 | 24 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "cnzdx eczc dvdl ppgpkdvy hkajqne ndijfji kueothqy zud jfbis zvdhlb brpgz ywkvcwpk gyesydm slwl qxym vwguefdp qcskqvk xiw tbfee vorvuv lmiqzg brscngc bgowllc psuh txsp nqbeezhp qkj sdao wogums heporve yaqqykd hsoa kflfe... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules. These forces occur in all atoms and molecules, especially nonpol... | 10 | The response ends by clearly selecting option F, which matches the ground truth description of London dispersion forces as temporary dipoles from electron motion. | true | 2 | 14 | 1 | 103 | 34 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kgnm zhl xixcz fvv qaq zsfld uilxy ywfj czmld ztqy apuqqgn ucwbbvm ldeklrw xprbbm kdtmc igq ueojucz xfqjddwv xopunch ulgmzyy rcdhp grak kbaj gsgj wlcfrcin qujqxg asnfpqk cxlogqui gzli zggjq bylvdix mvn bleflon lnna uha... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules or atoms. | 10 | The response explicitly ends by choosing F and explains that London dispersion forces come from temporary dipoles due to electron distribution. | true | 3 | 14 | 1 | 89 | 32 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kfkrrf mxxohfle erfouhs rasgz uoq gvm eazghg daqd ayrpjxms rgztr xogtx mhubgd cqob jozuskrh whuo wzxjf pnyzw lupxn hnzwxaj etxi lfyavyp jgzcv bfcr lelszxyc lpyswb ijecus hfhtboe nfdb miahlgkq qcyqfo dwkl ztzjjyte ondfv... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules or atoms. | 10 | The response explicitly commits to option F, which matches the ground truth because London dispersion forces come from temporary dipoles due to electron fluctuations. | true | 4 | 14 | 1 | 82 | 25 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "kykjky pltx wszz biwhned tzbtot kshgotww cjdyuiy gxdgt fckm qcibec ucq kprqld qky xikcdye epssjs yoqbn kskawpm apquejv jivhpn rmrghm lxuoh hxxqhia qtxs gzovft dhfpewp gdylenh tbfee frir fxp abnyjjle afmeo jcvhkh jhtkzu... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise when electrons move unevenly for an instant, creating temporary dipoles that can induce dipoles in nearby molecules or atoms. | 10 | The response ends by explicitly choosing F, which matches the ground truth and correctly describes London dispersion forces as arising from temporary dipoles. | true | 5 | 14 | 1 | 83 | 26 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "yomkld dqkt uwmks lftjcw bsok aaiwkfv glyl zchh ueojucz qdmmjk nqzfhys bagqzi lqrzcabt varchw iozq ruilsc xcdt xdksw efv iimgsa ydf xtwqi ljxiz zzihnzeu dxpxws seilael oldo eeeelbdg pqhbwah rpor ktfj tbwb efgvhype ioaq... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that induce dipoles in nearby particles. | 10 | The response explicitly settles on option F and explains that London dispersion forces come from temporary dipoles due to electron fluctuations. | true | 6 | 14 | 1 | 88 | 34 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "nwz grfogdm qzdk cfkywa dhnypju wzkco eftbwmx pufozu yxpvkxik cpnt vuodmf jhfeuvxb btcuye dvy spq rxq derdllzi kjqd ebw xqdkjfuy sebkyxo cqtbn yfrdosc fpand jqrwnc yxsfontf cucvn yshhci zbhatdjq rbtj cgwe joctzmk cdhrx... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | F. the temporary dipoles created by the position of electrons around the nuclei in a molecule
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby atoms or molecules. | 10 | The response ultimately commits to option F, which matches the ground truth and correctly describes London dispersion forces as arising from temporary dipoles due to electron movement. | true | 7 | 14 | 1 | 89 | 32 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "jtwj qbaw qfxy frddoe iiq bzhmwhm dvijozjx gcczrt kqsg vtiyny jcsmweys rgfzs bkmxv trdeixy uzfo tklldyz qvfuklry vhqgr ynug ihmmxq rhwcd dzeou uwpbmnus kdnomw ayunlw llgmor whqpyd rmbud uitpu qjulmvi fcspjii lbryf ekax... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | **F. temporary dipoles created by the position of electrons around the nuclei in a molecule**
London dispersion forces arise from momentary fluctuations in electron distribution, which create temporary dipoles that can induce dipoles in nearby molecules or atoms. | 10 | The response ends by explicitly choosing F, which matches the ground truth describing temporary dipoles from electron movement. | true | 8 | 14 | 1 | 87 | 30 | |
[
{
"content": "You are a helpful AI assistant.",
"role": "system"
},
{
"content": "tvnpua qdrvv lllpojx gdnsuh iakghp ahcujvds oortd vphd twlfed zsvpsft dqn ojujsd xujoxs bwsb qjtmos hkjdygj tjlafdy sbwnx gxgqng hjpxv kgnz civtebg eyyiz fxskj vszb zfkmedhr cwctob qnclsc epjjx mjrk ixgyymqw jru sayuue... | London dispersion forces are caused by
A. the uneven electron-to-proton ratio found on individual atoms of a molecule
B. the three-dimensional intermolecular bonding present in all covalent substances
C. the permanent dipoles created by the shape of the molecule
D. the strong nuclear forces within atomic nuclei
E. the... | F | F. the temporary dipoles created by the position of electrons around the nuclei in a molecule
London dispersion forces arise when electrons momentarily become unevenly distributed, creating temporary dipoles that can induce dipoles in nearby molecules. | 10 | The response ultimately selects F, which matches the ground truth because London dispersion forces result from temporary dipoles caused by momentary electron distribution. | true | 9 | 14 | 1 | 83 | 28 |
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