id string | year int32 | paper int32 | subject string | q_number int32 | section int32 | type string | is_paragraph bool | paragraph dict | question_text string | images images list | image_ids list | options dict | marking dict | answer_kind string | correct_answer string | answer_raw string | source dict | review dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2022_P1_Mathematics_Q01 | 2,022 | 1 | Mathematics | 1 | 1 | numerical | false | null | Considering only the principal values of the inverse trigonometric functions, the value of
$$
\frac{3}{2} \cos^{-1} \sqrt{\frac{2}{2 + \pi^2}} + \frac{1}{4} \sin^{-1} \frac{2\sqrt{2} \, \pi}{2 + \pi^2} + \tan^{-1} \frac{\sqrt{2}}{\pi}
$$
is _________ . | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 2.35, "max": 2.37} | 2.36 . Range (2.35 - 2.37) | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q02 | 2,022 | 1 | Mathematics | 2 | 1 | numerical | false | null | Let $\alpha$ be a positive real number. Let $f \colon \mathbb{R} \to \mathbb{R}$ and $g \colon (\alpha, \infty) \to \mathbb{R}$ be the functions defined by
$$
f(x) = \sin \left( \frac{\pi x}{12} \right) \quad \text{and} \quad g(x) = \frac{2 \, \log_e \left( \sqrt{x} - \sqrt{\alpha} \right)}{\log_e \left( e^{\sqrt{x}} -... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.49, "max": 0.51} | 0.50 . Range (0.49 - 0.51) | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q03 | 2,022 | 1 | Mathematics | 3 | 1 | numerical | false | null | In a study about a pandemic, data of 900 persons was collected. It was found that
- 190 persons had symptom of fever,
- 220 persons had symptom of cough,
- 220 persons had symptom of breathing problem,
- 330 persons had symptom of fever or cough or both,
- 350 persons had symptom of cough or breathing problem or both,... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.79, "max": 0.81} | 0.80 . Range (0.79 - 0.81) | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q04 | 2,022 | 1 | Mathematics | 4 | 1 | numerical | false | null | Let $z$ be a complex number with non-zero imaginary part. If
$$
\frac{2 + 3z + 4z^2}{2 - 3z + 4z^2}
$$
is a real number, then the value of $|z|^2$ is _________. | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.49, "max": 0.51} | 0.50 Range (0.49 - 0.51) | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q05 | 2,022 | 1 | Mathematics | 5 | 1 | numerical | false | null | Let $\bar{z}$ denote the complex conjugate of a complex number $z$ and let $i = \sqrt{-1}$. In the set of complex numbers, the number of distinct roots of the equation
$$
\bar{z} - z^2 = i(\bar{z} + z^2)
$$
is _________. | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 4, "max": 4} | 4 Range (4 - 4) | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q06 | 2,022 | 1 | Mathematics | 6 | 1 | numerical | false | null | Let $l_1, l_2, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$, and let $w_1, w_2, \ldots, w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_2$, where $d_1 d_2 = 10$. For each $i = 1, 2, \ldots, 100$, let $R_i$ be a rectangle with l... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 18900, "max": 18900} | 18900 Range (18900 - 18900) | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q07 | 2,022 | 1 | Mathematics | 7 | 1 | numerical | false | null | The number of 4-digit integers in the closed interval $[2022, 4482]$ formed by using the digits $0, 2, 3, 4, 6, 7$ is _________. | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 569, "max": 569} | 569 Range (569 - 569) | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q08 | 2,022 | 1 | Mathematics | 8 | 1 | numerical | false | null | Let $ABC$ be the triangle with $AB = 1$, $AC = 3$ and $\angle BAC = \frac{\pi}{2}$. If a circle of radius $r > 0$ touches the sides $AB$, $AC$ and also touches internally the circumcircle of the triangle $ABC$, then the value of $r$ is _________. | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.82, "max": 0.86} | 0.84 Range (0.82 - 0.86) | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P1_Mathematics_Q09 | 2,022 | 1 | Mathematics | 9 | 2 | multi_correct | false | null | Consider the equation
$$
\int_{1}^{e} \frac{(\log_e x)^{1/2}}{x \left(a - (\log_e x)^{3/2}\right)^2} dx = 1, \quad a \in (-\infty, 0) \cup (1, \infty).
$$
Which of the following statements is/are TRUE ? | [] | {
"choices": [
{
"label": "A",
"text": "No $a$ satisfies the above equation"
},
{
"label": "B",
"text": "An integer $a$ satisfies the above equation"
},
{
"label": "C",
"text": "An irrational number $a$ satisfies the above equation"
},
{
"label": "... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["C", "D"]} | C, D | {
"pages": [
3
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Mathematics_Q10 | 2,022 | 1 | Mathematics | 10 | 2 | multi_correct | false | null | Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1 = 7$ and common difference $8$. Let $T_1, T_2, T_3, \ldots$ be such that $T_1 = 3$ and $T_{n+1} - T_n = a_n$ for $n \geq 1$. Then, which of the following is/are TRUE? | [] | {
"choices": [
{
"label": "A",
"text": "$T_{20} = 1604$"
},
{
"label": "B",
"text": "$\\sum_{k=1}^{20} T_k = 10510$"
},
{
"label": "C",
"text": "$T_{30} = 3454$"
},
{
"label": "D",
"text": "$\\sum_{k=1}^{30} T_k = 35610$"
}
],
"list_I... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C"]} | Answer: B, C | {
"pages": [
4
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Mathematics_Q11 | 2,022 | 1 | Mathematics | 11 | 2 | multi_correct | false | null | Let $P_1$ and $P_2$ be two planes given by
$$
P_1: \ 10x + 15y + 12z - 60 = 0 \ ,
$$
$$
P_2: \ -2x + 5y + 4z - 20 = 0 \ .
$$
Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $P_1$ and $P_2$ ? | [] | {
"choices": [
{
"label": "A",
"text": "$\\frac{x-1}{0} = \\frac{y-1}{0} = \\frac{z-1}{5}$"
},
{
"label": "B",
"text": "$\\frac{x-6}{-5} = \\frac{y}{2} = \\frac{z}{3}$"
},
{
"label": "C",
"text": "$\\frac{x}{-2} = \\frac{y-4}{5} = \\frac{z}{4}$"
},
{
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "D"]} | Answer: A, B, D | {
"pages": [
4
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Mathematics_Q12 | 2,022 | 1 | Mathematics | 12 | 2 | multi_correct | false | null | Let $S$ be the reflection of a point $Q$ with respect to the plane given by
$$
\vec{r} = -(t + p)\hat{i} + t\hat{j} + (1 + p)\hat{k}
$$
where $t, p$ are real parameters and $\hat{i}, \hat{j}, \hat{k}$ are the unit vectors along the three positive coordinate axes. If the position vectors of $Q$ and $S$ are $10\hat{i} + ... | [] | {
"choices": [
{
"label": "A",
"text": "$3(\\alpha + \\beta) = -101$"
},
{
"label": "B",
"text": "$3(\\beta + \\gamma) = -71$"
},
{
"label": "C",
"text": "$3(\\gamma + \\alpha) = -86$"
},
{
"label": "D",
"text": "$3(\\alpha + \\beta + \\gamma... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "C"]} | Answer: A, B, C | {
"pages": [
4
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Mathematics_Q13 | 2,022 | 1 | Mathematics | 13 | 2 | multi_correct | false | null | Consider the parabola $y^2 = 4x$. Let $S$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $P = (-2, 1)$ meet the parabola at $P_1$ and $P_2$. Let $Q_1$ and $Q_2$ be points on the lines $SP_1$ and $SP_2$ respectively such that $PQ_1$ is perpendicular to $SP_1$ and $PQ_2$ is perpendi... | [] | {
"choices": [
{
"label": "A",
"text": "$SQ_1 = 2$"
},
{
"label": "B",
"text": "$Q_1Q_2 = \\frac{3\\sqrt{10}}{5}$"
},
{
"label": "C",
"text": "$PQ_1 = 3$"
},
{
"label": "D",
"text": "$SQ_2 = 1$"
}
],
"list_I": null,
"list_II": null
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C", "D"]} | B, C, D | {
"pages": [
5
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Mathematics_Q14 | 2,022 | 1 | Mathematics | 14 | 2 | multi_correct | false | null | Let $|M|$ denote the determinant of a square matrix $M$. Let $g: \left[0, \frac{\pi}{2}\right] \to \mathbb{R}$ be the function defined by
$$
g(\theta) = \sqrt{f(\theta) - 1} + \sqrt{f\left(\frac{\pi}{2} - \theta\right) - 1}
$$
where
$$
f(\theta) = \frac{1}{2} \left| \begin{array}{ccc} 1 & \sin \theta & 1 \\ -\sin \thet... | [] | {
"choices": [
{
"label": "A",
"text": "$p\\left(\\frac{3+\\sqrt{2}}{4}\\right) < 0$"
},
{
"label": "B",
"text": "$p\\left(\\frac{1+3\\sqrt{2}}{4}\\right) > 0$"
},
{
"label": "C",
"text": "$p\\left(\\frac{5\\sqrt{2}-1}{4}\\right) > 0$"
},
{
"label"... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "C"]} | A, C | {
"pages": [
5
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Mathematics_Q15 | 2,022 | 1 | Mathematics | 15 | 3 | matrix_match | false | null | Consider the following lists:
The correct option is: | [] | {
"choices": [
{
"label": "A",
"text": "$(I) \\to (P);\\ (II) \\to (S);\\ (III) \\to (P);\\ (IV) \\to (S)$"
},
{
"label": "B",
"text": "$(I) \\to (P);\\ (II) \\to (P);\\ (III) \\to (T);\\ (IV) \\to (R)$"
},
{
"label": "C",
"text": "$(I) \\to (Q);\\ (II) \\to (P)... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["B"]} | B | {
"pages": [
6
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 6: PDF text line not transcribed: 'The correct option is:'",
"second model disagrees: List-I count 4 vs 0",
"second model disagrees: List-II count 5 vs 0",
"second model disagrees: text differs (100% / 86% token overlap)... | |
2022_P1_Mathematics_Q16 | 2,022 | 1 | Mathematics | 16 | 3 | matrix_match | false | null | Two players, $P_1$ and $P_2$, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let $x$ and $y$ denote the readings on the die rolled by $P_1$ and $P_2$, respectively. If $x > y$, then $P_1$ scores 5 points and $P_2$ ... | [] | {
"choices": [
{
"label": "A",
"text": "(I) $\\to$ (Q); (II) $\\to$ (R); (III) $\\to$ (T); (IV) $\\to$ (S)"
},
{
"label": "B",
"text": "(I) $\\to$ (Q); (II) $\\to$ (R); (III) $\\to$ (T); (IV) $\\to$ (T)"
},
{
"label": "C",
"text": "(I) $\\to$ (P); (II) $\\to$ (R... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
7
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 7: PDF text line not transcribed: 'The correct option is:'"
],
"notes": []
} | |
2022_P1_Mathematics_Q17 | 2,022 | 1 | Mathematics | 17 | 3 | matrix_match | false | null | Let $p, q, r$ be nonzero real numbers that are, respectively, the $10^{th}$, $100^{th}$ and $1000^{th}$ terms of a harmonic progression. Consider the system of linear equations
$$
x + y + z = 1
$$
$$
10x + 100y + 1000z = 0
$$
$$
qr\, x + pr\, y + pq\, z = 0 \quad .
$$
The correct option is: | [] | {
"choices": [
{
"label": "A",
"text": "(I) $\\to$ (T); (II) $\\to$ (R); (III) $\\to$ (S); (IV) $\\to$ (T)"
},
{
"label": "B",
"text": "(I) $\\to$ (Q); (II) $\\to$ (S); (III) $\\to$ (S); (IV) $\\to$ (R)"
},
{
"label": "C",
"text": "(I) $\\to$ (Q); (II) $\\to$ (R... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["B"]} | Answer: B | {
"pages": [
8
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 8: PDF text line not transcribed: 'The correct option is:'"
],
"notes": []
} | |
2022_P1_Mathematics_Q18 | 2,022 | 1 | Mathematics | 18 | 3 | matrix_match | false | null | Consider the ellipse
$$
\frac{x^2}{4} + \frac{y^2}{3} = 1 \,.
$$
Let $H(\alpha, 0)$, $0 < \alpha < 2$, be a point. A straight line drawn through $H$ parallel to the $y$-axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ respectively, in the first quadrant. The tangent to the ellipse at the point $E... | [] | {
"choices": [
{
"label": "A",
"text": "(I) $\\to$ (R); (II) $\\to$ (S); (III) $\\to$ (Q); (IV) $\\to$ (P)"
},
{
"label": "B",
"text": "(I) $\\to$ (R); (II) $\\to$ (T); (III) $\\to$ (S); (IV) $\\to$ (P)"
},
{
"label": "C",
"text": "(I) $\\to$ (Q); (II) $\\to$ (T... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["C"]} | C | {
"pages": [
9
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 9: PDF text line not transcribed: 'The correct option is:'"
],
"notes": []
} | |
2022_P1_Physics_Q01 | 2,022 | 1 | Physics | 1 | 1 | numerical | false | null | Two spherical stars $A$ and $B$ have densities $\rho_A$ and $\rho_B$, respectively. $A$ and $B$ have the same radius, and their masses $M_A$ and $M_B$ are related by $M_B = 2M_A$. Due to an interaction process, star $A$ loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 2.2, "max": 2.4} | 2.3. Range (2.2 - 2.4) | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 10: drawing at [109, 389, 524, 473] is in no figure (possible missed figure)"
],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q02 | 2,022 | 1 | Physics | 2 | 1 | numerical | false | null | The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction $^{16}_7\mathrm{N} + {}^4_2\mathrm{He} \to {}^1_1\mathrm{H} + {}^{19}_8\mathrm{O}$ in a laboratory frame is $n$ (in $\mathrm{MeV}$). Assume that $^{16}_7\mathrm{N}$ is at rest in the laboratory frame. The masses of $^{16}_7\mathrm{N}$,... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 2.3, "max": 2.35} | 2.33. Range (2.30 - 2.35) | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 10: drawing at [109, 389, 524, 473] is in no figure (possible missed figure)",
"second model disagrees: text differs (88% / 100% token overlap)"
],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1,... | |
2022_P1_Physics_Q03 | 2,022 | 1 | Physics | 3 | 1 | numerical | false | null | In the following circuit $C_1 = 12\,\mu\mathrm{F}$, $C_2 = C_3 = 4\,\mu\mathrm{F}$ and $C_4 = C_5 = 2\,\mu\mathrm{F}$. The charge stored in $C_3$ is ____ $\mu\mathrm{C}$.
[FIG_1] | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 7.9, "max": 8.1} | 8. Range (7.9 - 8.1) | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 10: drawing at [109, 389, 524, 473] is in no figure (possible missed figure)"
],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q04 | 2,022 | 1 | Physics | 4 | 1 | numerical | false | null | A rod of length $2\,\mathrm{cm}$ makes an angle $\frac{2\pi}{3}\,\mathrm{rad}$ with the principal axis of a thin convex lens. The lens has a focal length of $10\,\mathrm{cm}$ and is placed at a distance of $\frac{40}{3}\,\mathrm{cm}$ from the object as shown in the figure. The height of the image is $\frac{30\sqrt{3}}{... | [
"FIG_2"
] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 5.95, "max": 6.05} | 6. Range (5.95 - 6.05) | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 10: drawing at [109, 389, 524, 473] is in no figure (possible missed figure)"
],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q05 | 2,022 | 1 | Physics | 5 | 1 | numerical | false | null | At time $t = 0$, a disk of radius $1\,m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha = \frac{2}{3}\,\mathrm{rad\,s^{-2}}$. A small stone is stuck to the disk. At $t = 0$, it is at the contact point of the disk and the plane. Later, at time $t = \sqrt{\pi}\,\mathrm{s}$, ... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.48, "max": 0.56} | 0.52. Range (0.48 - 0.56) | {
"pages": [
11
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q06 | 2,022 | 1 | Physics | 6 | 1 | numerical | false | null | A solid sphere of mass $1\,\mathrm{kg}$ and radius $1\,\mathrm{m}$ rolls without slipping on a fixed inclined plane with an angle of inclination $\theta = 30^\circ$ from the horizontal. Two forces of magnitude $1\,\mathrm{N}$ each, parallel to the incline, act on the sphere, both at distance $r = 0.5\,\mathrm{m}$ from ... | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 2.8, "max": 2.92} | 2.86 m s⁻². Range (2.80 - 2.92) | {
"pages": [
11
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q07 | 2,022 | 1 | Physics | 7 | 1 | numerical | false | null | Consider an LC circuit, with inductance $L = 0.1\,\mathrm{H}$ and capacitance $C = 10^{-3}\,\mathrm{F}$, kept on a plane. The area of the circuit is $1\,\mathrm{m^2}$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t = 0$, the magnetic field stre... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 3.98, "max": 4.02} | 4 mA. Range (3.98 - 4.02) | {
"pages": [
11
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q08 | 2,022 | 1 | Physics | 8 | 1 | numerical | false | null | A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of the projectile is $d$. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g' = \frac{g... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.93, "max": 0.97} | 0.95. Range (0.93 - 0.97) | {
"pages": [
11
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: marks differ (PDF (3, 0, 0, ()), model (3, 0, -1, ())); using the PDF"
]
} | |
2022_P1_Physics_Q09 | 2,022 | 1 | Physics | 9 | 2 | multi_correct | false | null | A medium having dielectric constant $K > 1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown in Figure (a). Now, both the plates are moved by a distance of $\frac{d}{2}$ fr... | [
"FIG_1",
"FIG_2"
] | {
"choices": [
{
"label": "A",
"text": "The electric field inside the dielectric material is reduced by a factor of $2K$."
},
{
"label": "B",
"text": "The capacitance is decreased by a factor of $\\frac{1}{K+1}$."
},
{
"label": "C",
"text": "The voltage between ... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B"]} | B | {
"pages": [
13
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 13: PDF text line not transcribed: 'In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of'",
"page 13: PDF text line not transcribed: 'the following statement(s) is(are) correct?'"... | |
2022_P1_Physics_Q10 | 2,022 | 1 | Physics | 10 | 2 | multi_correct | false | null | The figure shows a circuit having eight resistances of $1\,\Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages $\mathcal{E}_1 = 12\,V$ and $\mathcal{E}_2 = 6\,V$.
[FIG_1]
Which of the following statement(s) is(are) correct? | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "The magnitude of current flowing through $R_1$ is $7.2\\,\\mathrm{A}$."
},
{
"label": "B",
"text": "The magnitude of current flowing through $R_2$ is $1.2\\,\\mathrm{A}$."
},
{
"label": "C",
"text": "The magnitude of curre... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "C", "D"]} | A, B, C, D | {
"pages": [
14
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Physics_Q11 | 2,022 | 1 | Physics | 11 | 2 | multi_correct | false | null | An ideal gas of density $\rho = 0.2\,kg\,m^{-3}$ enters a chimney of height $h$ at the rate of $\alpha = 0.8\,kg\,s^{-1}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1 = 0.1\,m^2$ and the upper end is $A_2 = 0.4\,m^2$. The pressure and th... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "The pressure of the gas at the upper end of the chimney is $300\\,Pa$."
},
{
"label": "B",
"text": "The velocity of the gas at the lower end of the chimney is $40\\,m\\,s^{-1}$ and at the upper end is $20\\,m\\,s^{-1}$."
},
{
"l... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B"]} | B | {
"pages": [
15
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: figure count 1 vs 2"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Physics_Q12 | 2,022 | 1 | Physics | 12 | 2 | multi_correct | false | null | Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l > 0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configura... | [
"FIG_2"
] | {
"choices": [
{
"label": "A",
"text": "The ray of light will come out for $\\theta = 30^\\circ$, for $0 < l < L$."
},
{
"label": "B",
"text": "There is an angle for $l = \\frac{L}{2}$ at which the ray of light will come out after two reflections."
},
{
"label": "C",
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B"]} | A, B | {
"pages": [
15
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: figure count 1 vs 2"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Physics_Q13 | 2,022 | 1 | Physics | 13 | 2 | multi_correct | false | null | Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center O of the hexagon and is bisected by the side.
[FIG_1]
Which of the fol... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "When $x = q$, the magnitude of the electric field at O is zero."
},
{
"label": "B",
"text": "When $x = -q$, the magnitude of the electric field at O is $\\frac{q}{6\\pi \\epsilon_o a^2}$."
},
{
"label": "C",
"text": "When ... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "C"]} | A, B, C | {
"pages": [
16
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 16: PDF text line not transcribed: 'Which of the following statement(s) is(are) correct in SI units?'",
"page 16: PDF text line not transcribed: 'Which of the following statement(s) is(are) correct?'",
"second model disagree... | |
2022_P1_Physics_Q14 | 2,022 | 1 | Physics | 14 | 2 | multi_correct | false | null | The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus.
Which of the following statement(s) is(are) ... | [] | {
"choices": [
{
"label": "A",
"text": "$E_b^p - E_b^n$ is proportional to $Z(Z - 1)$ where $Z$ is the atomic number of the nucleus."
},
{
"label": "B",
"text": "$E_b^p - E_b^n$ is proportional to $A^{-\\frac{1}{3}}$ where $A$ is the mass number of the nucleus."
},
{
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "D"]} | A, B, D | {
"pages": [
16
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 16: PDF text line not transcribed: 'Which of the following statement(s) is(are) correct in SI units?'",
"page 16: PDF text line not transcribed: 'Which of the following statement(s) is(are) correct?'",
"second model disagree... | |
2022_P1_Physics_Q15 | 2,022 | 1 | Physics | 15 | 3 | matrix_match | false | null | A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the figure. The magnetic field due to the solenoid is in $... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "I $\\to$ Q, II $\\to$ P, III $\\to$ S, IV $\\to$ T"
},
{
"label": "B",
"text": "I $\\to$ S, II $\\to$ T, III $\\to$ Q, IV $\\to$ P"
},
{
"label": "C",
"text": "I $\\to$ Q, II $\\to$ P, III $\\to$ S, IV $\\to$ R"
},
... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | bonus | {"kind": "bonus", "note": "Question dropped Marks for All"} | Question dropped Marks for All | {
"pages": [
17
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"matrix-match question without both List-I and List-II",
"second model disagrees: List-I count 0 vs 4",
"second model disagrees: List-II count 0 vs 5"
],
"notes": []
} | |
2022_P1_Physics_Q16 | 2,022 | 1 | Physics | 16 | 3 | matrix_match | false | null | List I describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities (in $m\,s^{-1}$) at time $t = \frac{\pi}{3}\,s$.
Which one of the following options is correct? | [
"FIG_1",
"FIG_2",
"FIG_3",
"FIG_4"
] | {
"choices": [
{
"label": "A",
"text": "I $\\to$ R, II $\\to$ T, III $\\to$ P, IV $\\to$ S"
},
{
"label": "B",
"text": "I $\\to$ S, II $\\to$ P, III $\\to$ Q, IV $\\to$ R"
},
{
"label": "C",
"text": "I $\\to$ S, II $\\to$ T, III $\\to$ P, IV $\\to$ R"
},
... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["C"]} | Answer: C | {
"pages": [
18
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 18: PDF text line not transcribed: 'Which one of the following options is correct?'"
],
"notes": []
} | |
2022_P1_Physics_Q17 | 2,022 | 1 | Physics | 17 | 3 | matrix_match | false | null | List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.
Which one of the following options is correct? | [] | {
"choices": [
{
"label": "A",
"text": "$I \\to T$, $II \\to R$, $III \\to S$, $IV \\to Q$"
},
{
"label": "B",
"text": "$I \\to S$, $II \\to P$, $III \\to T$, $IV \\to P$"
},
{
"label": "C",
"text": "$I \\to P$, $II \\to R$, $III \\to T$, $IV \\to Q$"
},
... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["C"]} | Answer: C | {
"pages": [
19
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 19: PDF text line not transcribed: 'Which one of the following options is correct?'",
"second model disagrees: text differs (81% / 96% token overlap)"
],
"notes": []
} | |
2022_P1_Physics_Q18 | 2,022 | 1 | Physics | 18 | 3 | matrix_match | false | null | List I contains four combinations of two lenses (1 and 2) whose focal lengths (in $cm$) are indicated in the figures. In all cases, the object is placed $20\,cm$ from the first lens on the left, and the distance between the two lenses is $5\,cm$. List II contains the positions of the final images.
Which one of the fol... | [
"FIG_1",
"FIG_2",
"FIG_3",
"FIG_4"
] | {
"choices": [
{
"label": "A",
"text": "$(I) \\to P;\\ (II) \\to R;\\ (III) \\to Q;\\ (IV) \\to T$"
},
{
"label": "B",
"text": "$(I) \\to Q;\\ (II) \\to P;\\ (III) \\to T;\\ (IV) \\to S$"
},
{
"label": "C",
"text": "$(I) \\to P;\\ (II) \\to T;\\ (III) \\to R;\\ ... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
20
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 20: PDF text line not transcribed: 'Which one of the following options is correct?'",
"second model disagrees: text differs (100% / 90% token overlap)"
],
"notes": []
} | |
2022_P1_Chemistry_Q01 | 2,022 | 1 | Chemistry | 1 | 1 | numerical | false | null | 2 mol of $\mathrm{Hg}(g)$ is combusted in a fixed volume bomb calorimeter with excess of $\mathrm{O_2}$ at 298 K and 1 atm into $\mathrm{HgO}(s)$. During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of $\mathrm{Hg}(g)$ are 20.00 $\mathrm... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 89.0, "max": 91.0} | 90.39. Range (89.00-91.00) | {
"pages": [
22
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 22: PDF text line not transcribed: '[Given: Gas constant R = 8.3 J K-1 mol-1]'"
],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P1_Chemistry_Q02 | 2,022 | 1 | Chemistry | 2 | 1 | numerical | false | null | The reduction potential ($E^0$, in V) of $\mathrm{MnO_4^-}(aq)/\mathrm{Mn}(s)$ is _______.
[Given: $E^0_{(\mathrm{MnO_4^-}(aq)/\mathrm{MnO_2}(s))} = 1.68\ \mathrm{V}$; $E^0_{(\mathrm{MnO_2}(s)/\mathrm{Mn^{2+}}(aq))} = 1.21\ \mathrm{V}$; $E^0_{(\mathrm{Mn^{2+}}(aq)/\mathrm{Mn}(s))} = -1.03\ \mathrm{V}$ ] | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.74, "max": 0.8} | 0.77. Range (0.74-0.80) | {
"pages": [
22
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 22: PDF text line not transcribed: '[Given: Gas constant R = 8.3 J K-1 mol-1]'"
],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P1_Chemistry_Q03 | 2,022 | 1 | Chemistry | 3 | 1 | numerical | false | null | A solution is prepared by mixing $0.01$ mol each of $\mathrm{H_2CO_3}$, $\mathrm{NaHCO_3}$, $\mathrm{Na_2CO_3}$, and $\mathrm{NaOH}$ in $100\ \mathrm{mL}$ of water. $p\mathrm{H}$ of the resulting solution is _______.
[Given: $p\mathrm{K_{a1}}$ and $p\mathrm{K_{a2}}$ of $\mathrm{H_2CO_3}$ are 6.37 and 10.32, respective... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 10.0, "max": 10.04} | 10.02. Range (10.00-10.04) | {
"pages": [
23
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 23: PDF text line not transcribed: '[Given: pKa1 and pKa2 of H2CO3 are 6.37 and 10.32, respectively; log 2 = 0.30]'",
"page 23: PDF text line not transcribed: '[Given: Atomic mass of H = 1, N = 14, O = 16, S = 32, K = 39, Cu = 6... | |
2022_P1_Chemistry_Q04 | 2,022 | 1 | Chemistry | 4 | 1 | numerical | false | null | The treatment of an aqueous solution of $3.74\ \mathrm{g}$ of $\mathrm{Cu(NO_3)_2}$ with excess $\mathrm{KI}$ results in a brown solution along with the formation of a precipitate. Passing $\mathrm{H_2S}$ through this brown solution gives another precipitate $\mathrm{X}$. The amount of $\mathrm{X}$ (in $\mathrm{g}$) is... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 0.31, "max": 0.33} | 0.32. Range (0.31-0.33) | {
"pages": [
23
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
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"flags": [
"page 23: PDF text line not transcribed: '[Given: pKa1 and pKa2 of H2CO3 are 6.37 and 10.32, respectively; log 2 = 0.30]'",
"page 23: PDF text line not transcribed: '[Given: Atomic mass of H = 1, N = 14, O = 16, S = 32, K = 39, Cu = 6... | |
2022_P1_Chemistry_Q05 | 2,022 | 1 | Chemistry | 5 | 1 | numerical | false | null | Dissolving $1.24\ \mathrm{g}$ of white phosphorous in boiling $\mathrm{NaOH}$ solution in an inert atmosphere gives a gas $\mathrm{Q}$. The amount of $\mathrm{CuSO_4}$ (in $\mathrm{g}$) required to completely consume the gas $\mathrm{Q}$ is _______.
[Given: Atomic mass of H = 1, O = 16, Na = 23, P = 31, S = 32, Cu = 6... | [] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 2.37, "max": 2.41} | 2.39 Range (2.37-2.41) | {
"pages": [
23
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
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"page 23: PDF text line not transcribed: '[Given: Atomic mass of H = 1, N = 14, O = 16, S = 32, K = 39, Cu = 6... | |
2022_P1_Chemistry_Q06 | 2,022 | 1 | Chemistry | 6 | 1 | numerical | false | null | Consider the following reaction.
[FIG_1]
On estimation of bromine in $1.00\ \mathrm{g}$ of $\mathbf{R}$ using Carius method, the amount of $\mathrm{AgBr}$ formed (in $\mathrm{g}$) is ________.
[Given: Atomic mass of $\mathrm{H} = 1$, $\mathrm{C} = 12$, $\mathrm{O} = 16$, $\mathrm{P} = 31$, $\mathrm{Br} = 80$, $\math... | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 1.49, "max": 1.51} | 1.50. Range (1.49-1.51) | {
"pages": [
24
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P1_Chemistry_Q07 | 2,022 | 1 | Chemistry | 7 | 1 | numerical | false | null | The weight percentage of hydrogen in $\mathbf{Q}$, formed in the following reaction sequence, is ________.
[FIG_2]
[Given: Atomic mass of $\mathrm{H} = 1$, $\mathrm{C} = 12$, $\mathrm{N} = 14$, $\mathrm{O} = 16$, $\mathrm{S} = 32$, $\mathrm{Cl} = 35$] | [
"FIG_2"
] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 1.3, "max": 1.32} | 1.31. Range (1.30-1.32) | {
"pages": [
24
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: text differs (100% / 62% token overlap)"
],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P1_Chemistry_Q08 | 2,022 | 1 | Chemistry | 8 | 1 | numerical | false | null | If the reaction sequence given below is carried out with $15$ moles of acetylene, the amount of the product $\mathbf{D}$ formed (in $\mathrm{g}$) is ________.
[FIG_3]
The yields of $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$ and $\mathbf{D}$ are given in parentheses.
[Given: Atomic mass of $\mathrm{H} = 1$, $\mathrm{C}... | [
"FIG_3"
] | null | {
"full": 3,
"zero": 0,
"negative": 0,
"partial": []
} | range | {"kind": "range", "min": 135.8, "max": 136.2} | 136.00. Range (135.80-136.20) | {
"pages": [
24
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P1_Chemistry_Q09 | 2,022 | 1 | Chemistry | 9 | 2 | multi_correct | false | null | For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $2p_z$ orbitals is(are) | [] | {
"choices": [
{
"label": "A",
"text": "$\\sigma$ orbital has a total of two nodal planes."
},
{
"label": "B",
"text": "$\\sigma^*$ orbital has one node in the $xz$-plane containing the molecular axis."
},
{
"label": "C",
"text": "$\\pi$ orbital has one node in ... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | any_of | {"kind": "any_of", "value": [{"kind": "option", "value": ["A", "D"]}, {"kind": "option", "value": ["D"]}]} | [A, D] or [D] | {
"pages": [
25
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Chemistry_Q10 | 2,022 | 1 | Chemistry | 10 | 2 | multi_correct | false | null | The correct option(s) related to adsorption processes is(are) | [] | {
"choices": [
{
"label": "A",
"text": "Chemisorption results in a unimolecular layer."
},
{
"label": "B",
"text": "The enthalpy change during physisorption is in the range of 100 to 140 $\\mathrm{kJ\\,mol^{-1}}$."
},
{
"label": "C",
"text": "Chemisorption is an... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "D"]} | A, D | {
"pages": [
25
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Chemistry_Q11 | 2,022 | 1 | Chemistry | 11 | 2 | multi_correct | false | null | The electrochemical extraction of aluminum from bauxite ore involves | [] | {
"choices": [
{
"label": "A",
"text": "the reaction of $\\mathrm{Al_2O_3}$ with coke (C) at a temperature $> 2500\\ {}^\\circ\\mathrm{C}$."
},
{
"label": "B",
"text": "the neutralization of aluminate solution by passing $\\mathrm{CO_2}$ gas to precipitate hydrated alumina ($\\math... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C", "D"]} | B, C, D | {
"pages": [
26
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"LaTeX: KaTeX: KaTeX parse error: Got group of unknown type: 'internal'"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Chemistry_Q12 | 2,022 | 1 | Chemistry | 12 | 2 | multi_correct | false | null | The treatment of galena with $\mathrm{HNO_3}$ produces a gas that is | [] | {
"choices": [
{
"label": "A",
"text": "paramagnetic"
},
{
"label": "B",
"text": "bent in geometry"
},
{
"label": "C",
"text": "an acidic oxide"
},
{
"label": "D",
"text": "colorless"
}
],
"list_I": null,
"list_II": null
} | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "D"]} | A, D | {
"pages": [
26
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Chemistry_Q13 | 2,022 | 1 | Chemistry | 13 | 2 | multi_correct | false | null | Considering the reaction sequence given below, the correct statement(s) is(are)
[FIG_1] | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "$\\mathbf{P}$ can be reduced to a primary alcohol using $\\mathrm{NaBH_4}$."
},
{
"label": "B",
"text": "Treating $\\mathbf{P}$ with conc. $\\mathrm{NH_4OH}$ solution followed by acidification gives $\\mathbf{Q}$."
},
{
"label":... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C", "D"]} | B, C, D | {
"pages": [
26
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: figure count 1 vs 2",
"second model disagrees: text differs (100% / 78% token overlap)"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Chemistry_Q14 | 2,022 | 1 | Chemistry | 14 | 2 | multi_correct | false | null | Considering the following reaction sequence,
[FIG_6]
the correct option(s) is(are) | [
"FIG_1",
"FIG_2",
"FIG_3",
"FIG_4",
"FIG_5",
"FIG_6"
] | {
"choices": [
{
"label": "A",
"text": "$\\mathrm{P} = \\mathrm{H_2/Pd,\\ ethanol} \\quad \\mathrm{R} = \\mathrm{NaNO_2/HCl} \\quad \\mathrm{U} = 1.\\ \\mathrm{H_3PO_2} \\quad 2.\\ \\mathrm{KMnO_4 - KOH,\\ heat}$"
},
{
"label": "B",
"text": "$\\mathrm{P} = \\mathrm{Sn/HCl} \\quad \... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "C"]} | Answer: A, B, C | {
"pages": [
27
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: figure count 5 vs 6",
"second model disagrees: text differs (100% / 86% token overlap)"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P1_Chemistry_Q15 | 2,022 | 1 | Chemistry | 15 | 3 | matrix_match | false | null | Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. $X_s$ and $k$ are constants having appropriate units. | [
"FIG_1",
"FIG_2",
"FIG_3",
"FIG_4",
"FIG_5"
] | {
"choices": [
{
"label": "A",
"text": "$I \\to P$; $II \\to Q$; $III \\to S$; $IV \\to T$"
},
{
"label": "B",
"text": "$I \\to R$; $II \\to S$; $III \\to S$; $IV \\to T$"
},
{
"label": "C",
"text": "$I \\to P$; $II \\to Q$; $III \\to Q$; $IV \\to R$"
},
... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
29
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 29: 2022_P1_Chemistry_Q15_FIG_1.png and 2022_P1_Chemistry_Q15_FIG_P.png got the same crop (the model's boxes or figure ids are off)",
"page 29: 2022_P1_Chemistry_Q15_FIG_2.png and 2022_P1_Chemistry_Q15_FIG_Q.png got the same cro... | |
2022_P1_Chemistry_Q16 | 2,022 | 1 | Chemistry | 16 | 3 | matrix_match | false | null | LIST-I contains compounds and LIST-II contains reactions
Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option | [] | {
"choices": [
{
"label": "A",
"text": "$I \\to Q$; $II \\to P$; $III \\to S$; $IV \\to R$"
},
{
"label": "B",
"text": "$I \\to T$; $II \\to P$; $III \\to Q$; $IV \\to R$"
},
{
"label": "C",
"text": "$I \\to T$; $II \\to R$; $III \\to Q$; $IV \\to P$"
},
... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["D"]} | Answer: D | {
"pages": [
30
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 30: PDF text line not transcribed: 'Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct'",
"page 30: PDF text line not transcribed: 'Match each metal species in LIST-I with their prope... | |
2022_P1_Chemistry_Q17 | 2,022 | 1 | Chemistry | 17 | 3 | matrix_match | false | null | LIST-I contains metal species and LIST-II contains their properties.
[Given: Atomic number of $\mathrm{Cr} = 24$, $\mathrm{Ru} = 44$, $\mathrm{Fe} = 26$]
Match each metal species in LIST-I with their properties in LIST-II, and choose the correct option | [] | {
"choices": [
{
"label": "A",
"text": "$I \\to R, T$; $II \\to P, S$; $III \\to Q, T$; $IV \\to P, Q$"
},
{
"label": "B",
"text": "$I \\to R, S$; $II \\to P, T$; $III \\to P, Q$; $IV \\to Q, T$"
},
{
"label": "C",
"text": "$I \\to P, R$; $II \\to R, S$; $III \\... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
30
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 30: PDF text line not transcribed: 'Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct'",
"page 30: PDF text line not transcribed: 'Match each metal species in LIST-I with their prope... | |
2022_P1_Chemistry_Q18 | 2,022 | 1 | Chemistry | 18 | 3 | matrix_match | false | null | Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option. | [] | {
"choices": [
{
"label": "A",
"text": "$\\mathrm{I} \\to \\mathrm{P}, \\mathrm{Q}; \\mathrm{II} \\to \\mathrm{S}; \\mathrm{III} \\to \\mathrm{Q}, \\mathrm{R}; \\mathrm{IV} \\to \\mathrm{P}$"
},
{
"label": "B",
"text": "$\\mathrm{I} \\to \\mathrm{P}; \\mathrm{II} \\to \\mathrm{R}, ... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["D"]} | D | {
"pages": [
31
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 3: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Mathematics_Q01 | 2,022 | 2 | Mathematics | 1 | 1 | single_digit_integer | false | null | Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4} < \beta < 0 < \alpha < \frac{\pi}{4}$. If $\sin(\alpha + \beta) = \frac{1}{3}$ and $\cos(\alpha - \beta) = \frac{2}{3}$, then the greatest integer less than or equal to
$$
\left( \frac{\sin \alpha}{\cos \beta} + \frac{\cos \beta}{\sin \alpha} + \frac{\c... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 1} | 1 | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q02 | 2,022 | 2 | Mathematics | 2 | 1 | single_digit_integer | false | null | If $y(x)$ is the solution of the differential equation
$$
xdy - (y^2 - 4y)dx = 0 \text{ for } x > 0, \quad y(1) = 2,
$$
and the slope of the curve $y = y(x)$ is never zero, then the value of $10\, y(\sqrt{2})$ is ________. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 8} | 8 | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q03 | 2,022 | 2 | Mathematics | 3 | 1 | single_digit_integer | false | null | The greatest integer less than or equal to
$$
\int_1^2 \log_2(x^3 + 1)\, dx + \int_1^{\log_2 9} (2^x - 1)^{\frac{1}{3}}\, dx
$$
is ________. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 5} | 5 | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q04 | 2,022 | 2 | Mathematics | 4 | 1 | single_digit_integer | false | null | The product of all positive real values of $x$ satisfying the equation
$$
x^{(16(\log_5 x)^3 - 68 \log_5 x)} = 5^{-16}
$$
is ________. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 1} | 1 | {
"pages": [
1
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q05 | 2,022 | 2 | Mathematics | 5 | 1 | single_digit_integer | false | null | If
$$
\beta = \lim_{x \to 0} \frac{e^{x^3} - (1 - x^3)^{\frac{1}{3}} + ((1 - x^2)^{\frac{1}{2}} - 1) \sin x}{x \sin^2 x},
$$
then the value of $6\beta$ is ________. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 5} | 5 | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q06 | 2,022 | 2 | Mathematics | 6 | 1 | single_digit_integer | false | null | Let $\beta$ be a real number. Consider the matrix
$$
A = \begin{pmatrix} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{pmatrix}.
$$
If $A^7 - (\beta - 1)A^6 - \beta A^5$ is a singular matrix, then the value of $9\beta$ is ________. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 3} | 3 | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q07 | 2,022 | 2 | Mathematics | 7 | 1 | single_digit_integer | false | null | Consider the hyperbola
$$
\frac{x^2}{100} - \frac{y^2}{64} = 1
$$
with foci at $S$ and $S_1$, where $S$ lies on the positive $x$-axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $\angle SPS_1 = \alpha$, with $\alpha < \frac{\pi}{2}$. The straight line passing through the point $S$ and having the sa... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 7} | 7 | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q08 | 2,022 | 2 | Mathematics | 8 | 1 | single_digit_integer | false | null | Consider the functions $f,\ g : \mathbb{R} \to \mathbb{R}$ defined by
$$
f(x) = x^2 + \frac{5}{12} \quad \text{and} \quad g(x) =
\begin{cases}
2\left(1 - \frac{4|x|}{3}\right), & |x| \leq \frac{3}{4}, \\
0, & |x| > \frac{3}{4}.
\end{cases}
$$
If $\alpha$ is the area of the region
$$
\left\{ (x, y) \in \mathbb{R} \time... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 6} | 6 | {
"pages": [
2
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q09 | 2,022 | 2 | Mathematics | 9 | 2 | multi_correct | false | null | Let $PQRS$ be a quadrilateral in a plane, where $QR = 1$, $\angle PQR = \angle QRS = 70^\circ$, $\angle PQS = 15^\circ$ and $\angle PRS = 40^\circ$. If $\angle RPS = \theta^\circ$, $PQ = \alpha$ and $PS = \beta$, then the interval(s) that contain(s) the value of $4\,\alpha\,\beta\,\sin\theta^\circ$ is/are | [] | {
"choices": [
{
"label": "A",
"text": "$(0,\\,\\sqrt{2})$"
},
{
"label": "B",
"text": "$(1,\\,2)$"
},
{
"label": "C",
"text": "$(\\sqrt{2},\\,3)$"
},
{
"label": "D",
"text": "$(2\\sqrt{2},\\,3\\sqrt{2})$"
}
],
"list_I": null,
"list... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B"]} | A, B | {
"pages": [
3
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Mathematics_Q10 | 2,022 | 2 | Mathematics | 10 | 2 | multi_correct | false | null | Let
$$
\alpha = \sum_{k=1}^{\infty} \sin^{2k} \left( \frac{\pi}{6} \right) \,.
$$
Let $g : [0, 1] \to \mathbb{R}$ be the function defined by
$$
g(x) = 2^{\alpha x} + 2^{\alpha (1-x)} \,.
$$
Then, which of the following statements is/are TRUE ? | [] | {
"choices": [
{
"label": "A",
"text": "The minimum value of $g(x)$ is $2^{\\frac{7}{6}}$"
},
{
"label": "B",
"text": "The maximum value of $g(x)$ is $1 + 2^{\\frac{1}{3}}$"
},
{
"label": "C",
"text": "The function $g(x)$ attains its maximum at more than one poi... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "C"]} | Answer: A, B, C | {
"pages": [
4
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Mathematics_Q11 | 2,022 | 2 | Mathematics | 11 | 2 | multi_correct | false | null | Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of
$$
(\bar{z})^2 + \frac{1}{z^2}
$$
are integers, then which of the following is/are possible value(s) of $|z|$ ? | [] | {
"choices": [
{
"label": "A",
"text": "$\\left( \\frac{43 + 3\\sqrt{205}}{2} \\right)^{\\frac{1}{4}}$"
},
{
"label": "B",
"text": "$\\left( \\frac{7 + \\sqrt{33}}{4} \\right)^{\\frac{1}{4}}$"
},
{
"label": "C",
"text": "$\\left( \\frac{9 + \\sqrt{65}}{4} \\righ... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
4
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Mathematics_Q12 | 2,022 | 2 | Mathematics | 12 | 2 | multi_correct | false | null | Let $G$ be a circle of radius $R > 0$. Let $G_1, G_2, \ldots, G_n$ be $n$ circles of equal radius $r > 0$. Suppose each of the $n$ circles $G_1, G_2, \ldots, G_n$ touches the circle $G$ externally. Also, for $i = 1, 2, \ldots, n-1$, the circle $G_i$ touches $G_{i+1}$ externally, and $G_n$ touches $G_1$ externally. Then... | [] | {
"choices": [
{
"label": "A",
"text": "If $n = 4$, then $(\\sqrt{2} - 1)r < R$"
},
{
"label": "B",
"text": "If $n = 5$, then $r < R$"
},
{
"label": "C",
"text": "If $n = 8$, then $(\\sqrt{2} - 1)r < R$"
},
{
"label": "D",
"text": "If $n = 12... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["C", "D"]} | Answer: C, D | {
"pages": [
5
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Mathematics_Q13 | 2,022 | 2 | Mathematics | 13 | 2 | multi_correct | false | null | Let $\hat{i}, \hat{j}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let
$$
\begin{aligned}
\vec{a} &= 3\hat{i} + \hat{j} - \hat{k} \, , \\
\vec{b} &= \hat{i} + b_2\hat{j} + b_3\hat{k} \, , \qquad b_2, b_3 \in \mathbb{R} \, , \\
\vec{c} &= c_1\hat{i} + c_2\hat{j} + c_3\hat{k} \, , \qquad c... | [] | {
"choices": [
{
"label": "A",
"text": "$\\vec{a} \\cdot \\vec{c} = 0$"
},
{
"label": "B",
"text": "$\\vec{b} \\cdot \\vec{c} = 0$"
},
{
"label": "C",
"text": "$|\\vec{b}| > \\sqrt{10}$"
},
{
"label": "D",
"text": "$|\\vec{c}| \\leq \\sqrt{11... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C", "D"]} | Answer: B, C, D | {
"pages": [
5
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"LaTeX: LaTeX command outside $...$: \\begin"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Mathematics_Q14 | 2,022 | 2 | Mathematics | 14 | 2 | multi_correct | false | null | For $x \in \mathbb{R}$, let the function $y(x)$ be the solution of the differential equation
$$
\frac{dy}{dx} + 12y = \cos\left(\frac{\pi}{12}x\right), \quad y(0) = 0 \,.
$$
Then, which of the following statements is/are TRUE ? | [] | {
"choices": [
{
"label": "A",
"text": "$y(x)$ is an increasing function"
},
{
"label": "B",
"text": "$y(x)$ is a decreasing function"
},
{
"label": "C",
"text": "There exists a real number $\\beta$ such that the line $y = \\beta$ intersects the curve $y = y(x)$... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["C"]} | C | {
"pages": [
6
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Mathematics_Q15 | 2,022 | 2 | Mathematics | 15 | 3 | single_correct | false | null | Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ? | [] | {
"choices": [
{
"label": "A",
"text": "21816"
},
{
"label": "B",
"text": "85536"
},
{
"label": "C",
"text": "12096"
},
{
"label": "D",
"text": "156816"
}
],
"list_I": null,
"list_II": null
} | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
7
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q16 | 2,022 | 2 | Mathematics | 16 | 3 | single_correct | false | null | If $M = \left( \begin{array}{cc} \frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2} \end{array} \right)$, then which of the following matrices is equal to $M^{2022}$ ? | [] | {
"choices": [
{
"label": "A",
"text": "$\\left( \\begin{array}{cc} 3034 & 3033 \\\\ -3033 & -3032 \\end{array} \\right)$"
},
{
"label": "B",
"text": "$\\left( \\begin{array}{cc} 3034 & -3033 \\\\ 3033 & -3032 \\end{array} \\right)$"
},
{
"label": "C",
"text": "... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
7
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q17 | 2,022 | 2 | Mathematics | 17 | 3 | single_correct | false | null | Suppose that
Box-I contains 8 red, 3 blue and 5 green balls,
Box-II contains 24 red, 9 blue and 15 green balls,
Box-III contains 1 blue, 12 green and 3 yellow balls,
Box-IV contains 10 green, 16 orange and 6 white balls.
A ball is chosen randomly from Box-I; call this ball $b$. If $b$ is red then a ball is chosen ... | [] | {
"choices": [
{
"label": "A",
"text": "$\\frac{15}{256}$"
},
{
"label": "B",
"text": "$\\frac{3}{16}$"
},
{
"label": "C",
"text": "$\\frac{5}{52}$"
},
{
"label": "D",
"text": "$\\frac{1}{8}$"
}
],
"list_I": null,
"list_II": null
} | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["C"]} | C | {
"pages": [
8
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Mathematics_Q18 | 2,022 | 2 | Mathematics | 18 | 3 | single_correct | false | null | For positive integer $n$, define
$$
f(n) = n + \frac{16 + 5n - 3n^2}{4n + 3n^2} + \frac{32 + n - 3n^2}{8n + 3n^2} + \frac{48 - 3n - 3n^2}{12n + 3n^2} + \cdots + \frac{25n - 7n^2}{7n^2} \ .
$$
Then, the value of $\lim_{n \to \infty} f(n)$ is equal to | [] | {
"choices": [
{
"label": "A",
"text": "$3 + \\frac{4}{3} \\log_e 7$"
},
{
"label": "B",
"text": "$4 - \\frac{3}{4} \\log_e \\left(\\frac{7}{3}\\right)$"
},
{
"label": "C",
"text": "$4 - \\frac{4}{3} \\log_e \\left(\\frac{7}{3}\\right)$"
},
{
"labe... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["B"]} | B | {
"pages": [
8
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q01 | 2,022 | 2 | Physics | 1 | 1 | single_digit_integer | false | null | A particle of mass $1\,kg$ is subjected to a force which depends on the position as $\vec{F} = -k(x\,\hat{i} + y\,\hat{j})\,kg\,m\,s^{-2}$ with $k = 1\,kg\,s^{-2}$. At time $t = 0$, the particle's position $\vec{r} = \left(\frac{1}{\sqrt{2}}\,\hat{i} + \sqrt{2}\,\hat{j}\right)m$ and its velocity $\vec{v} = \left(-\sqrt... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 3} | 3 | {
"pages": [
9
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q02 | 2,022 | 2 | Physics | 2 | 1 | single_digit_integer | false | null | In a radioactive decay chain reaction, $^{230}_{90}\mathrm{Th}$ nucleus decays into $^{214}_{84}\mathrm{Po}$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$ particles emitted in this process is $\underline{\qquad}$. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 2} | 2 | {
"pages": [
9
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q03 | 2,022 | 2 | Physics | 3 | 1 | single_digit_integer | false | null | Two resistances $R_1 = X\,\Omega$ and $R_2 = 1\,\Omega$ are connected to a wire $AB$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2\,mm$ at $A$ to $1\,mm$ at $B$. A galvanometer (G) connected to the center of the wire, $50\,cm$ from each end along its axi... | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 5} | 5 | {
"pages": [
9
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q04 | 2,022 | 2 | Physics | 4 | 1 | single_digit_integer | false | null | In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, electron mass $m_e$, Planck's constant $h$, and Coulomb's constant $k = \frac{1}{4\pi\epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magne... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 4} | 4 | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q05 | 2,022 | 2 | Physics | 5 | 1 | single_digit_integer | false | null | Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of height $h = \frac{1}{3} \, \mathrm{cm}$, and the second and third layers are of equal thickness $d = \frac{\sqrt{3}-1}{2} \, \mathrm{cm}$, and refractive indices $\mu_1 = \sqrt{\frac{3}{2}}$ and $\mu_... | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 4} | 4 | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q06 | 2,022 | 2 | Physics | 6 | 1 | single_digit_integer | false | null | A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n\,q}{6\,\epsilon_0}$ (in SI units). The value of $n$ is ______.
[FIG_2] | [
"FIG_2"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 3} | 3 | {
"pages": [
10
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q07 | 2,022 | 2 | Physics | 7 | 1 | single_digit_integer | false | null | On a frictionless horizontal plane, a bob of mass $m = 0.1 \, \mathrm{kg}$ is attached to a spring with natural length $l_0 = 0.1 \, \mathrm{m}$. The spring constant is $k_1 = 0.009 \, \mathrm{N} \, \mathrm{m}^{-1}$ when the length of the spring $l > l_0$ and is $k_2 = 0.016 \, \mathrm{N} \, \mathrm{m}^{-1}$ when $l < ... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 6} | 6 | {
"pages": [
11
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q08 | 2,022 | 2 | Physics | 8 | 1 | single_digit_integer | false | null | An object and a concave mirror of focal length $f = 10 \, \mathrm{cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0 = 15 \, \mathrm{cm} \, \mathrm{s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at ... | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 3} | 3 | {
"pages": [
11
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q09 | 2,022 | 2 | Physics | 9 | 2 | multi_correct | false | null | In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A = 1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A = kr$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "If $r_B = \\sqrt{\\frac{3}{2}}$, then the electric field is zero everywhere outside $B$."
},
{
"label": "B",
"text": "If $r_B = \\frac{3}{2}$, then the electric potential just outside $B$ is $\\frac{k}{\\varepsilon_0}$."
},
{
"l... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B"]} | B | {
"pages": [
12
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: figure count 1 vs 2"
],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Physics_Q10 | 2,022 | 2 | Physics | 10 | 2 | multi_correct | false | null | In Circuit-1 and Circuit-2 shown in the figures, $R_1 = 1\ \Omega$, $R_2 = 2\ \Omega$ and $R_3 = 3\ \Omega$. $P_1$ and $P_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in open conditions, respectively. $Q_1$ and $Q_2$ are the power dissipations in Circuit-1 and Circuit-2... | [
"FIG_1",
"FIG_2"
] | {
"choices": [
{
"label": "A",
"text": "When a voltage source of $6\\ V$ is connected across A and B in both circuits, $P_1 < P_2$."
},
{
"label": "B",
"text": "When a constant current source of $2\\ Amp$ is connected across A and B in both circuits, $P_1 > P_2$."
},
{
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B", "C"]} | A, B, C | {
"pages": [
13
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Physics_Q11 | 2,022 | 2 | Physics | 11 | 2 | multi_correct | false | null | A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma = \frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a1}$, the radius of the bubble is found to be $r_1$ and the temperature of the enc... | [] | {
"choices": [
{
"label": "A",
"text": "If the surface of the bubble is a perfect heat insulator, then $\\left(\\frac{r_1}{r_2}\\right)^5 = \\frac{P_{a2} + \\frac{2S}{r_2}}{P_{a1} + \\frac{2S}{r_1}}$."
},
{
"label": "B",
"text": "If the surface of the bubble is a perfect heat insul... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["C", "D"]} | C, D | {
"pages": [
13
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Physics_Q12 | 2,022 | 2 | Physics | 12 | 2 | multi_correct | false | null | A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $xy$ plane with its center at the origin. The Coulomb potential along the $z$-axis is
$$
V(z) = \frac{\sigma}{2\varepsilon_0} \left( \sqrt{R^2 + z^2} - z \right).
$$
A particle of positive charge $q$ is placed initially at rest at a poi... | [] | {
"choices": [
{
"label": "A",
"text": "For $\\beta = \\frac{1}{4}$ and $z_0 = \\frac{25}{7}R$, the particle reaches the origin."
},
{
"label": "B",
"text": "For $\\beta = \\frac{1}{4}$ and $z_0 = \\frac{3}{7}R$, the particle reaches the origin."
},
{
"label": "C",
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "C", "D"]} | A, C, D | {
"pages": [
14
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Physics_Q13 | 2,022 | 2 | Physics | 13 | 2 | multi_correct | false | null | A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_2$. The other slit is at the interface of this medium with another medium 1 of refractive index $n_1 (\ne n_2)$. The line joining the slits is perpendicular to the interface and the distance between the slits is $d$. The ... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "The phase difference between the two rays is independent of $d$."
},
{
"label": "B",
"text": "The two rays interfere constructively at the detector."
},
{
"label": "C",
"text": "The phase difference between the two rays de... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["A", "B"]} | A, B | {
"pages": [
14
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Physics_Q14 | 2,022 | 2 | Physics | 14 | 2 | multi_correct | false | null | In the given $P$-$V$ diagram, a monoatomic gas ($\gamma = \frac{5}{3}$) is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5$, $\ln 2 \simeq 0.7$].
[FIG_1]
Which of the following statement(s) is(are)... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "The magnitude of the total work done in the process $A \\to B \\to C$ is $144\\,\\mathrm{kJ}$."
},
{
"label": "B",
"text": "The magnitude of the work done in the process $B \\to C$ is $84\\,\\mathrm{kJ}$."
},
{
"label": "C",
... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | bonus | {"kind": "bonus", "note": "Question Dropped Marks for all"} | Question Dropped Marks for all | {
"pages": [
15
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Physics_Q15 | 2,022 | 2 | Physics | 15 | 3 | single_correct | false | null | A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$, as shown in the figure. A flat surface of $B$ also lies on the plane of the table. The center of mass of $B$ ... | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "2"
},
{
"label": "B",
"text": "5"
},
{
"label": "C",
"text": ") $\\frac{7}{2}$"
},
{
"label": "D",
"text": ") $\\frac{9}{2}$"
}
],
"list_I": null,
"list_II": null
} | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["B"]} | Answer: B | {
"pages": [
17
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: figure count 1 vs 2"
],
"notes": []
} | |
2022_P2_Physics_Q16 | 2,022 | 2 | Physics | 16 | 3 | single_correct | false | null | When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0\,\mathrm{V}$. This potential drops to $0.6\,\mathrm{V}$ if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the... | [] | {
"choices": [
{
"label": "A",
"text": "$1.72 \\times 10^{-7}\\,\\mathrm{m},\\,1.20\\,\\mathrm{eV}$"
},
{
"label": "B",
"text": "$1.72 \\times 10^{-7}\\,\\mathrm{m},\\,5.60\\,\\mathrm{eV}$"
},
{
"label": "C",
"text": "$3.78 \\times 10^{-7}\\,\\mathrm{m},\\,5.60\... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["A"]} | Answer: A | {
"pages": [
17
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": []
} | |
2022_P2_Physics_Q17 | 2,022 | 2 | Physics | 17 | 3 | single_correct | false | null | Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5\ \mathrm{mm}$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.
$$
\begin{array}{|l|l|l|}
\hline
... | [] | {
"choices": [
{
"label": "A",
"text": "$2.22 \\pm 0.02\\ \\mathrm{mm},\\ \\pi(1.23 \\pm 0.02)\\mathrm{mm}^2$"
},
{
"label": "B",
"text": "$2.22 \\pm 0.01\\ \\mathrm{mm},\\ \\pi(1.23 \\pm 0.01)\\mathrm{mm}^2$"
},
{
"label": "C",
"text": "$2.14 \\pm 0.02\\ \\math... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | bonus | {"kind": "bonus", "note": "Question Dropped Marks for All"} | Question Dropped Marks for All | {
"pages": [
18
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"answer key read by one model only (primary 'Question Dropped Marks for All', second None)"
],
"notes": []
} | |
2022_P2_Physics_Q18 | 2,022 | 2 | Physics | 18 | 3 | single_correct | false | null | Which one of the following options represents the magnetic field $\vec{B}$ at O due to the current flowing in the given wire segments lying on the $xy$ plane?
[FIG_1] | [
"FIG_1"
] | {
"choices": [
{
"label": "A",
"text": "$\\vec{B} = \\frac{-\\mu_o I}{L} \\left( \\frac{3}{2} + \\frac{1}{4\\sqrt{2}\\pi} \\right) \\hat{k}$"
},
{
"label": "B",
"text": "$\\vec{B} = -\\frac{\\mu_o I}{L} \\left( \\frac{3}{2} + \\frac{1}{2\\sqrt{2}\\pi} \\right) \\hat{k}$"
},
... | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | option | {"kind": "option", "value": ["C"]} | Answer: C | {
"pages": [
18
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"second model disagrees: text differs (100% / 90% token overlap)"
],
"notes": []
} | |
2022_P2_Chemistry_Q01 | 2,022 | 2 | Chemistry | 1 | 1 | single_digit_integer | false | null | Concentration of $\mathrm{H_2SO_4}$ and $\mathrm{Na_2SO_4}$ in a solution is $1\ \mathrm{M}$ and $1.8 \times 10^{-2}\ \mathrm{M}$, respectively. Molar solubility of $\mathrm{PbSO_4}$ in the same solution is $X \times 10^{-Y}\ \mathrm{M}$ (expressed in scientific notation). The value of $Y$ is ________.
[Given: Solubil... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 6} | 6 | {
"pages": [
19
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Chemistry_Q02 | 2,022 | 2 | Chemistry | 2 | 1 | single_digit_integer | false | null | An aqueous solution is prepared by dissolving $0.1\ \mathrm{mol}$ of an ionic salt in $1.8\ \mathrm{kg}$ of water at $35\ ^\circ\mathrm{C}$. The salt remains $90\%$ dissociated in the solution. The vapour pressure of the solution is $59.724\ \mathrm{mm}$ of Hg. Vapor pressure of water at $35\ ^\circ\mathrm{C}$ is $60.0... | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 5} | 5 | {
"pages": [
19,
20
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 20: 2022_P2_Chemistry_Q02_FIG_1.png and 2022_P2_Chemistry_Q03_FIG_1.png got the same crop (the model's boxes or figure ids are off)",
"second model disagrees: figure count 1 vs 0",
"second model disagrees: text differs (66% ... | |
2022_P2_Chemistry_Q03 | 2,022 | 2 | Chemistry | 3 | 1 | single_digit_integer | false | null | Consider the strong electrolytes $Z_mX_n$, $U_mY_p$ and $V_mX_n$. Limiting molar conductivity ($\Lambda^0$) of $U_mY_p$ and $V_mX_n$ are 250 and 440 $\mathrm{S\,cm^2\,mol^{-1}}$, respectively. The value of $(m + n + p)$ is _______.
Given:
$$
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Ion} & Z^{n+} & U^{p+} & V^{n+} & X... | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 7} | 7 | {
"pages": [
20
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 20: 2022_P2_Chemistry_Q02_FIG_1.png and 2022_P2_Chemistry_Q03_FIG_1.png got the same crop (the model's boxes or figure ids are off)",
"second model disagrees: figure count 0 vs 1",
"second model disagrees: text differs (83% ... | |
2022_P2_Chemistry_Q04 | 2,022 | 2 | Chemistry | 4 | 1 | single_digit_integer | false | null | The reaction of Xe and $O_2F_2$ gives a Xe compound $\mathbf{P}$. The number of moles of HF produced by the complete hydrolysis of 1 mol of $\mathbf{P}$ is _______. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | any_of | {"kind": "any_of", "value": [{"kind": "number", "value": 2}, {"kind": "number", "value": 4}, {"kind": "number", "value": 6}]} | 2 or 4 or 6 | {
"pages": [
20
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 20: 2022_P2_Chemistry_Q02_FIG_1.png and 2022_P2_Chemistry_Q03_FIG_1.png got the same crop (the model's boxes or figure ids are off)"
],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Chemistry_Q05 | 2,022 | 2 | Chemistry | 5 | 1 | single_digit_integer | false | null | Thermal decomposition of $\mathrm{AgNO_3}$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _______. | [] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 6} | 6 | {
"pages": [
20
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [
"page 20: 2022_P2_Chemistry_Q02_FIG_1.png and 2022_P2_Chemistry_Q03_FIG_1.png got the same crop (the model's boxes or figure ids are off)"
],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Chemistry_Q06 | 2,022 | 2 | Chemistry | 6 | 1 | single_digit_integer | false | null | The number of isomeric tetraenes (NOT containing $sp$-hybridized carbon atoms) that can be formed from the following reaction sequence is ________.
[FIG_1] | [
"FIG_1"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 2} | 2 | {
"pages": [
21
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Chemistry_Q07 | 2,022 | 2 | Chemistry | 7 | 1 | single_digit_integer | false | null | The number of $-CH_2-$ (methylene) groups in the product formed from the following reaction sequence is ________.
[FIG_2] | [
"FIG_2"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 0} | 0 | {
"pages": [
21
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Chemistry_Q08 | 2,022 | 2 | Chemistry | 8 | 1 | single_digit_integer | false | null | The total number of chiral molecules formed from one molecule of $\mathbf{P}$ on complete ozonolysis ($O_3$, $Zn/H_2O$) is ________.
[FIG_3] | [
"FIG_3"
] | null | {
"full": 3,
"zero": 0,
"negative": -1,
"partial": []
} | number | {"kind": "number", "value": 2} | 2 | {
"pages": [
21
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "auto_ok",
"reviewer": null,
"flags": [],
"notes": [
"section 1: box not readable; matches the PDF box of Mathematics"
]
} | |
2022_P2_Chemistry_Q09 | 2,022 | 2 | Chemistry | 9 | 2 | multi_correct | false | null | To check the principle of multiple proportions, a series of pure binary compounds ($P_m Q_n$) were analyzed and their composition is tabulated below. The correct option(s) is(are)
$$\begin{array}{|c|c|c|} \hline \text{Compound} & \text{Weight \% of P} & \text{Weight \% of Q} \\ \hline 1 & 50 & 50 \\ \hline 2 & 44.4 & ... | [] | {
"choices": [
{
"label": "A",
"text": "If empirical formula of compound 3 is $P_3Q_4$, then the empirical formula of compound 2 is $P_3Q_5$."
},
{
"label": "B",
"text": "If empirical formula of compound 3 is $P_3Q_2$ and atomic weight of element P is 20, then the atomic weight of ... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C"]} | B, C | {
"pages": [
22
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} | |
2022_P2_Chemistry_Q10 | 2,022 | 2 | Chemistry | 10 | 2 | multi_correct | false | null | The correct option(s) about entropy (S) is(are) [R = gas constant, F = Faraday constant, T = Temperature] | [] | {
"choices": [
{
"label": "A",
"text": "For the reaction, $\\mathrm{M}(s) + 2\\mathrm{H}^{+}(aq) \\rightarrow \\mathrm{H}_{2}(g) + \\mathrm{M}^{2+}(aq)$, if $\\frac{dE_{cell}}{dT} = \\frac{R}{F}$, then the entropy change of the reaction is R (assume that entropy and internal energy changes are tempera... | {
"full": 4,
"zero": 0,
"negative": -2,
"partial": [
{
"marks": 3,
"condition": "If all the four options are correct but ONLY three options are chosen;"
},
{
"marks": 2,
"condition": "If three or more options are correct but ONLY two options are chosen, both of which are corr... | option | {"kind": "option", "value": ["B", "C", "D"]} | B, C, D | {
"pages": [
23
],
"extractor": "qwen/qwen3-vl-235b-a22b-instruct",
"prompt": "v6"
} | {
"status": "model_verified",
"reviewer": "claude-opus-5-5",
"flags": [],
"notes": [
"section 2: values from reviewed corrections"
]
} |
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