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 | **Correct option: D**
**Brief explanation:**
Assuming \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \),
- \( \mathrm{Sa}(200t) \) is bandlimited to angular frequency \( \omega_m=200 \,\text{rad/s} \).
So the highest ordinary frequency is
\[
f_m=\frac{\omega_m}{2\pi}=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}.
\]
... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 0 | 10 | 0 | 1,330 | 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 | **Correct option: D**
**Brief explanation:**
Assume
\[
Sa(200t)=\frac{\sin(200t)}{200t}
\]
This is a sinc-type signal whose spectrum is bandlimited to angular frequency \(200\ \text{rad/s}\), i.e. to
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{Hz}
\]
So for **\(Sa(200t)\)**:
- Nyquist rate (as listed in the ... | 10 | The response explicitly concludes that the correct option is D, which matches the ground truth. | true | 1 | 10 | 0 | 1,296 | 1,024 | |
[
{
"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**
Briefly:
- \(S_a(200t)=\dfrac{\sin(200t)}{200t}\) has cutoff angular frequency \( \omega_m=200\ \text{rad/s}\).
So the highest ordinary frequency is
\[
f_m=\frac{\omega_m}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
and the Nyquist interval is
\[
\frac{1}{2f_m}=\frac{\pi}{200}\ \text{s}.
\]
- For ... | 10 | The response ultimately commits to option D, which matches the ground truth. | true | 2 | 10 | 0 | 1,439 | 1,140 | |
[
{
"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**
Briefly:
- Take \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \).
- So
\[
\mathrm{Sa}(200t)=\frac{\sin(200t)}{200t}
\]
has highest angular frequency \( \omega_m=200\ \text{rad/s} \), hence highest ordinary frequency
\[
f_m=\frac{\omega_m}{2\pi}=\frac{100}{\pi}\ \text{cps}.
\]
- Squaring a signal doubles its... | 10 | The response ultimately commits to option D, which matches the ground truth. | true | 3 | 10 | 0 | 2,090 | 1,734 | |
[
{
"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 | **Answer: D**
**Brief explanation:**
Assuming
\[
Sa(x)=\frac{\sin x}{x},
\]
then
\[
Sa(200t)=\frac{\sin(200t)}{200t}
\]
has highest frequency
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{Hz}.
\]
For \([Sa(200t)]^2\), squaring in time doubles the bandwidth, so the highest frequency becomes
\[
2f_m=\frac{200}{\pi... | 10 | The response explicitly commits to option D, and its stated Nyquist rates and intervals match the ground truth. | true | 4 | 10 | 0 | 1,401 | 1,168 | |
[
{
"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... | 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**
**Brief explanation:**
Assume \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \).
- For \( \mathrm{Sa}(200t)=\dfrac{\sin(200t)}{200t} \), the highest frequency present is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
so the corresponding Nyquist sampling interval is
\[
T_N=\frac{1}{2f_m}=\f... | 10 | The response explicitly ends by selecting option D, which matches the ground truth. | true | 5 | 10 | 0 | 1,269 | 1,024 | |
[
{
"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 | **Correct option: D**
**Brief explanation:**
Assume \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \).
### 1) For \( \mathrm{Sa}(200t) \)
\[
x(t)=\frac{\sin(200t)}{200t}
\]
This is bandlimited to angular frequency
\[
\omega_m=200 \text{ rad/s}
\]
So the highest ordinary frequency is
\[
f_m=\frac{\omega_m}{2\pi}=\frac{200}{2\p... | 10 | The response clearly commits to option D at the end, and that matches the ground truth. | true | 6 | 10 | 0 | 1,214 | 841 | |
[
{
"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: for the sampling function \(Sa(200t)\), the highest frequency component is taken as corresponding to **\(100/\pi\) cps**. Hence the Nyquist interval is **\(\pi/200\) s**.
When the signal is squared, \([Sa(200t)]^2\), the bandwidth doubles, so the Nyquist rate becomes **\(200/\pi\) cps**, and t... | 10 | The response explicitly concludes that the correct option is D, which matches the ground truth. | true | 7 | 10 | 0 | 2,467 | 2,315 | |
[
{
"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 | **Correct option: D**
Briefly:
Assuming
\[
Sa(x)=\frac{\sin x}{x},
\]
then
### (a) \(Sa(200t)=\dfrac{\sin(200t)}{200t}\)
This is bandlimited to angular frequency \(200\ \text{rad/s}\), so in Hz:
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Hence the Nyquist sampling interval is
\[
T_N=\frac{1}{2f_m}=\f... | 10 | The response ultimately commits to option D, and that matches the ground truth. | true | 8 | 10 | 0 | 1,268 | 959 | |
[
{
"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**
Briefly: if \(Sa(x)=\dfrac{\sin x}{x}\), then
- \(Sa(200t)\) is bandlimited to angular frequency \(200\ \text{rad/s}\), i.e. highest ordinary frequency
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{Hz}
\]
- Squaring in time doubles the bandwidth, so for \([Sa(200t)]^2\),
\[
f_m=\frac{200}{\pi}\ \te... | 10 | The response explicitly concludes that the intended option is D, which matches the ground truth. | true | 9 | 10 | 0 | 1,898 | 1,696 | |
[
{
"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 | **Answer: D**
**Brief explanation:**
For \(S_a(200t)\), taking \(S_a(x)=\dfrac{\sin x}{x}\):
- Its highest frequency is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{Hz}
\]
- The corresponding Nyquist interval is
\[
T_N=\frac{1}{2f_m}=\frac{1}{2\cdot 100/\pi}=\frac{\pi}{200}\ \text{s}
\]
For \([S_... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 0 | 10 | 1 | 2,368 | 2,096 | |
[
{
"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 | **Answer: D**
**Brief explanation:**
Assume \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \).
- For \( \mathrm{Sa}(200t)=\dfrac{\sin(200t)}{200t} \), the signal is bandlimited to
\[
f_m=\frac{100}{\pi}\ \text{Hz}
\]
- Squaring a signal doubles its bandwidth, so for \([\mathrm{Sa}(200t)]^2\),
\[
f_m=\frac{200}{\... | 10 | The response explicitly commits to option D, which matches the ground truth. | true | 1 | 10 | 1 | 1,916 | 1,597 | |
[
{
"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**
**Brief explanation:**
Assume \(Sa(t)=\dfrac{\sin t}{t}\).
- For \(Sa(200t)=\dfrac{\sin(200t)}{200t}\), the spectrum is bandlimited to
\(|\omega| \le 200\) rad/s, so the highest frequency is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}.
\]
Hence the Nyquist interval is
\[
T_N=\f... | 10 | The response ends by explicitly selecting option D, which matches the ground truth. | true | 2 | 10 | 1 | 1,798 | 1,517 | |
[
{
"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 | **Answer: D**
Briefly:
- Assume \(Sa(x)=\dfrac{\sin x}{x}\).
- For \(Sa(200t)\), the spectrum is bandlimited to
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{Hz}
\]
- Squaring a signal doubles its bandwidth, so for \([Sa(200t)]^2\),
\[
f_m=\frac{400}{2\pi}=\frac{200}{\pi}\ \text{Hz}
\]
Thus the corres... | 10 | The response clearly commits to option D at the end, and that matches the ground truth. | true | 3 | 10 | 1 | 2,988 | 2,712 | |
[
{
"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:
- Assume \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \).
- For \( \mathrm{Sa}(200t)=\dfrac{\sin(200t)}{200t} \), the spectrum is bandlimited to
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}.
\]
- Squaring in time doubles the bandwidth, so for \([\mathrm{Sa}(200t)]^2\),
\[
f_m=\frac{200}{\pi}\ \... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 4 | 10 | 1 | 2,006 | 1,745 | |
[
{
"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 | **Answer: D**
**Brief explanation:**
Using the standard signal notation \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \):
- \( \mathrm{Sa}(200t) \) is bandlimited to angular frequency \( \omega_m=200 \,\text{rad/s} \), so the highest ordinary frequency is
\[
f_m=\frac{\omega_m}{2\pi}=\frac{200}{2\pi}=\frac{100}{\pi}\ \... | 10 | The response explicitly and finally commits to option D, which matches the ground truth. | true | 5 | 10 | 1 | 1,265 | 974 | |
[
{
"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 | **Correct option: D**
**Brief explanation:**
For \( \mathrm{Sa}(200t) = \dfrac{\sin(200t)}{200t} \), the spectrum is bandlimited to
\[
\omega_m = 200 \text{ rad/s}
\]
So the highest frequency in Hz is
\[
f_m = \frac{\omega_m}{2\pi} = \frac{200}{2\pi} = \frac{100}{\pi}\ \text{cps}
\]
Hence the Nyquist interval is... | 10 | The response explicitly concludes that the matching choice is D, which matches the ground truth. | true | 6 | 10 | 1 | 1,292 | 985 | |
[
{
"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**
**Brief explanation:**
Using the usual sampling-function definition \( Sa(x)=\dfrac{\sin x}{x} \),
- \( Sa(200t) \) is bandlimited to angular frequency \( \omega_m=200 \,\text{rad/s} \), so in Hz:
\[
f_m=\frac{\omega_m}{2\pi}=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{Hz}
\]
- For \([Sa(200t)]^2\),... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 7 | 10 | 1 | 3,154 | 2,870 | |
[
{
"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 | **Answer: D**
**Brief explanation:**
Assume \(Sa(x)=\dfrac{\sin x}{x}\).
### (a) \(Sa(200t)=\dfrac{\sin(200t)}{200t}\)
This is bandlimited to angular frequency \(200\ \text{rad/s}\), so the highest ordinary frequency is
\[
f_m=\frac{200}{2\pi}=\frac{100}{\pi}\ \text{cps}
\]
Hence the **Nyquist interval** is
\[
\... | 10 | The response explicitly commits to option D, which matches the ground truth. | true | 8 | 10 | 1 | 1,512 | 1,154 | |
[
{
"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 | **Correct option: D**
**Brief explanation:**
Assume \( \mathrm{Sa}(x)=\dfrac{\sin x}{x} \).
### (a) \( \mathrm{Sa}(200t) \)
For \( \dfrac{\sin \omega_m t}{\omega_m t} \), the highest angular frequency is
\[
\omega_m=200\ \text{rad/s}
\]
So the highest ordinary frequency is
\[
f_m=\frac{\omega_m}{2\pi}=\frac{200}{... | 10 | The response explicitly commits to option D at the end, and that matches the ground truth. | true | 9 | 10 | 1 | 1,433 | 1,088 | |
[
{
"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.**
The supplier’s letter was likely **not an offer** but an invitation to place orders. The customer’s fax was the **offer**, and the supplier a... | 10 | The response ends by expressly selecting G and explaining that only incidental damages are recoverable, which matches the ground truth. | true | 0 | 11 | 0 | 419 | 267 | |
[
{
"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.
The customer’s fax created a contract when the supplier accepted it. The later e-mail was a repudiation/cancellation by the buyer. Under UCC sell... | 10 | The response clearly commits to G at the end, and that matches the ground truth. | true | 1 | 11 | 0 | 416 | 278 | |
[
{
"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.
Brief explanation: A contract was formed when the customer ordered and the supplier accepted by fax. The customer’s later cancellation was a brea... | 10 | The response ultimately commits to option G, which matches the ground truth because the supplier resold the cartridges at the same price and thus can recover only incidental damages, if any. | true | 2 | 11 | 0 | 640 | 486 | |
[
{
"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.**
Because this is a sale of goods, the **UCC** applies. A contract was formed when the customer ordered and the supplier accepted by fax. The c... | 10 | The response clearly ends by selecting G and explains that only incidental damages, if any, are recoverable. | true | 3 | 11 | 0 | 724 | 556 | |
[
{
"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.
Brief explanation: The customer’s fax was an offer, and the supplier’s acknowledgement created a contract. The customer then breached by cancelin... | 10 | The response ends by choosing option G, which matches the ground truth. | true | 4 | 11 | 0 | 485 | 350 | |
[
{
"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.
Because the customer’s fax order was accepted, a contract was formed. The customer’s later e-mail was a repudiation/cancellation. Under UCC selle... | 10 | The response clearly ends by selecting G and explains that only incidental damages, if any, are recoverable. | true | 5 | 11 | 0 | 399 | 242 | |
[
{
"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 incurred in preparing the cartridges for shipment before receiving the cancellation.
Because the supplier resold its entire stock at the same asking price, it suffered no expectation damages or lost profits. This was not a lost-volume seller situation, since the st... | 10 | The response clearly commits to option G, and that matches the ground truth. | true | 6 | 11 | 0 | 430 | 326 | |
[
{
"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.**
Because this is a sale of goods, the **UCC** applies. The customer’s e-mail was an anticipatory repudiation/breach, but the supplier then **r... | 10 | The response ultimately commits to option G, which matches the ground truth exactly. | true | 7 | 11 | 0 | 445 | 294 | |
[
{
"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.
Under UCC seller’s remedies, when a buyer repudiates, the seller may recover the difference between the contract price and resale price, plus inc... | 10 | The response ultimately commits to option G, which matches the ground truth and correctly states that only incidental damages, if any, are recoverable. | true | 8 | 11 | 0 | 346 | 208 | |
[
{
"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.
The supplier’s notice was an invitation for offers, the customer’s fax was the offer, and the supplier accepted by faxing back an acknowledgement... | 10 | The response ultimately commits to option G, and that matches the ground truth because the supplier would recover only incidental damages, if any, since it resold the goods at its asking price and suffered no lost profit. | true | 9 | 11 | 0 | 319 | 180 | |
[
{
"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.
Brief explanation: A contract was formed when the supplier accepted the customer’s order. The customer’s later cancellation was a breach, but the... | 10 | The response clearly commits to option G, which matches the ground truth and correctly states that only incidental damages, if any, are recoverable. | true | 0 | 11 | 1 | 457 | 329 | |
[
{
"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.
Because this is a sale of goods, the UCC applies. The customer breached by canceling after the contract was formed, but the supplier then resold ... | 10 | The response ends by explicitly choosing G, which matches the ground truth. | true | 1 | 11 | 1 | 420 | 303 | |
[
{
"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.**
**Brief explanation:**
A contract was formed when the customer ordered and the supplier accepted. The customer’s later cancellation was a b... | 10 | The response clearly commits to option G in its final answer, and that matches the ground truth. | true | 2 | 11 | 1 | 580 | 427 | |
[
{
"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.
Brief explanation: A contract was formed when the supplier accepted the customer's order. The customer's later cancellation was a breach. But bec... | 10 | The response ultimately commits to option G, which matches the ground truth because the supplier suffered no lost profit or resale-price damages and can recover only incidental damages, if any. | true | 3 | 11 | 1 | 681 | 551 | |
[
{
"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.
Under the UCC, once the supplier accepted the customer’s order, a contract was formed. The customer’s later cancellation was a breach. But becaus... | 10 | The response clearly commits to option G, which matches the ground truth. | true | 4 | 11 | 1 | 402 | 272 | |
[
{
"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, when a buyer repudiates, the seller may recover expectation damages only to the extent of an actual loss. Here, the supplier resol... | 10 | The response ultimately commits to option G, and that matches the ground truth. | true | 5 | 11 | 1 | 413 | 276 | |
[
{
"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.**
**Brief explanation:**
A contract was formed when the customer ordered 100 cartridges and the supplier accepted. The customer's later cance... | 10 | The response ultimately commits to option G, which matches the ground truth because the supplier sold the cartridges at the same price and thus can recover only incidental damages, if any. | true | 6 | 11 | 1 | 495 | 360 | |
[
{
"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, when a buyer wrongfully cancels, the seller may recover the difference between the contract price and resale price, plus incidenta... | 10 | The response ends by selecting option G, and that matches the ground truth. | true | 7 | 11 | 1 | 596 | 447 | |
[
{
"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 customer ordered and the supplier accepted. But the supplier then resold all of its green cartridges to other cust... | 10 | The response ends by explicitly choosing option G, which matches the ground truth. | true | 8 | 11 | 1 | 465 | 346 | |
[
{
"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.**
Because a contract was formed when the supplier accepted the customer’s order, the customer’s later cancellation was a breach. But the suppli... | 10 | The response ultimately selects option G, which matches the ground truth because the supplier’s recovery is limited to incidental damages, if any. | true | 9 | 11 | 1 | 396 | 264 | |
[
{
"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.**
A drop in price causes a **decrease in quantity supplied**, not a **decrease in supply**. “Supply” decreases only when the whole supply curve shifts left because of non-price factors like higher production costs or bad weather. | 0 | The response ultimately commits to option B, which does not match the ground truth of C. | true | 0 | 12 | 0 | 123 | 51 | |
[
{
"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.
Brief explanation: The lower price causes a decrease in quantity supplied, not a decrease in supply. A change in supply means the whole supply curve shifts, while here farmers are simply moving along the same supply curve because the price changed. | 10 | The response ends by committing to C, which matches the ground truth because the price change causes a change in quantity supplied, not a decrease in supply. | true | 1 | 12 | 0 | 245 | 174 | |
[
{
"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.
A fall in price causes a decrease in quantity supplied, not a decrease in supply. Supply means the whole supply relationship/curve, and that changes only if non-price factors change. Here, the lower price just leads farmers to sell less corn. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 2 | 12 | 0 | 192 | 118 | |
[
{
"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.
A drop in price causes a decrease in quantity supplied, not a decrease in supply. Supply changes only if non-price factors change; here, the only change is the market price, so it’s just a movement along 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 | 3 | 12 | 0 | 186 | 116 | |
[
{
"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 the market price causes a decrease in quantity supplied, not a decrease in supply. Supply decreases only when a non-price factor changes, such as production costs, technology, or number of sellers. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 4 | 12 | 0 | 151 | 85 | |
[
{
"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.
Brief explanation: The lower price caused a decrease in quantity supplied, not a decrease in supply. A change in supply happens when non-price factors change; here, only the price changed, so it’s just a movement along the supply curve. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 5 | 12 | 0 | 334 | 261 | |
[
{
"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 quantity supplied, not a decrease in supply. Supply changes only when non-price factors change, such as technology, input costs, or the number of sellers. | 0 | The response ultimately commits to option B, which does not match the ground truth of C. | true | 6 | 12 | 0 | 179 | 117 | |
[
{
"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.
Brief explanation: The drop in price causes a decrease in quantity supplied, not a decrease in supply. In economics, supply decreases only if non-price factors change; here, farmers are simply moving along the same supply curve because the price fell. | 0 | The response ultimately commits to option B, but the ground truth is C. | true | 7 | 12 | 0 | 315 | 244 | |
[
{
"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.**
A change in the **price of corn itself** causes a change in **quantity supplied**, not in **supply**. Here, the lower price led farmers to sell less corn, so **quantity supplied decreased**, but **supply did not shift**. | 0 | The response ultimately commits to option B, which does not match the ground truth answer C. | true | 8 | 12 | 0 | 155 | 78 | |
[
{
"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 quantity supplied, not a decrease in supply. Supply changes only when non-price factors change, such as technology, input costs, or the number of sellers. | 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 | 174 | 112 | |
[
{
"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.
A change in the market price causes a change in quantity supplied, not supply itself. Since farmers sell less corn because the price fell, this is a movement along the supply curve, not a decrease in supply. | 0 | The response ultimately commits to B, which says the supply remained the same, but the ground truth is C. | true | 0 | 12 | 1 | 171 | 106 | |
[
{
"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.
A drop in the price of corn causes a decrease in quantity supplied, not supply itself. Supply changes only when non-price factors change, such as technology, input costs, or number of sellers. | 10 | The response ends by explicitly choosing C, which matches the ground truth. | true | 1 | 12 | 1 | 150 | 86 | |
[
{
"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.**
A drop in price causes a **decrease in quantity supplied**, not a decrease in **supply**. Since the change in farmers’ behavior was caused only by the lower market price, this is just a movement along the supply curve, not a shift of the supply curve. | 0 | The response ultimately commits to option B, but the ground truth is C. | true | 2 | 12 | 1 | 220 | 139 | |
[
{
"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.
A fall in price causes a decrease in quantity supplied, not a decrease in supply. Since farmers sold less because the price dropped, this is a movement along the supply curve, not a shift of the supply curve itself. | 0 | The response commits to option B, but the ground truth is C, so it does not match. | true | 3 | 12 | 1 | 263 | 196 | |
[
{
"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 lower market price causes a decrease in quantity supplied, not a decrease in supply. Supply changes only when non-price factors change, such as technology, input costs, or weather. | 10 | The response explicitly ends with option C, which matches the ground truth. | true | 4 | 12 | 1 | 145 | 84 | |
[
{
"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.**
A fall in price from **$1.00 to $0.75** causes a **decrease in quantity supplied**, not a decrease in **supply**. Supply changes only if non-price factors change, such as technology, input costs, or number of sellers. | 0 | The response ultimately commits to option B, which does not match the ground truth of C. | true | 5 | 12 | 1 | 192 | 112 | |
[
{
"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.
A drop in price causes a decrease in quantity supplied, not a decrease in supply. Supply decreases only when non-price factors shift the supply curve left. Here, farmers are just moving along the same supply curve because the price fell. | 10 | The response ultimately commits to option C, which matches the ground truth. | true | 6 | 12 | 1 | 172 | 101 | |
[
{
"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 the market price of corn causes a decrease in quantity supplied, not a decrease in supply. A decrease in supply would require a shift of the supply curve due to factors other than corn’s own price, such as higher input costs or bad weather. | 0 | The response ultimately chooses B, which says the supply remained the same, but the ground truth is C. | true | 7 | 12 | 1 | 223 | 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 | C. No, the supply of corn to the market has not decreased.
Brief explanation: The lower price caused a decrease in quantity supplied, not a decrease in supply. A decrease in supply means the entire supply curve shifts left because of non-price factors, while here farmers are simply moving along the same supply curve i... | 10 | The response explicitly commits to option C, which matches the ground truth. | true | 8 | 12 | 1 | 316 | 237 | |
[
{
"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 change in the good’s own price causes a change in quantity supplied, not supply itself. Here, the lower corn price led farmers to sell less corn, which is a movement along the supply curve rather than a decrease in supply. | 0 | The response ultimately commits to option B, but the ground truth is C, so it is incorrect. | true | 9 | 12 | 1 | 141 | 71 | |
[
{
"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 persisted for well over a million years, making it one of the most successful and long-lasting hominid species. The other options are incorrect because upright walking and stone tool use both appeared earlier, and agriculture developed much later with modern humans. | 10 | The response explicitly concludes with option E and explains that Homo erectus was a long-lasting, successful species. | true | 0 | 13 | 0 | 260 | 189 | |
[
{
"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 persisted for an exceptionally long time—roughly from about 1.9 million to around 100,000–150,000 years ago, depending on the population—so it is considered a very successful, stable species rather than a short-lived one. | 10 | The response ends by clearly committing to option E, which matches the ground truth that Homo erectus was a stable, long-lived species. | true | 1 | 13 | 0 | 212 | 138 | |
[
{
"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 persisted for an unusually long time—roughly from about 1.9 million years ago to well under 200,000 years ago in some regions—so it is best described as a successful, stable, long-lived hominid species. | 10 | The response explicitly commits to option E and describes Homo erectus as a stable, long-lived species, which matches the ground truth. | true | 2 | 13 | 0 | 260 | 188 | |
[
{
"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 persisted for an exceptionally long time—roughly from about 1.9 million to as late as around 100,000 years ago in some regions—so it is generally considered a successful, stable, long-lived hominid species. | 10 | The response ultimately commits to option E and explains that Homo erectus persisted for a very long time, matching the ground truth. | true | 3 | 13 | 0 | 228 | 157 | |
[
{
"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.**
**Brief explanation:** *Homo erectus* persisted for an unusually long time—roughly **1.8 million years**—making it one of the most successful and enduring hominid species. The other options are incorrect because earlier hominids were already bipedal, stone tools predated *H. erectu... | 10 | The response clearly commits to option E, and that matches the ground truth. | true | 4 | 13 | 0 | 247 | 150 | |
[
{
"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 well over a million years and spread across Africa and Eurasia, making it one of the most successful and enduring hominid species in human evolution. | 10 | The response ultimately commits to option E, and that matches the ground truth. | true | 5 | 13 | 0 | 272 | 217 | |
[
{
"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 persisted for well over a million years, making it one of the most successful and long-lasting hominid species. The other options are incorrect or not well supported by evidence. | 10 | The response ultimately commits to option E and explains that Homo erectus was long-lived and stable, which matches the ground truth. | true | 6 | 13 | 0 | 247 | 189 | |
[
{
"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.**
**Brief explanation:** *Homo erectus* survived for an exceptionally long time—roughly from about 1.9 million to around 100,000 years ago—making it one of the most successful and long-lasting hominid species. | 10 | The response ultimately commits to option E, which matches the ground truth. | true | 7 | 13 | 0 | 225 | 154 | |
[
{
"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. an stable, long-lived species.
Homo erectus persisted for an exceptionally long time—roughly from about 1.9 million years ago to well under 200,000 years ago—making it one of the most successful and enduring hominid species. | 10 | The response commits to option E and explains that Homo erectus was a long-lived, enduring species. | true | 8 | 13 | 0 | 237 | 172 | |
[
{
"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 persisted for well over a million years, making it one of the most successful and long-lasting hominid species. The other options are incorrect because upright walking, stone tools, and other traits appeared earlier, and agriculture developed much later with Homo sapiens. | 10 | The response explicitly commits to option E in its opening and explanation, which matches the ground truth. | true | 9 | 13 | 0 | 270 | 196 | |
[
{
"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 persisted for an exceptionally long time—roughly from about 1.9 million years ago to around 100,000 years ago—making it one of the most successful and enduring hominid species. | 10 | The response clearly commits to option E and its explanation describes Homo erectus as a long-lived species, which matches the ground truth. | true | 0 | 13 | 1 | 290 | 226 | |
[
{
"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 persisted for an exceptionally long time—roughly from about 1.9 million to around 100,000–150,000 years ago in some regions—making it one of the most successful and enduring hominid species. | 10 | The response clearly commits to option E and describes Homo erectus as an exceptionally long-lived species, which matches the ground truth. | true | 1 | 13 | 1 | 179 | 110 | |
[
{
"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 persisted for an unusually long time—roughly from about 1.9 million years ago to well under 200,000 years ago in some regions—making it one of the most successful and long-lasting hominid species. | 10 | The response ultimately commits to option E, which matches the ground truth that Homo erectus was a stable, long-lived species. | true | 2 | 13 | 1 | 270 | 201 | |
[
{
"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 persisted for an unusually long time—roughly from about 1.9 million years ago to around 100,000 years ago—and spread widely across Africa and Eurasia, which makes it a notably successful, long-lasting hominid species. | 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 | 3 | 13 | 1 | 253 | 181 | |
[
{
"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.**
**Brief explanation:** *Homo erectus* survived for an exceptionally long time—roughly from about 1.9 million years ago to well under 200,000 years ago in some regions—making it one of the most successful and enduring hominid species. The other options are incorrect because upright ... | 10 | The response explicitly commits to option E, which matches the ground truth. | true | 4 | 13 | 1 | 303 | 202 | |
[
{
"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.**
**Brief explanation:** *Homo erectus* survived for an unusually long time in evolutionary terms—roughly from about 1.9 million years ago to well under 200,000 years ago in some regions—so it is best described as a successful, stable, long-lived hominid species. | 10 | The response ultimately commits to option E, which matches the ground truth. | true | 5 | 13 | 1 | 341 | 258 | |
[
{
"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* persisted for an unusually long time—roughly from about 1.9 million years ago to around 100,000 years ago—so it is considered a successful, stable, long-lived hominid species. Other options are incorrect because upright walking and stone tool u... | 10 | The response explicitly commits to option E and explains that *Homo erectus* was a long-lived, stable species, matching the ground truth. | true | 6 | 13 | 1 | 283 | 186 | |
[
{
"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 persisted for an exceptionally long time—roughly from about 1.9 million to around 100,000 years ago—and spread across much of Africa and Eurasia, which makes it one of the most successful and long-lasting hominid species. | 10 | The response ultimately commits to option E, stating that Homo erectus was a stable, long-lived species, which matches the ground truth. | true | 7 | 13 | 1 | 223 | 150 | |
[
{
"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 persisted for an unusually long time in human evolution—roughly from about 1.9 million years ago to as late as around 100,000 years ago in some regions—so it is best described as a successful, stable, long-lived species. | 10 | The response ultimately commits to option E and supports it by describing Homo erectus as a long-lived species. | true | 8 | 13 | 1 | 255 | 181 | |
[
{
"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 persisted for an exceptionally long time—roughly from about 1.9 million to around 100,000 years ago—so it is generally considered a highly successful, stable hominid species rather than a short-lived one. | 10 | The response clearly commits to option E and explains that Homo erectus was long-lived and stable. | true | 9 | 13 | 1 | 241 | 172 | |
[
{
"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 electron clouds fluctuate, creating momentary dipoles that induce dipoles in nearby particles, producing weak intermolecular attractions. | 10 | The response clearly commits to option F, which matches the ground truth because London dispersion forces come from temporary dipoles caused by fluctuating electron positions. | true | 0 | 14 | 0 | 83 | 27 | |
[
{
"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.** London dispersion forces are caused by **temporary dipoles created by the position of electrons around the nuclei in a molecule**.
These arise when electron density fluctuates momentarily, creating an instantaneous dipole that induces dipoles in nearby particles. | 10 | The response ultimately commits to option F and explains that London dispersion forces come from temporary dipoles caused by electron fluctuations. | true | 1 | 14 | 0 | 88 | 26 | |
[
{
"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 when electrons momentarily become unevenly distributed, creating temporary dipoles that 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 momentary electron distribution. | true | 2 | 14 | 0 | 77 | 24 | |
[
{
"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 when electrons momentarily distribute unevenly, creating temporary dipoles that induce dipoles in nearby particles. | 10 | The response explicitly commits to F and explains that London dispersion forces come from temporary dipoles caused by uneven electron distribution. | true | 3 | 14 | 0 | 83 | 31 | |
[
{
"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 when electrons are momentarily distributed unevenly, creating temporary dipoles that induce dipoles in neighboring particles. These weak intermolecular forces are present in all atoms and molecules. | 10 | The response ultimately selects F and explains that London dispersion forces come from temporary dipoles caused by uneven electron distribution. | true | 4 | 14 | 0 | 93 | 27 | |
[
{
"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
**Brief explanation:** London dispersion forces arise when electrons momentarily become unevenly distributed, creating a temporary dipole that induces dipoles in nearby particles. These weak intermolecular forces occur in all... | 10 | The response explicitly commits to option F, which matches the ground truth. | true | 5 | 14 | 0 | 96 | 24 | |
[
{
"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 when electron density fluctuates, creating instantaneous temporary dipoles that induce dipoles in nearby particles. | 10 | The response clearly commits to option F, which matches the ground truth because London dispersion forces are caused by temporary dipoles from electron fluctuations. | true | 6 | 14 | 0 | 75 | 24 | |
[
{
"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.** London dispersion forces arise from **temporary dipoles created by the position of electrons around the nuclei in a molecule**. These momentary uneven electron distributions can induce dipoles in nearby particles, creating weak intermolecular attractions. | 10 | The response explicitly commits to option F, which matches the ground truth. | true | 7 | 14 | 0 | 80 | 23 | |
[
{
"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.** London dispersion forces are caused by **temporary dipoles created by the position of electrons around the nuclei in a molecule**. Random electron motion can create momentary uneven charge distributions, which induce dipoles in nearby particles and produce weak attractions. | 10 | The response clearly commits to option F, which matches the ground truth. | true | 8 | 14 | 0 | 86 | 25 | |
[
{
"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.** 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 particles. | 10 | The response ultimately commits to option F, which matches the ground truth because London dispersion forces are caused by temporary dipoles from momentary electron distribution. | true | 9 | 14 | 0 | 99 | 42 | |
[
{
"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.** London dispersion forces are caused by **temporary dipoles created by the position of electrons around the nuclei in a molecule**. These arise from momentary fluctuations in electron distribution, which induce dipoles in neighboring particles. | 10 | The response ultimately commits to option F, which matches the ground truth and correctly describes London dispersion forces as arising from temporary dipoles. | true | 0 | 14 | 1 | 50 | 0 | |
[
{
"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 particles. | 10 | The response explicitly commits to option F, which matches the ground truth and correctly describes temporary dipoles from electron movement. | true | 1 | 14 | 1 | 89 | 36 | |
[
{
"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. London dispersion forces are caused by **temporary dipoles** created by the momentary positions of electrons around the nuclei in a molecule, which induce dipoles in nearby particles. | 10 | The response ultimately commits to option F, which matches the ground truth that London dispersion forces are caused by temporary dipoles. | true | 2 | 14 | 1 | 40 | 0 | |
[
{
"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 when electron clouds fluctuate, creating instantaneous temporary dipoles that induce dipoles in neighboring particles. | 10 | The response clearly commits to option F and explains that London dispersion forces come from temporary dipoles due to fluctuating electron clouds. | true | 3 | 14 | 1 | 75 | 25 | |
[
{
"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.** London dispersion forces are caused by **temporary dipoles created by the position of electrons around the nuclei in a molecule**. Random electron movement can produce momentary uneven charge distributions, which induce dipoles in nearby particles and create weak intermolecular attractions. | 10 | The response explicitly commits to option F, which matches the ground truth definition of London dispersion forces. | true | 4 | 14 | 1 | 57 | 0 | |
[
{
"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 are momentarily distributed unevenly, creating **temporary dipoles** that induce dipoles in nearby particles. These weak intermolecular forces occur in **all atoms and molecules**... | 10 | The response explicitly commits to option F, which matches the ground truth. | true | 5 | 14 | 1 | 94 | 24 | |
[
{
"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 when electron movement creates instantaneous, temporary dipoles, which then induce dipoles in nearby particles. | 10 | The response explicitly ends by choosing F and explains London dispersion forces as arising from temporary dipoles caused by electron movement. | true | 6 | 14 | 1 | 76 | 25 | |
[
{
"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 when electrons are momentarily distributed unevenly, creating temporary dipoles that induce dipoles in nearby particles. | 10 | The response clearly commits to option F and explains that London dispersion forces come from temporary dipoles caused by uneven electron distribution. | true | 7 | 14 | 1 | 82 | 29 | |
[
{
"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 when electrons are momentarily distributed unevenly, creating temporary dipoles that induce dipoles in nearby particles. | 10 | The response clearly commits to option F and explains that London dispersion forces come from temporary dipoles caused by electron distribution. | true | 8 | 14 | 1 | 78 | 25 | |
[
{
"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. temporary dipoles created by the position of electrons around the nuclei in a molecule
London dispersion forces arise when electrons are momentarily distributed unevenly, creating temporary dipoles that induce dipoles in nearby particles. | 10 | The response explicitly commits to option F and explains London dispersion forces as temporary dipoles from uneven electron distribution. | true | 9 | 14 | 1 | 77 | 24 |
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