CUET Mathematics 2026 15th May Shift 1 PYQs

The number of corner points of the feasible region of an LPP determined by the constraints $x - y \geq 0$, $2y \leq x + 2, x \geq 0, y \geq 0$ is

If $f(x) = x^4 - \dfrac{2x^3}{3}$, then $f(x)$ is A. increasing in $\left(\dfrac{1}{2}, \infty\right)$ B. decreasing in $\left(\dfrac{1}{2}, \infty\right)$ C. increasing in $(-\infty, 0)$ D. decreasing in $(-\infty, 0) \cup \left(0, \dfrac{1}{2}\right)$ Choose the correct answer from the options given below:

The value of $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix}$ is:

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 30$ is

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$)

The area (in sq. units) bounded by the parabola $y^2 = x$ and line $x = 4$ in first quadrant is equal to $A$, then which of the following statements is/are TRUE ? A. $A = \dfrac{16}{3}$ B. $A = \displaystyle\int_0^4 \sqrt{x}\, dx$ C. $A = 2\displaystyle\int_0^4 \sqrt{x}\, dx$ D. $A = \displaystyle\int_0^2 y^2\, dy$ Choose the correct answer from the options given below:

The solution of the differential equation $\dfrac{dy}{dx} = 2^{x+y}$ is

If $A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then

Which of the following statements are TRUE? A. $\displaystyle\int_4^9 \dfrac{1}{\sqrt{x}}\, dx = 2$ B. $\displaystyle\int_{-4}^4 (x^{101} + x^{201} + x^{301})\, dx = 4\left(\dfrac{1}{102} + \dfrac{1}{202} + \dfrac{1}{302}\right)$ C. $\displaystyle\int_{-1}^1 x^{1012}\, dx = \dfrac{2}{1013}$ D. $\displaystyle\int (x^2 + 2x + 1)\, dx = \dfrac{(x+1)^3}{3} + c$ where $c$ is an arbitrary constant Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{dx}{(x^2+4)^{\frac{3}{2}}}$ is equal to ( where $c$ is an arbitrary constant)

The order and degree of differential equation $y = px + \sqrt{a^2p^2 + b^2}, p = \dfrac{dy}{dx}$, $a$ and $b$ are constants are:

If $c$ is an arbitrary constant, then Match the LIST-I with LIST-II | | LIST-I (Differential Equation) | | LIST-II (Solution) | |---|---|---|---| | A. | $\dfrac{dy}{dx} = 1 + x + y + xy$ | I. | $\log_e \vert y \vert = 2x + \log_e (x-1)^2 + c$ | | B. | $(x-1)\dfrac{dy}{dx} = 2xy$ | II. | $y = cx$ | | C. | $\dfrac{dy}{dx} = 1 - x + y - xy$ | III. | $\log_e \vert 1+y \vert = x + \dfrac{x^2}{2} + c$ | | D. | $x\,dy = y\,dx$ | IV. | $\log_e \vert 1+y \vert = x - \dfrac{x^2}{2} + c$ | Choose the correct answer from the options given below:

Three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls. Let X denote the number of white balls. Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $P(X=0)$ | I. $10/21$ | | B. $P(X=1)$ | II. $5/42$ | | C. $P(X=2)$ | III. $1/21$ | | D. $P(X=3)$ | IV. $5/14$ | Choose the correct answer from the options given below:

If $A = [a_{ij}]_{3\times3}$ is a square matrix, where $a_{ij} = i - j + 3$, then the value of $a_{21} + a_{31} - a_{23}$ is

The graph of a function $f: R \to R$ is shown below, where $R$ is a real numbers <img src="https://balti.afterboards.in/Yr0dUdX5uueWSIW" width="400px"/> Then which of following statements is correct?

If an open box with a square base is to be made out of a given card board of area $K^2$ square units, then the maximum volume of the box is

A company manufactured fans with three units A, B and C. Unit A, B and C produces 2%, 10% and 14% defective fans respectively. Units A, B and C produces 40%, 40% and 20% fans of total products respectively. A fan is randomly chosen that is found to be defective then the probability that the chosen fan is produced from unit C, is

Consider a function $f: \left[0, \dfrac{\pi}{2}\right] \to R$ given by $f(x) = \sin x$ and $g: \left[0, \dfrac{\pi}{2}\right] \to R$ given by $g(x) = \cos x$, where $R$ is set of real numbers then which of the following are correct? A. $f$ is one-one B. $g$ is one-one C. $f + g$ is one-one D. $f + g$ is not one-one Choose the correct answer from the options given below:

The value of $\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)$ is equal to

For $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ where $a, b, c$ are roots of equation $x^3 + px + q = 0$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $a + b + c$ | I. | $p - q$ | | B. | $\Delta$ | II. | $-q$ | | C. | $ab + bc + ca$ | III. | $0$ | | D. | $abc$ | IV. | $p$ | Choose the correct answer from the options given below:

Let P be a matrix such that $P = \begin{bmatrix} 1 & -1 \\ 0 & 3 \end{bmatrix}$, then which of the following statements are True? A. P is a symmetric matrix B. P is not a skew-symmetric matrix C. The determinant of P is non-zero D. P is an invertible matrix Choose the correct answer from the options given below:

Let A and B are two events associated to a random experiment, then Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $P(A \cap B) + P(A \cap \overline{B})$ | I. $P(A \cup B)$ | | B. $P(A \cap B) + P(\overline{A} \cap B)$ | II. $P(A) + P(B)$ | | C. $P(A \cap B) + P(\overline{A} \cap B) + P(A \cap \overline{B})$ | III. $P(A)$ | | D. $P(A \cup B) + P(A \cap B)$ | IV. $P(B)$ | Choose the correct answer from the options given below:

If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$, then R is

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ x & y & -1 \end{bmatrix}$, then $A^2$ is

If $y = \log_e \sin(e^x + 5x + 500)$ then $\dfrac{dy}{dx}$ is equal to

If C is an arbitrary constant, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\displaystyle\int \sqrt{x^2+a^2}\, dx$ | I. | $\dfrac{x}{2}\sqrt{a^2-x^2} + \dfrac{a^2}{2}\sin^{-1}\dfrac{x}{a} + C$ | | B. | $\displaystyle\int \sqrt{a^2-x^2}\, dx$ | II. | $\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$ | | C. | $\displaystyle\int \dfrac{1}{\sqrt{x^2+a^2}}\, dx$ | III. | $\sin^{-1}\dfrac{x}{a} + C$ | | D. | $\displaystyle\int \dfrac{1}{\sqrt{a^2-x^2}}\, dx$ | IV. | $\dfrac{x}{2}\sqrt{x^2+a^2} + \dfrac{a^2}{2}\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$ | Choose the correct answer from the options given below:

If $A = [a_{ij}]_{3\times3}, a_{ij} = 2i-j$ then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert A \vert$ | I. | $4$ | | B. | $\vert A - I \vert$, I is identity matrix | II. | $-7$ | | C. | minor of $a_{32}$ | III. | $0$ | | D. | cofactor $a_{32}$ | IV. | $-4$ | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I (Equation of Line) | | LIST-II (Direction Ratio of line) | |---|---|---|---| | A. | $\dfrac{2-x}{1} = \dfrac{2y+1}{1} = \dfrac{z}{1}$ | I. | $2, 1, 1$ | | B. | $x = 2y+3,\ z = y+1$ | II. | $1, -2, 2$ | | C. | $\dfrac{x-1}{1} = \dfrac{y+1}{2},\ z = 1$ | III. | $-2, 1, 2$ | | D. | $\vec{r} = \hat{i} + \hat{j} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k})$ | IV. | $1, 2, 0$ | Choose the correct answer from the options given below:

The area (in sq. units) bounded by the curves $x = y^2$ and $x = y$ in the first quadrant is:

Value of $\displaystyle\int \dfrac{dx}{\sin^{\frac{3}{5}}x \cdot \cos^{\frac{7}{5}}x}$ is (where c is an arbitrary constant)

If $f(x) = \begin{cases} \dfrac{1}{|x|}, & x \geq 1 \\ ax^2+b, & x < 1 \end{cases}$ is differentiable at $x=1$ then

If E and F are two independent events such that $P(E)=\dfrac{1}{3}, P(F)=\dfrac{3}{5}$, then which of the following is/are correct ? A. $P(E \cap F) = \dfrac{1}{5}$ B. $P\left(\dfrac{\overline{E}}{F}\right) = \dfrac{2}{3}$ C. $P\left(\dfrac{E}{\overline{F}}\right) = \dfrac{2}{3}$ D. $P\left(\dfrac{E}{F}\right) = \dfrac{2}{3}$ Choose the correct answer from the options given below:

If $p$ and $q$ are degree and order of the differential equation $\left(\dfrac{d^2y}{dx^2}\right)^3 - 2\left(\dfrac{dy}{dx}\right)^4 = 6$ respectively. Then the value of $2p+3q$ is

The corner points of a bounded feasible region are $A(15,0), B(40,0), C(4,18)$ and $D(6,12)$. If the objective function is $z = 20x + 10y$, then the difference in maximum and minimum value of $z$ is

If $\vec a, \vec b$ and $\vec c$ are vectors such that $|\vec a|=5, |\vec b|=12, |\vec c|=13$ and $\vec a+\vec b+\vec c=\vec 0$, then Match List-I with List-II | LIST-I | LIST-II | |---|---| | A. $\vec{a}.\vec{c} + \vec{b}.\vec{c}$ | I. $-25$ | | B. $\vec{a}.\vec{b} + \vec{a}.\vec{c}$ | II. $-338$ | | C. $\vec{a}.\vec{b} + \vec{b}.\vec{c}$ | III. $-169$ | | D. $2\left(\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}\right)$ | IV. $-144$ | Choose the correct answer from the options given below:

If '[.]' is greatest integer function, then value of $\displaystyle\int_0^{1.5}[x^2]\,dx$ is equal to :

The point('s) at which the function $f$ given by $f(x) = \begin{cases} \dfrac{|x|}{2x}, & x<0 \\ -\dfrac{1}{2}, & x\geq0 \end{cases}$ is continuous is (are)

If $A\begin{bmatrix} 1 & -2 \\ 1 & 4 \end{bmatrix} = \begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix}$, then matrices $A$ is

The matrix $\begin{bmatrix} 2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4 \end{bmatrix}$ is not invertible for

If $|\vec a|=2, |\vec b|=7, \vec a \times \vec b = 3\hat i + 2\hat j + 6\hat k$, then the angle between $\vec a$ and $\vec b$ is equal to

For the graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are <img src="https://balti.afterboards.in/6x4u2Pqg4sLxIlV" width="500px"/>

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x^2+xy+y^2}{x^2}$ for $x>0, y>0$ at $x=1, y=2$ is

For the vector $\vec a = \dfrac{1}{3}(2\hat i - 2\hat j + \hat k)$, which of the following statements is/are TRUE ? A. vector $\vec a$ is a unit vector B. vector $\vec a$ is making an angle $\dfrac{\pi}{3}$ with vector $2\hat i - 4\hat j + 3\hat k$ C. vector $\vec a$ is parallel to vector $-\hat i + \hat j - \dfrac{1}{2}\hat k$ D. vector $\vec a$ is perpendicular to vector $3\hat i + 2\hat j - 2\hat k$ Choose the correct answer from the options given below:

The probability of simultaneous occurrence of at least one of two events E and F is $p$. If the probability that exactly one of E, F occurs is $q$, then $P(\overline{E}) + P(\overline{F})$ is equal to

For the function $f(x) = \dfrac{3}{2}x^4 - 4x^3 - 45x^2 + 49$. Which of the following statements is/are TRUE ? A. $f(x)$ is increasing in $(-\infty, -3)$ B. $f(x)$ is increasing in $(-3, 0) \cup (5, \infty)$ C. $f(x)$ is decreasing in $(-\infty, -3) \cup (0, 5)$ D. $f(x)$ is decreasing in $(-\infty, -3) \cup (5, \infty)$ Choose the correct answer from the options given below:

Water is running into a conical vessel, 18cm deep and 6cm in radius, at the rate of 0.1 $cm^3$/sec. If the water is 4cm deep, then the water level rising at the rate

If $\vec a = 4\hat i+5\hat j-\hat k, \vec b=\hat i-4\hat j+5\hat k$ and $\vec c=3\hat i+\hat j-\hat k$. If a vector $\vec d$ is perpendicular to both $\vec a$ and $\vec b$ and $\vec c.\vec d=21$, then unit vector along $\vec d$ is

The area of the region bounded by the curves $y = 1+|x-1|, x=-1, x=2, y=0$ is

The shortest distance between the lines $\dfrac{x+1}{7}=\dfrac{-y-1}{6}=\dfrac{z+1}{1}$ and $\dfrac{x-3}{1}=\dfrac{-y+5}{2}=\dfrac{z-7}{1}$ is

If the lines $\dfrac{x+1}{3}=\dfrac{y+3}{5}=\dfrac{z+\lambda}{7}$ and $\dfrac{x-2}{1}=\dfrac{y-4}{3}=\dfrac{z-6}{5}$ are intersecting , then the value of '$\lambda$' is