CUET Mathematics 2026 29th May Shift 1 PYQs

Let $A = \begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 6 \\ -2 & 2 \end{bmatrix}$ and $C$ be a matrix such that $C = AB$. Then $|(BC)^{-1}|$ is equal to

If $A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & -2 \\ k & 1 & 0 \end{bmatrix}$ is non-singular matrix, then the value(s) of $k$ belongs to: [Where $R$ is the set of real numbers]

Match List-I with List-II | List-I (Differential Equation) | List-II (Degree) | |---|---| | (A) $\left(\dfrac{dy}{dx}\right)^3+\left(\dfrac{d^2y}{dx^2}\right)^2=0$ | (I) Not defined | | (B) $\left(\dfrac{d^2y}{dx^2}\right)^3+\left(\dfrac{dy}{dx}\right)^2+1=0$ | (II) 2 | | (C) $\sqrt{1+\dfrac{d^2y}{dx^2}}=\dfrac{dy}{dx}+x$ | (III) 1 | | (D) $\dfrac{d^2y}{dx^2}+e^{\frac{dy}{dx}}=0$ | (IV) 3 | Choose the correct answer from the options given below:

The area (in sq.units) bounded by the lines $y=2x+3$, $y=0$ between $x=-2$ and $x=1$ is

Let $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ and $I$ be an identity matrix of order 3. If $A^TA=I$, then $x^2+y^2+z^2$ is equal to:

Let $A=[a_{ij}]$ be a matrix of order $3 \times 4$ such that $a_{ij}=\begin{cases}2i-3j, & i \ge j \\ 3i+j, & i<j\end{cases}$ then the sum of all the elements of the first two rows of this matrix is:

If A and B are event such that $P(A)=\dfrac{1}{2}$, $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE? (A) Events A and B are independent if $p=\dfrac{1}{5}$ (B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$ (C) Events A and B are independent then $P(A \cap B)=\dfrac{1}{10}$ (D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$ Choose the correct answer from the options given below:

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

The function $f(x)=81-3x^3$ has

The general solution of the differential equation $(x+1)\dfrac{dy}{dx}=2e^{-y}-1$ is: (where C is an arbitrary constant)

The maximum value of $z=5x+3y$ subjected to the constraints $2x+3y \ge 60, 2x+y \le 40; x,y \ge 0$ is:

The general solution of the differential equation $\dfrac{dy}{dx}=2^{-y}$ is: (where $c$ is an arbitrary constant)

Rate of change of area of a circle with respect to radius (A) When r = 2 cm is $4\pi$ cm²/cm. (B) When r = 6 cm is $12\pi$ cm²/cm. (C) When r = 12 cm is $6\pi$ cm²/cm. (D) When r = 16 cm is $8\pi$ cm²/cm. Choose the correct answer from the options given below:

If $e^y(1+x)=1$, then $\dfrac{d^2y}{dx^2}$ is:

$\displaystyle\int_1^e x\log_ex\,dx$ is equal to:

$\displaystyle\int \dfrac{(x-3)e^x}{(x-1)^3}dx$ is equal to: (where C is an arbitrary constant)

If the shortest distance between the lines $\vec r=(\hat i+2\hat j+3\hat k)+\lambda(2\hat i+3\hat j+4\hat k)$ and $\vec r=(a\hat i+4\hat j+5\hat k)+\mu(4\hat i+6\hat j+8\hat k)$, $a \in N$, where $\lambda$ and $\mu$ are parameters, is $\sqrt{\dfrac{5}{29}}$, then $a$ is equal to

If $\overrightarrow{AB}=2\hat i+3\hat j-\hat k$ and $\overrightarrow{AC}=3\hat i-2\hat j+4\hat k$ are the two sides of a triangle ABC, then the length of the median through vertex A is equal to

The value of $\tan^{-1}(\sqrt3)-\sec^{-1}(-2)$ is

If $A=\begin{bmatrix} x & p & x+p \\ y & q & y+q \\ z & r & z+r \end{bmatrix}$, then $|A|$ is

If $\begin{bmatrix} x-2 & 3 & y \\ -3 & 0 & 2 \\ 4 & z-1 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $x+y+z$ is:

Let $A=\begin{bmatrix}1 & 0 \\ -1 & 7\end{bmatrix}$ and $B=\begin{bmatrix}0 & 4 \\ -1 & 7\end{bmatrix}$ then Match List-I with List-II | List-I | List-II | |---|---| | **Determinants** | **Value** | | (A) $\left\vert A^{2} \right\vert$ | (I) $28$ | | (B) $\left\vert AB^{T} \right\vert$ | (II) $7$ | | (C) $\left\vert \text{adj } A \right\vert$ | (III) $16$ | | (D) $\left\vert 2B \right\vert$ | (IV) $49$ | Choose the correct answer from the options given below:

The substitution $y=vx$ transforms the differential equation $xdy-ydx=\sqrt{x^2+y^2}dx$ into

An open box is made from a cardboard measuring 12cm x 12cm by cutting off equal squares from the corner and turning up the side. Then maximum possible volume of the box would be:

Match List-I with List-II | List-I (Function $y=$) | List-II ($\dfrac{dy}{dx}$ at $x=0$) | |---|---| | (A) $x+e^x$ | (I) 1 | | (B) $\tan^{-1}x-\dfrac{x}{2}$ | (II) $\dfrac{1}{2}$ | | (C) $\tan^{-1}x$ | (III) 0 | | (D) $x+\cos^{-1}x$ | (IV) 2 | Choose the correct answer from the options given below:

Which of the following statements are correct? (A) The angle between the vectors with direction ratios proportional to -3, 5, 4 and 4, 5, 3 is $\dfrac{\pi}{3}$ (B) The direction cosines of Y-axis is 0, 1, 0. (C) The cartesian equation of a line is $3x-6=2y+1=2z-1$, then its direction ratios are proportional to 2, 2, 3 (D) The vector equation of the line passing through the point $(2,-1,-1)$ and direction ratios 1, 2, 3 is $\vec r=(2\hat i-\hat j-\hat k)+\lambda(\hat i+2\hat j+3\hat k)$ Choose the correct answer from the options given below:

Let $R_1, R_2, R_3, R_4$ be the relations defined on the set $A=\{1,2,3\}$. then Match List-I with List-II | List-I (Relation) | List-II (Type) | |---|---| | (A) $R_1=\{(1,1),(2,2),(3,3)\}$ | (I) Only transitive | | (B) $R_2=\{(1,2),(2,3),(1,3)\}$ | (II) Equivalence relation | | (C) $R_3=\{(1,2),(2,1),(1,1),(2,2)\}$ | (III) Reflexive and symmetric but not transitive | | (D) $R_4=\{(1,1),(2,2),(3,3),(2,3),(3,2),(1,2),(2,1)\}$ | (IV) Symmetric and transitive but not reflexive | Choose the correct answer from the options given below:

$\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & a+b & c \end{vmatrix}$ is equal to:

If the function $f(x)=\begin{cases}3x-6, & x \le 5 \\ 4k, & x>5\end{cases}$ is continuous at $x=5$, then the value of $k$ is:

For the function $f(x)=|\cos x|$, which of the following statements are correct? (A) $f(x)$ is continuous for all $x \in \mathbb{R}$ (B) $f(x)$ is differentiable for all $x \in \mathbb{R}$ (C) $f(x)$ is not differentiable at $x=(2n+1)\dfrac{\pi}{2}, n \in \mathbb{Z}$ (D) $f(x)$ is not differentiable at $x=n\pi, n \in \mathbb{Z}$ Choose the correct answer from the options given below:

$\displaystyle\int_1^3 \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}}dx$ is equal to:

Consider a function $f:[-1,1] \to Y$ defined as $f(x)=\dfrac{x}{x+2}$ and $Y=range(f(x))$, then which of following statements are correct? (A) Function $f(x)$ is one-one (B) Function $f(x)$ is not one-one (C) Function $f(x)$ is onto (D) Function $f(x)$ is invertible Choose the correct answer from the options given below:

The feasible region determined by the following constraints of a LPP $x+y \ge 5$ $y \le 8$ $x \ge 0, y \ge 0$ is

Bag A contains 3 red and 5 white balls and bag B contains 4 red and 4 white balls. A bag is selected at random, and a ball is drawn. Then the probability of getting a red ball is:

If the area bounded by the parabola $x^2+my=0, m>0$ between its vertex and the latus rectum is $\dfrac{3}{2}$ square units, then the value of $m$ is

If the function $f(x)=\sin x+\cos x, 0 \le x \le 2\pi$ is increasing in the interval $(\alpha,\beta) \cup (\gamma,\delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to:

Let A and B be two independent events such that $P(A)=k$, $P(B)=2k$ and probability of occurrence of exactly one of them is $\dfrac{5}{9}$. Then the value(s) of $k$ is/are:

If E and F are two events such that $P(E \cup F)=P(E)$, then

If a unit vector $\hat a$ makes an angle $\dfrac{\pi}{3}$ with $\hat i$, $\dfrac{\pi}{4}$ with $\hat j$ and an acute angle $\theta$ with $\hat k$, then the respective value of $\theta$ and $\hat a$ are

A letter is known to have come either from LONDON or CLIFTON. On the envelope, just two consecutive letters 'ON' are visible then the probability that the letter has come from CLIFTON is:

Let $A=\begin{bmatrix}2 & 2 & 2 \\ 0 & 2 & 2 \\ 0 & 0 & 2\end{bmatrix}$, then $A^6$ is equal to:

The local maximum value of the function $f(x)=\dfrac{b^2}{a^4}(a^2x^2-x^4), a,b>0$ is equal to:

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\displaystyle\int_{-2}^{2}\cos^4x\sin^5x\,dx$ | (I) $\pi$ | | (B) $\displaystyle\int_{-1}^{1}\lvert x \rvert dx$ | (II) $\dfrac{\pi}{4}$ | | (C) $\displaystyle\int_0^{\pi/2}\cos^2x\,dx$ | (III) 0 | | (D) $\displaystyle\int_{-\pi/2}^{\pi/2}(x^3+x\cos x+\tan^5x+1)dx$ | (IV) 1 | Choose the correct answer from the options given below:

Let $A=\begin{bmatrix}a & 0 \\ b & 0\end{bmatrix}$ and $A^2=\begin{bmatrix}4 & c \\ 2 & 0\end{bmatrix}$, $a,b,c \in \mathbb{Z}$. Then the minimum value of $a+b+c$ is:

Let the corner points of the bounded feasible region of an LPP determined by a set of constraints are A(1, 5), B(3, 2) and C(2, 1). If the objective function $z=2ax+by$, $a,b>0$ has maximum values at points A and B, and z has minimum value 8 at point C, then the value of $4a+b$ is:

The area of the smaller region bounded by ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{9}=1$ and the straight line $3x+4y=12$ is

For the vectors $\vec a=\hat i-2\hat j+3\hat k$ and $\vec b=3\hat i-2\hat j+\hat k$, Which of the following are correct? (A) $|\vec a|=14$ (B) $|\vec a|=|\vec b|$ (C) $\vec a . \vec b=10$ (D) angle between $\vec a$ and $\vec b$ is $\cos^{-1}\left(\dfrac{5}{7}\right)$ Choose the correct answer from the options given below:

If the angle between the vectors $\vec a=2\lambda^2\hat i+4\lambda\hat j+\hat k$ and $\vec b=7\hat i-2\hat j+\lambda\hat k$ is obtuse, then

A line in space is uniquely determined if (A) It passes through a given point and has a given direction. (B) It passes through two given points. (C) It passes through a given point. (D) It has a given direction. Choose the correct answer from the options given below:

Match List-I with List-II | List-I (Differential equation) | List-II (Integrating factor) | |---|---| | (A) $\dfrac{xdy}{dx}-y=x^2e^x$ | (I) $x$ | | (B) $\dfrac{dy}{dx}-2y=e^x$ | (II) $x^4$ | | (C) $\dfrac{xdy}{dx}+y=1$ | (III) $\dfrac{1}{x}$ | | (D) $\dfrac{xdy}{dx}+4y=x^4$ | (IV) $e^{-2x}$ | Choose the correct answer from the options given below: