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The dataset generation failed
Error code: DatasetGenerationError
Exception: ArrowNotImplementedError
Message: Cannot write struct type 'additional_data' with no child field to Parquet. Consider adding a dummy child field.
Traceback: Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1831, in _prepare_split_single
writer.write_table(table)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 642, in write_table
self._build_writer(inferred_schema=pa_table.schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 457, in _build_writer
self.pa_writer = self._WRITER_CLASS(self.stream, schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/pyarrow/parquet/core.py", line 1010, in __init__
self.writer = _parquet.ParquetWriter(
File "pyarrow/_parquet.pyx", line 2157, in pyarrow._parquet.ParquetWriter.__cinit__
File "pyarrow/error.pxi", line 154, in pyarrow.lib.pyarrow_internal_check_status
File "pyarrow/error.pxi", line 91, in pyarrow.lib.check_status
pyarrow.lib.ArrowNotImplementedError: Cannot write struct type 'additional_data' with no child field to Parquet. Consider adding a dummy child field.
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1847, in _prepare_split_single
num_examples, num_bytes = writer.finalize()
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 661, in finalize
self._build_writer(self.schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 457, in _build_writer
self.pa_writer = self._WRITER_CLASS(self.stream, schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/pyarrow/parquet/core.py", line 1010, in __init__
self.writer = _parquet.ParquetWriter(
File "pyarrow/_parquet.pyx", line 2157, in pyarrow._parquet.ParquetWriter.__cinit__
File "pyarrow/error.pxi", line 154, in pyarrow.lib.pyarrow_internal_check_status
File "pyarrow/error.pxi", line 91, in pyarrow.lib.check_status
pyarrow.lib.ArrowNotImplementedError: Cannot write struct type 'additional_data' with no child field to Parquet. Consider adding a dummy child field.
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1456, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1055, in convert_to_parquet
builder.download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 894, in download_and_prepare
self._download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 970, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1702, in _prepare_split
for job_id, done, content in self._prepare_split_single(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1858, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
question
string | answer
string | question_type
int64 | options
list | correct_options
list | additional_data
dict | metadata
dict |
|---|---|---|---|---|---|---|
If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha + \beta + \gamma$ is equal to:
|
\frac{46}{3}
| 1 |
[
"\\frac{47}{3}",
"\\frac{46}{3}",
"18",
"13"
] |
[
1
] |
{}
|
{}
|
Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $\int_1^x f(t)\,dt = 5x f(x) - x^5 - 9$ for all $x \geq 1$, then the value of $f(3)$ is:
|
32
| 1 |
[
"18",
"32",
"22",
"26"
] |
[
1
] |
{}
|
{}
|
The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is:
|
4
| 1 |
[
"4",
"10",
"6",
"8"
] |
[
0
] |
{}
|
{}
|
Let $A = \{1, 2, 3, \ldots, 10\}$ and $R$ be a relation on $A$ such that $R = \{(a, b) : a = 2b + 1\}$. Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), \ldots, (a_k, a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer $k$, for which such a sequence exists, is equal to:
|
5
| 1 |
[
"6",
"7",
"5",
"8"
] |
[
2
] |
{}
|
{}
|
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is:
|
\frac{4}{\sqrt{17}}
| 1 |
[
"\\frac{4}{\\sqrt{17}}",
"\\frac{\\sqrt{3}}{16}",
"\\frac{3}{\\sqrt{19}}",
"\\frac{\\sqrt{5}}{7}"
] |
[
0
] |
{}
|
{}
|
The line $L_1$ is parallel to the vector $\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k}$ and passes through the point $(7, 6, 2)$ and the line $L_2$ is parallel to the vector $\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}$ and passes through the point $(5, 3, 4)$. The shortest distance between the lines $L_1$ and $L_2$ is:
|
\frac{23}{\sqrt{38}}
| 1 |
[
"\\frac{23}{\\sqrt{38}}",
"\\frac{21}{\\sqrt{57}}",
"\\frac{23}{\\sqrt{57}}",
"\\frac{21}{\\sqrt{38}}"
] |
[
0
] |
{}
|
{}
|
Let $(a, b)$ be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second quadrant. Then the integral $I = \int_a^b \frac{9x^2}{1 + 5^x} \, dx$ is equal to:
|
24
| 1 |
[
"24",
"27",
"18",
"21"
] |
[
0
] |
{}
|
{}
|
If the system of equations \\
$2x + \lambda y + 3z = 5$ \\
$3x + 2y - z = 7$ \\
$4x + 5y + \mu z = 9$ \\
has infinitely many solutions, then $(\lambda^2 + \mu^2)$ is equal to:
|
26
| 1 |
[
"22",
"18",
"26",
"30"
] |
[
2
] |
{}
|
{}
|
If $\theta \in \left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right]$, then the number of solutions of \\
$\sqrt{3}\csc^2\theta - 2(\sqrt{3} - 1)\csc\theta - 4 = 0$, is equal to:
|
6
| 1 |
[
"6",
"8",
"10",
"7"
] |
[
0
] |
{}
|
{}
|
Given three identical bags each containing 10 balls, whose colours are as follows: \\
\textbf{Bag I:} Red = 3, Blue = 2, Green = 5 \\
\textbf{Bag II:} Red = 4, Blue = 3, Green = 3 \\
\textbf{Bag III:} Red = 5, Blue = 1, Green = 4 \\
A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is $p$ and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left( \frac{1}{p} + \frac{1}{q} \right)$ is:
|
7
| 1 |
[
"6",
"9",
"7",
"8"
] |
[
2
] |
{}
|
{}
|
If the mean and the variance of $6,\ 4,\ a,\ 8,\ b,\ 12,\ 10,\ 13$ are $9$ and $9.25$ respectively, then $a + b + ab$ is equal to:
|
103
| 1 |
[
"105",
"103",
"100",
"106"
] |
[
1
] |
{}
|
{}
|
If the domain of the function \\
$f(x) = \frac{1}{\sqrt{10 + 3x - x^2}} + \frac{1}{\sqrt{x + |x|}}$ is $(a,\ b)$, then $(1 + a)^2 + b^2$ is equal to:
|
26
| 1 |
[
"26",
"29",
"25",
"30"
] |
[
0
] |
{}
|
{}
|
$4\int_0^1 \left(\frac{1}{\sqrt{3 + x^2} + \sqrt{1 + x^2}}\right) dx - 3 \log_e(\sqrt{3})$ is equal to:
|
$2 - \sqrt{2} - \log_e(1 + \sqrt{2})$
| 1 |
[
"$2 + \\sqrt{2} + \\log_e(1 + \\sqrt{2})$",
"$2 - \\sqrt{2} - \\log_e(1 + \\sqrt{2})$",
"$2 + \\sqrt{2} - \\log_e(1 + \\sqrt{2})$",
"$2 - \\sqrt{2} + \\log_e(1 + \\sqrt{2})$"
] |
[
1
] |
{}
|
{}
|
If $\lim\limits_{x \to 0} \frac{\cos(2x) + a\cos(4x) - b}{x^4}$ is finite, then $(a + b)$ is equal to:
|
$\frac{1}{2}$
| 1 |
[
"$\\frac{1}{2}$",
"0",
"$\\frac{3}{4}$",
"$-1$"
] |
[
0
] |
{}
|
{}
|
If $\sum_{r=0}^{10} \left(\frac{10^{r+1} - 1}{10^r}\right) \cdot {}^{11}C_{r+1} = \frac{\alpha^{11} - 11^{11}}{10^{10}}$, then $\alpha$ is equal to:
|
20
| 1 |
[
"15",
"11",
"24",
"20"
] |
[
3
] |
{}
|
{}
|
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is: \\
(Figure: 3 rows of boxes, arranged in a T-shape, with a total of 8 boxes)
|
5760
| 1 |
[
"5880",
"960",
"840",
"5760"
] |
[
3
] |
{}
|
{}
|
Let the point $P$ of the focal chord $PQ$ of the parabola $y^2 = 16x$ be $(1, -4)$. If the focus of the parabola divides the chord $PQ$ in the ratio $m : n$, $\gcd(m, n) = 1$, then $m^2 + n^2$ is equal to:
|
17
| 1 |
[
"17",
"10",
"37",
"26"
] |
[
0
] |
{}
|
{}
|
Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$, $\vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k}$ and a vector $\vec{c}$ be such that $(\vec{a} - \vec{c}) \times \vec{b} = -18\hat{i} - 3\hat{j} + 12\hat{k}$ and $\vec{a} \cdot \vec{c} = 3$. If $\vec{b} \times \vec{c} = \vec{d}$, then $|\vec{a} \cdot \vec{d}|$ is equal to:
|
15
| 1 |
[
"18",
"12",
"9",
"15"
] |
[
3
] |
{}
|
{}
|
Let the area of the triangle formed by a straight line $L : x + by + c = 0$ with coordinate axes be $48$ square units. If the perpendicular drawn from the origin to the line $L$ makes an angle of $45^\circ$ with the positive x-axis, then the value of $b^2 + c^2$ is:
|
97
| 1 |
[
"90",
"93",
"97",
"83"
] |
[
2
] |
{}
|
{}
|
Let $A$ be a $3 \times 3$ real matrix such that $A^2(A - 2I) - 4(A - I) = O$, where $I$ and $O$ are the identity and null matrices, respectively. If $A^5 = \alpha A^2 + \beta A + \gamma I$, where $\alpha$, $\beta$ and $\gamma$ are real constants, then $\alpha + \beta + \gamma$ is equal to:
|
12
| 1 |
[
"12",
"20",
"76",
"4"
] |
[
0
] |
{}
|
{}
|
Let $y = y(x)$ be the solution of the differential equation
$\frac{dy}{dx} + 2y \sec^2 x = 2\sec^2 x + 3 \tan x \cdot \sec^2 x$, such that $y(0) = \frac{5}{4}$. Then $12 \left( y\left(\frac{\pi}{4}\right) - e^{-2} \right)$ is equal to:
|
21
| 0 |
[] |
[] |
{}
|
{}
|
If the sum of the first 10 terms of the series
\( \frac{4 \cdot 1}{1 + 4 \cdot 1^4} + \frac{4 \cdot 2}{1 + 4 \cdot 2^4} + \frac{4 \cdot 3}{1 + 4 \cdot 3^4} + \ldots \) is \( \frac{m}{n} \), where gcd(m, n) = 1, then m + n is equal to:
|
441
| 0 |
[] |
[] |
{}
|
{}
|
If $y = \cos\left(\frac{\pi}{3} + \cos^{-1}\frac{x}{2}\right)$, then $(x - y)^2 + 3y^2$ is equal to:
|
3
| 0 |
[] |
[] |
{}
|
{}
|
Let $A(4, -2)$, $B(1, 1)$ and $C(9, -3)$ be the vertices of a triangle $ABC$. Then the maximum area of the parallelogram $AFDE$, formed with vertices $D$, $E$, and $F$ on the sides $BC$, $CA$ and $AB$ of the triangle $ABC$ respectively, is:
|
3
| 0 |
[] |
[] |
{}
|
{}
|
If the set of all $a \in \mathbb{R} \setminus \{1\}$, for which the roots of the equation $(1 - a)x^2 + 2(a - 3)x + 9 = 0$ are positive is $(-\infty, -\alpha] \cup [\beta, \gamma)$, then $2\alpha + \beta + \gamma$ is equal to:
|
7
| 0 |
[] |
[] |
{}
|
{}
|
The largest $n\in\mathbb{N}$ such that $3^n$ divides $50!$ is:
|
22
| 1 |
[
"21",
"22",
"20",
"23"
] |
[
1
] |
{}
|
{}
|
The number of sequences of ten terms, whose terms are either $0$, $1$, or $2$, that contain exactly five $1$βs and exactly three $2$βs is equal to:
|
2520
| 1 |
[
"360",
"45",
"2520",
"1820"
] |
[
2
] |
{}
|
{}
|
Let one focus of the hyperbola $H:\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1$ be at $(\sqrt{10},0)$ and the corresponding directrix be $x=\tfrac{9}{\sqrt{10}}$. If $e$ and $l$ respectively are the eccentricity and the length of the latus rectum of $H$, then $9\,(e^2+l)$ is equal to:
|
16
| 1 |
[
"14",
"15",
"16",
"12"
] |
[
2
] |
{}
|
{}
|
Let $f:\mathbb{R}\to\mathbb{R}$ be a twice-differentiable function such that
$(\sin x\cos y)\bigl[f(2x+2y)-f(2x-2y)\bigr]=(\cos x\sin y)\bigl[f(2x+2y)+f(2x-2y)\bigr]$
for all $x,y\in\mathbb{R}$. If $f'(0)=\tfrac12$, then the value of $24\,f''\bigl(\tfrac{5\pi}{3}\bigr)$ is:
|
-3
| 1 |
[
"2",
"-3",
"3",
"-2"
] |
[
1
] |
{}
|
{}
|
Let $A=\begin{pmatrix}\alpha-1 & -1\\6 & \beta\end{pmatrix}$, $\alpha>0$, such that $\det(A)=0$ and $\alpha+\beta=1$. If $I$ denotes the $2\times2$ identity matrix, then the matrix $(I+A)^8$ is:
|
\begin{pmatrix}766 & -255\\1530 & -509\end{pmatrix}
| 1 |
[
"\\begin{pmatrix}4 & -1\\\\6 & -1\\end{pmatrix}",
"\\begin{pmatrix}257 & -64\\\\514 & -127\\end{pmatrix}",
"\\begin{pmatrix}1025 & -511\\\\2024 & -1024\\end{pmatrix}",
"\\begin{pmatrix}766 & -255\\\\1530 & -509\\end{pmatrix}"
] |
[
3
] |
{}
|
{}
|
The term independent of $x$ in the expansion of
$\displaystyle\bigl(\tfrac{x+1}{x^{2/3}+1-x^{1/3}} - \tfrac{x+1}{x-x^{1/2}}\bigr)^{10}$,
for $x>1$, is:
|
210
| 1 |
[
"210",
"150",
"240",
"120"
] |
[
0
] |
{}
|
{}
|
If $\theta \in [-2\pi, 2\pi]$, then the number of solutions of $2\sqrt{2}\cos^2\theta + (2-\sqrt{6})\cos\theta - \sqrt{3} = 0$ is equal to:
|
8
| 1 |
[
"12",
"6",
"8",
"10"
] |
[
2
] |
{}
|
{}
|
Let $a_1,a_2,a_3,\dots$ be in an A.P. such that $\displaystyle\sum_{k=1}^{12}a_{2k-1}=-\tfrac{72}{5}a_1$, $a_1\neq0$. If $\displaystyle\sum_{k=1}^n a_k=0$, then $n$ is:
|
11
| 1 |
[
"11",
"10",
"18",
"17"
] |
[
0
] |
{}
|
{}
|
If the function $f(x)=2x^3 - 9a x^2 + 12a^2 x + 1$, where $a>0$, attains its local maximum and local minimum at $p$ and $q$ respectively, such that $p^2 = q$, then $f(3)$ is equal to:
|
37
| 1 |
[
"55",
"10",
"23",
"37"
] |
[
3
] |
{}
|
{}
|
Let $z$ be a complex number such that $|z|=1$. If $\displaystyle\frac{2 + k^2 z}{k + \overline{z}} = k z$, $k\in\mathbb{R}$, then the maximum distance of $k + i k^2$ from the circle $|z - (1 + 2i)| = 1$ is:
|
\sqrt{5} + 1
| 1 |
[
"\\sqrt{5} + 1",
"2",
"3",
"\\sqrt{3} + 1"
] |
[
0
] |
{}
|
{}
|
If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$, $\hat{i}+2\hat{j}-2\hat{k}$, and $\hat{k}$ are equal, then a unit vector along $\vec{a}$ is:
|
\frac{1}{\sqrt{155}}(7\hat{i} + 9\hat{j} + 5\hat{k})
| 1 |
[
"\\frac{1}{\\sqrt{155}}(-7\\hat{i} + 9\\hat{j} + 5\\hat{k})",
"\\frac{1}{\\sqrt{155}}(-7\\hat{i} + 9\\hat{j} - 5\\hat{k})",
"\\frac{1}{\\sqrt{155}}(7\\hat{i} + 9\\hat{j} + 5\\hat{k})",
"\\frac{1}{\\sqrt{155}}(7\\hat{i} + 9\\hat{j} - 5\\hat{k})"
] |
[
2
] |
{}
|
{}
|
Let $A$ be the set of all functions $f: \mathbb{Z} \to \mathbb{Z}$ and $R$ be a relation on $A$ such that $R = \{(f,g): f(0)=g(1) \text{ and } f(1)=g(0)\}$. Then $R$ is:
|
Symmetric but neither reflective nor transitive
| 1 |
[
"Symmetric and transitive but not reflective",
"Symmetric but neither reflective nor transitive",
"Reflexive but neither symmetric nor transitive",
"Transitive but neither reflexive nor symmetric"
] |
[
1
] |
{}
|
{}
|
For \(\alpha,\beta,\gamma\in\mathbb{R}\), if \(\displaystyle\lim_{x\to0}\frac{x^2\sin(\alpha x)+(\gamma-1)e^{x^2}}{\sin(2x)-\beta x}=3\), then \(\beta+\gamma-\alpha\) is equal to:
|
7
| 1 |
[
"7",
"4",
"6",
"-1"
] |
[
0
] |
{}
|
{}
|
Let \(P_n=\alpha^n+\beta^n,\ n\in\mathbb{N}\). If \(P_{10}=123,\ P_9=76,\ P_8=47\) and \(P_1=1\), then the quadratic equation having roots \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) is:
|
x^2 + x - 1 = 0
| 1 |
[
"x^2 - x + 1 = 0",
"x^2 + x - 1 = 0",
"x^2 - x - 1 = 0",
"x^2 + x + 1 = 0"
] |
[
1
] |
{}
|
{}
|
If the system of linear equations $3x + y + \beta z = 3$, $2x + \alpha y - z = -3$, $x + 2y + z = 4$ has infinitely many solutions, then the value of $22\beta - 9\alpha$ is:
|
31
| 1 |
[
"49",
"31",
"43",
"37"
] |
[
1
] |
{}
|
{}
|
If $S$ and $S'$ are the foci of the ellipse $\frac{x^2}{18} + \frac{y^2}{9} = 1$ and $P$ is a point on the ellipse, then $\min\bigl(SP\cdot S'P\bigr) + \max\bigl(SP\cdot S'P\bigr)$ is equal to:
|
27
| 1 |
[
"3(1+\\sqrt{2})",
"3(6+\\sqrt{2})",
"9",
"27"
] |
[
3
] |
{}
|
{}
|
Let the vertices Q and R of the triangle PQR lie on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}\), QR = 5, and the coordinates of the point P be \((0,2,3)\). If the area of the triangle PQR is \(\tfrac{m}{n}\), then:
|
2m - 5\sqrt{21}\,n = 0
| 1 |
[
"m - 5\\sqrt{21}\\,n = 0",
"2m - 5\\sqrt{21}\\,n = 0",
"5m - 2\\sqrt{21}\\,n = 0",
"5m - 21\\sqrt{2}\\,n = 0"
] |
[
1
] |
{}
|
{}
|
Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 square units respectively. Then the area (in square units) of ABCD is equal to:
|
\sqrt{110}
| 1 |
[
"\\sqrt{340}",
"12",
"\\sqrt{110}",
"7\\sqrt{3}"
] |
[
2
] |
{}
|
{}
|
Let $a\in\mathbb{R}$ and $A$ be a matrix of order $3\times3$ such that $\det(A)=-4$ and
$$A+I=\begin{pmatrix}1 & a & 1\\2 & 1 & 0\\a & 1 & 2\end{pmatrix},$$
where $I$ is the $3\times3$ identity. If
$$\det\bigl((a+1)\adj((a-1)A)\bigr)=2^m3^n,\quad m,n\in\{0,1,2,\dots,20\},$$
then $m+n$ is equal to:
|
16
| 1 |
[
"14",
"17",
"15",
"16"
] |
[
3
] |
{}
|
{}
|
Let the focal chord $PQ$ of the parabola $y^2 = 4x$ make an angle of $60^\circ$ with the positive x-axis, where $P$ lies in the first quadrant. If the circle, whose one diameter is $PS$, $S$ being the focus of the parabola, touches the y-axis at the point $(0,\alpha)$, then $5\alpha^2$ is equal to:
|
15
| 1 |
[
"15",
"25",
"30",
"20"
] |
[
0
] |
{}
|
{}
|
Let βΒ·β denote the greatest integer function. If
\[
\displaystyle\int_{0}^{e^3} \Bigl\lfloor\frac{1}{e^{x-1}}\Bigr\rfloor\,dx = \alpha - \ln 2,
\]
then \(\alpha^3\) is equal to:
|
8
| 0 |
[] |
[] |
{}
|
{}
|
Let \(f:\mathbb{R}\to\mathbb{R}\) be a thriceβdifferentiable odd function satisfying \(f''(x)=f(x)\), \(f(0)=0\), and \(f'(0)=3\). Then \(9f(\ln 3)\) is equal to:
|
36
| 0 |
[] |
[] |
{}
|
{}
|
If the area of the region \(\{(x,y):\;4 - x^2 \le y \le x^2,\;y \le 4,\;x \ge 0\}\) is \(\tfrac{80\sqrt{2}}{\alpha} - \beta\), where \(\alpha,\beta\in\mathbb{N}\), then \(\alpha + \beta\) is equal to:
|
22
| 0 |
[] |
[] |
{}
|
{}
|
Three distinct numbers are selected randomly from the set {1,2,3,β¦,40}. If the probability that the selected numbers are in an increasing G.P. is m/n, gcd(m,n)=1, then m+n is equal to:
|
2477
| 0 |
[] |
[] |
{}
|
{}
|
The absolute difference between the squares of the radii of the two circles passing through the point $(-9,4)$ and touching the lines $x+y=3$ and $x-y=3$ is equal to:
|
768
| 0 |
[] |
[] |
{}
|
{}
|
Let $f: \mathbb{R}\to\mathbb{R}$ be a function defined by $$f(x)=\lvert x+2\rvert - 2\lvert x\rvert.$$ If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$, then $m+n$ is:
|
3
| 1 |
[
"5",
"3",
"2",
"4"
] |
[
1
] |
{}
|
{}
|
Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y$- and $z$-axes, respectively, is half of the angle that this line makes with the positive $x$-axis. Then the sum of all possible values of the angle $\beta$ is:
|
$\tfrac{3\pi}{4}$
| 1 |
[
"$\\tfrac{3\\pi}{4}$",
"$\\pi$",
"$\\tfrac{\\pi}{2}$",
"$\\tfrac{3\\pi}{2}$"
] |
[
0
] |
{}
|
{}
|
If the four distinct points $(4,6)$, $(-1,5)$, $(0,0)$ and $(k,3k)$ lie on a circle of radius $r$, then $10k + r^2$ is equal to:
|
35
| 1 |
[
"32",
"33",
"34",
"35"
] |
[
3
] |
{}
|
{}
|
Let the mean and variance of five observations $x_1=1$, $x_2=3$, $x_3=a$, $x_4=7$ and $x_5=b$, with $a>b$, be $5$ and $10$ respectively. Then the variance of the observations $n + x_n$ for $n=1,2,\dots,5$ is:
|
16
| 1 |
[
"17",
"16.4",
"17.4",
"16"
] |
[
3
] |
{}
|
{}
|
Let $A=\{-2,-1,0,1,2,3\}$. Define a relation $R$ on $A$ by $xRy$ if and only if $y=\max(x,1)$. If $l$ is the number of elements in $R$, and $m$ and $n$ are the minimum numbers of ordered pairs that must be added to $R$ to make it reflexive and symmetric respectively, then $l+m+n$ is equal to:
|
12
| 1 |
[
"12",
"11",
"13",
"14"
] |
[
0
] |
{}
|
{}
|
Consider the lines $x(3\lambda+1)+y(7\lambda+2)=17\lambda+5$, $\lambda$ being a parameter, all passing through a point $P$. One of these lines (say $L$) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$, then the value of $d^2$ is:
|
20
| 1 |
[
"20",
"30",
"10",
"15"
] |
[
0
] |
{}
|
{}
|
Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $(k,\tfrac{k}{2})$ from the line $3x+4y+5=0$ is:
|
15
| 1 |
[
"15",
"5\\sqrt{3}",
"15\\sqrt{5}",
"12"
] |
[
0
] |
{}
|
{}
|
Line $L_1$ of slope $2$ and line $L_2$ of slope $\tfrac12$ intersect at the origin $O$. In the first quadrant, $P_1,P_2,\dots,P_{12}$ are 12 points on $L_1$ and $Q_1,Q_2,\dots,Q_9$ are 9 points on $L_2$. Then the total number of triangles that can be formed with vertices chosen from the 22 points $O,P_1,\dots,P_{12},Q_1,\dots,Q_9$ is:
|
1134
| 1 |
[
"1080",
"1134",
"1026",
"1188"
] |
[
1
] |
{}
|
{}
|
Let $f$ be a function such that $f(x) + 3\,f\bigl(24/x\bigr) = 4x$, $x\neq0$. Then $f(3) + f(8)$ is equal to:
|
11
| 1 |
[
"11",
"10",
"12",
"13"
] |
[
0
] |
{}
|
{}
|
The integral \(\displaystyle\int_{0}^{\pi}\frac{8x}{4\cos^2x + \sin^2x}\,dx\) is equal to:
|
$2\pi^2$
| 1 |
[
"$2\\pi^2$",
"$4\\pi^2$",
"$\\pi^2$",
"$\\tfrac{3\\pi^2}{2}$"
] |
[
0
] |
{}
|
{}
|
The area of the region $\{(x,y):\lvert x-y\rvert \le y \le 4\sqrt{x}\}$ is:
|
$\tfrac{1024}{3}$
| 1 |
[
"512",
"$\\tfrac{1024}{3}$",
"$\\tfrac{512}{3}$",
"$\\tfrac{2048}{3}$"
] |
[
1
] |
{}
|
{}
|
If the probability that the random variable $X$ takes the value $x$ is given by
$$P(X=x)=k\,(x+1)3^{-x},\quad x=0,1,2,\dots,$$
where $k$ is a constant, then $P(X\ge3)$ is equal to:
|
1/9
| 1 |
[
"7/27",
"4/9",
"8/27",
"1/9"
] |
[
3
] |
{}
|
{}
|
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx} + 3(\tan^2x)\,y + 3y = \sec^2x$, with $y(0)=\tfrac{1}{3}+e^3$. Then $y\bigl(\tfrac{\pi}{4}\bigr)$ is equal to:
|
\tfrac{4}{3}
| 1 |
[
"\\tfrac{2}{3}",
"\\tfrac{4}{3}",
"\\tfrac{4}{3} + e^3",
"\\tfrac{2}{3} + e^3"
] |
[
1
] |
{}
|
{}
|
If $z_1, z_2, z_3\in\mathbb{C}$ are the vertices of an equilateral triangle whose centroid is $z_0$, then $\displaystyle\sum_{k=1}^3 (z_k - z_0)^2$ is equal to:
|
0
| 1 |
[
"0",
"1",
"i",
"-i"
] |
[
0
] |
{}
|
{}
|
The number of solutions of the equation $$(4-\sqrt{3})\sin x - 2\sqrt{3}\cos^2x = -\frac{4}{1+\sqrt{3}},\quad x\in[-2\pi,\tfrac{5\pi}{2}]$$ is equal to:
|
5
| 1 |
[
"4",
"3",
"6",
"5"
] |
[
3
] |
{}
|
{}
|
The shortest distance between the curves $$y^2 = 8x$$ and $$x^2 + y^2 + 12y + 35 = 0$$ is:
|
2\sqrt{2} - 1
| 1 |
[
"2\\sqrt{3} - 1",
"\\sqrt{2}",
"3\\sqrt{2} - 1",
"2\\sqrt{2} - 1"
] |
[
3
] |
{}
|
{}
|
Let $C$ be the circle of minimum area enclosing the ellipse $\displaystyle\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $\tfrac12$ and foci $(\pm2,0)$. Let $PQR$ be a variable triangle whose vertex $P$ lies on $C$ and whose side $QR$ of length $29$ is parallel to the major axis of the ellipse and passes through the point where the ellipse intersects the negative $y$βaxis. Then the maximum area of $\triangle PQR$ is:
|
$8(2+\sqrt{3})$
| 1 |
[
"$6(3+\\sqrt{2})$",
"$8(3+\\sqrt{2})$",
"$6(2+\\sqrt{3})$",
"$8(2+\\sqrt{3})$"
] |
[
3
] |
{}
|
{}
|
The distance of the point $(7,10,11)$ from the line $\displaystyle\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\displaystyle\frac{x-9}{2}=\frac{y-13}{-3}=\frac{z-17}{6}$ is:
|
14
| 1 |
[
"18",
"14",
"12",
"16"
] |
[
1
] |
{}
|
{}
|
The sum \(1 + \tfrac{1+3}{2!} + \tfrac{1+3+5}{3!} + \tfrac{1+3+5+7}{4!} + \dots\) up to infinitely many terms is equal to:
|
2e
| 1 |
[
"6e",
"4e",
"3e",
"2e"
] |
[
3
] |
{}
|
{}
|
If the domain of the function $f(x)=\log_7\bigl(1-\log_4(x^2-9x+18)\bigr)$ is $(\alpha,\beta)\cup(\gamma,\delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to:
|
18
| 1 |
[
"18",
"16",
"15",
"17"
] |
[
0
] |
{}
|
{}
|
Let $I$ be the identity matrix of order $3\times3$ and let
$$A=\begin{pmatrix} \lambda & 2 & 3\\4 & 5 & 6\\7 & -1 & 2\end{pmatrix}$$
with $|A|=-1$. Let $B$ be the inverse of the matrix $\mathrm{adj}(A)\,\mathrm{adj}(A^2)$. Then $|\lambda B + I|$ is equal to:
|
38
| 0 |
[] |
[] |
{}
|
{}
|
Let \((1+x+x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \dots + a_{20} x^{20}\). If \((a_1 + a_3 + a_5 + \dots + a_{19}) - 11a_2 = 121k\), then \(k\) is equal to:
|
239
| 0 |
[] |
[] |
{}
|
{}
|
If \(\displaystyle\lim_{x\to0}\bigl(\tfrac{\tan x}{x}\bigr)^{1/x^2}=p\), then \(96\log_e p\) is equal to:
|
32
| 0 |
[] |
[] |
{}
|
{}
|
Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k}$, $\vec{b}=3\hat{i}-3\hat{j}+3\hat{k}$, $\vec{c}=2\hat{i}-\hat{j}+2\hat{k}$ and $\vec{d}$ be a vector such that $\vec{b}\times\vec{d}=\vec{c}\times\vec{d}$ and $\vec{a}\cdot\vec{d}=4$. Then $|\vec{a}\times\vec{d}|^2$ is equal to:
|
128
| 0 |
[] |
[] |
{}
|
{}
|
If the equation of the hyperbola with foci $(4,2)$ and $(8,2)$ is $$3x^2 - y^2 - ax + by + \gamma = 0,$$ then $a + b + \gamma$ is equal to:
|
141
| 0 |
[] |
[] |
{}
|
{}
|
Let $A$ be a matrix of order $3\times3$ with $\lvert A\rvert=5$. If \(\bigl\lvert 2\,\mathrm{adj}\bigl(3A\,\mathrm{adj}(2A)\bigr)\bigr\rvert=2^{\alpha}3^{\beta}5^{\gamma}\), where $\alpha,\beta,\gamma\in\mathbb{N}$, then $\alpha+\beta+\gamma$ is equal to:
|
27
| 1 |
[
"25",
"26",
"27",
"28"
] |
[
2
] |
{}
|
{}
|
Let a line passing through the point $(4,1,0)$ intersect the line $L_1:\;\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $A(\alpha,\beta,\gamma)$ and the line $L_2:\;x-6 = y - z + 4$ at the point $B(a,b,c)$. Then $\det\begin{pmatrix}1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c\end{pmatrix}$ is equal to:
|
8
| 1 |
[
"8",
"16",
"12",
"6"
] |
[
0
] |
{}
|
{}
|
Let $\alpha$ and $\beta$ be the roots of $x^2 + \sqrt{3}\,x - 16 = 0$, and $\gamma$ and $\delta$ be the roots of $x^2 + 3x - 1 = 0$. If $P_n = \alpha^n + \beta^n$ and $Q_n = \gamma^n + \delta^n$, then
$$\frac{P_{25} + \sqrt{3}\,P_{24}}{2P_{23}} \;+\; \frac{Q_{25} - Q_{23}}{Q_{24}}$$
is equal to:
|
5
| 1 |
[
"3",
"4",
"5",
"7"
] |
[
2
] |
{}
|
{}
|
The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is:
|
18817
| 1 |
[
"16923",
"3763",
"33845",
"18817"
] |
[
3
] |
{}
|
{}
|
Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $0 \le x^2 + 2y \le 4$. Let $\ell$ be the number of elements in $R$ and $m$ be the minimum number of elements required to be added to $R$ to make it a reflexive relation. Then $\ell + m$ is equal to:
|
18
| 1 |
[
"19",
"20",
"17",
"18"
] |
[
3
] |
{}
|
{}
|
A line passing through the point $P(\sqrt{5},\sqrt{5})$ intersects the ellipse $\dfrac{x^2}{36}+\dfrac{y^2}{25}=1$ at points $A$ and $B$ such that $(PA)\cdot(PB)$ is maximum. Then $5\bigl(PA^2+PB^2\bigr)$ is equal to:
|
338
| 1 |
[
"218",
"377",
"290",
"338"
] |
[
3
] |
{}
|
{}
|
The sum $1 + 3 + 11 + 25 + 45 + 71 + \dots$ up to 20 terms is equal to:
|
7240
| 1 |
[
"7240",
"7130",
"6982",
"8124"
] |
[
0
] |
{}
|
{}
|
If the domain of the function \(f(x)=\log_e\bigl(\tfrac{2x-3}{5+4x}\bigr)+\sin^{-1}\bigl(\tfrac{4+3x}{2-x}\bigr)\) is $[\alpha,\beta]$, then $\alpha^2+4\beta$ is equal to:
|
4
| 1 |
[
"5",
"4",
"3",
"7"
] |
[
1
] |
{}
|
{}
|
If \(\sum_{r=1}^9 \binom{r+3}{2} C_r = \alpha\bigl(\tfrac{3}{2}\bigr)^9 - \beta\), where \(\alpha,\beta\in\mathbb{N}\), then \((\alpha+\beta)^2\) is equal to:
|
81
| 1 |
[
"27",
"9",
"81",
"18"
] |
[
2
] |
{}
|
{}
|
If \(y(x)=\begin{vmatrix} \sin x & \cos x & \sin x+\cos x+1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix},\;x\in\mathbb{R},\) then \(\frac{d^2y}{dx^2}+y\) is equal to:
|
-1
| 1 |
[
"-1",
"28",
"27",
"1"
] |
[
0
] |
{}
|
{}
|
The number of solutions of the equation $2x + 3\tan x = \pi$, $x\in[-2\pi,2\pi]\setminus\{\pm\tfrac{\pi}{2},\pm\tfrac{3\pi}{2}\}$ is:
|
5
| 1 |
[
"6",
"5",
"4",
"3"
] |
[
1
] |
{}
|
{}
|
Let $g$ be a differentiable function such that $\displaystyle\int_0^x g(t)\,dt = x - \int_x^\pi g(t)\,dt$, $x\ge0$, and let $y=y(x)$ satisfy the differential equation $\frac{dy}{dx} - y\tan x = 2(x+1)\sec x\,g(x)$ for $x\in[0,\tfrac{\pi}{2}]$. If $y(0)=0$, then $y\bigl(\tfrac{\pi}{3}\bigr)$ is equal to:
|
\frac{4\pi}{3}
| 1 |
[
"\\frac{2\\pi}{3\\sqrt{3}}",
"\\frac{4\\pi}{3}",
"\\frac{2\\pi}{3}",
"\\frac{4\\pi}{\\sqrt{3}}"
] |
[
1
] |
{}
|
{}
|
A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_1:\;2x+y+6=0$ and $L_2:\;4x+2y-p=0,\;p>0$, at the points $A$ and $B$, respectively. If $AB=\tfrac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\tfrac{AM}{BM}$ is equal to:
|
3
| 1 |
[
"5",
"4",
"2",
"3"
] |
[
3
] |
{}
|
{}
|
Let $z\in\mathbb{C}$ be such that \(\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i\). Then the sum of all possible values of $z^2$ is:
|
-19 - 2i
| 1 |
[
"19 - 2i",
"-19 - 2i",
"19 + 2i",
"-19 + 2i"
] |
[
1
] |
{}
|
{}
|
Let f(x)=\int x^3\sqrt{3 - x^2}\,dx. If 5f(\sqrt{2}) = -4, then f(1) is equal to:
|
-6\sqrt{2}/5
| 1 |
[
"-2\\sqrt{2}/5",
"-8\\sqrt{2}/5",
"-4\\sqrt{2}/5",
"-6\\sqrt{2}/5"
] |
[
3
] |
{}
|
{}
|
Let $a_1, a_2, a_3, \dots$ be a G.P. of increasing positive numbers. If $a_3 a_5 = 729$ and $a_2 + a_4 = \tfrac{111}{4}$, then $24(a_1 + a_2 + a_3)$ is equal to:
|
129
| 1 |
[
"131",
"130",
"129",
"128"
] |
[
2
] |
{}
|
{}
|
Let the domain of the function \(f(x)=\log_2\bigl(\log_4\bigl(\log_6(3+4x-x^2)\bigr)\bigr)\) be \((a,b)\). If \(\displaystyle\int_0^a \lfloor x^2\rfloor\,dx = p - \sqrt{q} - \sqrt{r}\), with \(p,q,r\in\mathbb{N}\) and \(\gcd(p,q,r)=1\), where \(\lfloor\cdot\rfloor\) is the greatest integer function, then \(p+q+r\) is equal to:
|
10
| 1 |
[
"10",
"8",
"11",
"9"
] |
[
0
] |
{}
|
{}
|
The radius of the smallest circle which touches the parabolas $y = x^2 + 2$ and $x = y^2 + 2$ is:
|
\tfrac{7\sqrt{2}}{8}
| 1 |
[
"\\tfrac{7\\sqrt{2}}{2}",
"\\tfrac{7\\sqrt{2}}{16}",
"\\tfrac{7\\sqrt{2}}{4}",
"\\tfrac{7\\sqrt{2}}{8}"
] |
[
3
] |
{}
|
{}
|
Let \(f(x)=\begin{cases}(1+ax)^{1/x},&x<0,\\1+b,&x=0,\\\displaystyle\frac{\sqrt{x+4}-2}{\sqrt[3]{x+c}-2},&x>0\end{cases}\) be continuous at \(x=0\). Then \(e^a b c\) is equal to:
|
48
| 1 |
[
"64",
"72",
"48",
"36"
] |
[
2
] |
{}
|
{}
|
Line L1 passes through the point (1, 2, 3) and is parallel to the z-axis. Line L2 passes through the point (Ξ», 5, 6) and is parallel to the y-axis. If for Ξ» = Ξ»β, Ξ»β with Ξ»β < Ξ»β the shortest distance between these two lines is 3, then the square of the distance of the point (Ξ»β, Ξ»β, 7) from the line L1 is:
|
25
| 1 |
[
"40",
"32",
"25",
"37"
] |
[
2
] |
{}
|
{}
|
All five-letter words are made using all the letters A, B, C, D and E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by Wβ. Let the probability P(Wβ) of choosing the word Wβ satisfy P(Wβ) = 2Β·P(Wβββ) for n > 1. If P(CDBEA) = 2^Ξ± / (2^Ξ² β 1), with Ξ±, Ξ² β β, then Ξ± + Ξ² is equal to:
|
183
| 0 |
[] |
[] |
{}
|
{}
|
Let the product of the focal distances of the point P(4,2β3) on the hyperbola H: \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) be 32. Let the length of the conjugate axis of H be p and the length of its latus rectum be q. Then pΒ² + qΒ² is equal to:
|
120
| 0 |
[] |
[] |
{}
|
{}
|
Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=3\hat{i}+2\hat{j}-\hat{k}$, $\vec{c}=\lambda\hat{j}+\mu\hat{k}$ and $\hat{d}$ be a unit vector such that $\vec{a}\times\vec{c}=\vec{b}\times\hat{d}$ and $\vec{c}\cdot\hat{d}=1$. If $\vec{c}$ is perpendicular to $\vec{a}$, then $\lvert3\lambda\hat{d}+\mu\vec{c}\rvert^2$ is equal to:
|
5
| 0 |
[] |
[] |
{}
|
{}
|
If the number of sevenβdigit numbers such that the sum of their digits is even is $m\cdot n\cdot10^n$, where $m,n\in\{1,2,3,\dots,9\}$, then $m+n$ is equal to:
|
14
| 0 |
[] |
[] |
{}
|
{}
|
The area of the region bounded by the curve \(y = \max\{|x|,\,|x-2|\}\), the x-axis, and the lines \(x=-2\) and \(x=4\) is equal to:
|
12
| 0 |
[] |
[] |
{}
|
{}
|
End of preview.
JEE Mains 2025 Math Evaluation Set
π§Ύ Dataset Summary
This dataset contains 475 math questions from the official JEE Mains 2025 examination, covering both January and April sessions. It is curated to benchmark mathematical reasoning models under high-stakes exam conditions.
π How to Load the Dataset
You can load the evaluation data using the datasets library from Hugging Face:
from datasets import load_dataset
# Load January session evaluation set
jan_data = load_dataset("PhysicsWallahAI/JEE-Main-2025-Math", "jan", split="test")
# Load April session evaluation set
apr_data = load_dataset("PhysicsWallahAI/JEE-Main-2025-Math", "apr", split="test")
π Dataset Structure
Each sample is stored as a JSON object with the following fields:
| Field Name | Type | Description |
|---|---|---|
question |
string |
Math problem text (can include LaTeX) |
answer |
string |
Final answer (NAT or symbolic form) |
question_type |
int |
0 = Numerical Answer Type, 1 = Multiple Choice Question |
options |
list |
List of answer choices (present only for MCQ) |
correct_options |
list |
Indices of correct options in options[] (for MCQ only) |
additional_data |
dict |
Placeholder for extended fields used during model training or evaluation. |
metadata |
dict |
Optional metadata providing contextual information about the question. |
π Dataset Statistics
| Split | Papers | Questions |
|---|---|---|
| January 2025 | 10 | 250 |
| April 2025 | 9 | 225 |
| Total | 19 | 475 |
- MCQs: ~80%
- NATs: ~20%
π₯ Source
All questions were sourced from official JEE Mains 2025 mathematics papers publicly released by NTA. Answer keys were cross-verified with NTA final answer releases.
πΌ Intended Uses
- Benchmarking Indian math LLMs
- Evaluating symbolic + numeric reasoning
- Comparing SFT/RLHF/retrieval-based models on real exams
β οΈ Limitations
- Limited to mathematics domain
π Citation
@misc{jee2025math,
title = {JEE Mains 2025 Math Evaluation Set},
author = {Physics Wallah AI Research},
year = {2025},
note = {Official JEE Mains 2025 math questions curated for evaluating educational language models},
howpublished = {\url{https://huggingface.co/datasets/PhysicsWallahAI/JEE-Main-2025-Math}},
}
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