CUET Mathematics 2026 29th May Shift 2 PYQs

If the matrix $A = \begin{bmatrix} -2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is given, then which of the following statements is/are TRUE? A. A is a square matrix B. A is a symmetric matrix C. A is a scalar matrix D. A is a identity matrix Choose the correct answer from the options given below:

If $y = \log(\log x)$, then $\frac{d^2y}{dx^2}$ is equal to: (Consider $\log_e x = \log x$)

The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0$ is

The corner points of the bounded feasible region of an LPP are (0,0), (6,0), (4,3) and (0,6). Let $Z = ax + by$, where $a, b > 0$. Condition on $a$ and $b$ so that the maximum of $Z$ occurs at both (4, 3) and (0, 6) is

For the function $f(x) = (x-1)^3(x-2)^2$ Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | $f(x) \geq 0$ | I. $x \in (-\infty,1) \cup \left(1,\frac{8}{5}\right) \cup (2,\infty)$ | | B. | $f(x) < 0$ | II. $x \geq 1$ | | C. | $f(x)$ is increasing if | III. $x < 1$ | | D. | $f(x)$ is decreasing if | IV. $x \in \left(\frac{8}{5},2\right)$ | Choose the correct answer from the options given below:

For the function $f(x) = |x-1| + |x-2| + |x-3|$ Match the LIST-I with LIST-II | | LIST-I<br>Function $f(x) =$ | | LIST-II<br>For Interval | |---|---|---|---| | A. | $-3x + 6$ | I. | $x \geq 3$ | | B. | $-x + 4$ | II. | $x < 1$ | | C. | $x$ | III. | $1 \leq x < 2$ | | D. | $3x - 6$ | IV. | $2 \leq x < 3$ | Choose the correct answer from the options given below:

The solution of the differential equation $\frac{dy}{dx} + y = 1, y(1) = 0$ is

If $P(B) = \frac{2}{5}, P(A \cup B) = \frac{3}{5}, P(A \cap B) = \frac{3}{10}$ then $P(A/B) + 2P(B/A)$ equals

If $A+B = \begin{bmatrix}7 & 0\\2 & 5\end{bmatrix}$ and $A-B = \begin{bmatrix}3 & 0\\0 & 3\end{bmatrix}$, then

If A is a diagonal matrix of order 3 with diagonal elements as 2, 3, 4, then |adj A| is

The general solution of the differential equation $x\,dx = (x^2+1)\,dy$ is (where C is an arbitrary constant)

$\int_1^2 \frac{dx}{(x+1)(x+2)} =$

If $\int \frac{1}{\sqrt{(x-1)(x-2)}}\,dx = \log\left|(x-m)+\sqrt{ax^2+bx+n}\right| + C$ where C is an arbitrary constant and $m,n,a$ and $b$ are constant, then $2m+n+a+b$ is equal to:

If area of the triangle formed by A(1, 3), B(0, 0) and C(k, 0) is 3 sq. units, then which of the following is/are TRUE? A. k = 2 B. k = -2 C. k = 3 D. k = -3 Choose the correct answer from the options given below:

Area bounded by the curves $y=x^3$, $y=x+6$ and $x=0$ is

The perpendicular distance of point (1, 1, 3) on the line $\frac{x}{2}=\frac{y+1}{3}=\frac{-z-3}{-5}$ is

If A and B are square matrices of order 3×3 such that |A|=7 and |B|=6, then |B adj A| =

If $x=a(1-\cos\theta), y=a(\theta+\sin\theta)$ then $\frac{d^2y}{dx^2}$ is equal to

Let S be the set of all real numbers and let R be a relation on S, defined by $aRb \Leftrightarrow |a-b| \leq 1$. Then, R is

If $\lambda$ and $\mu$ are parameters, then Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | $\vec{r}=2\hat{i}+\hat{j}-3\hat{k}+\lambda(\hat{i}-\hat{j}+2\hat{k})$ parallel to the line | I. $\vec{r}=(\hat{j}+\hat{k})+\mu(-2\hat{i}+\hat{j}-2\hat{k})$ | | B. | $\vec{r}=\hat{i}+\hat{j}+\lambda(\hat{i}+\hat{j}-2\hat{k})$ perpendicular to the line | II. $\vec{r}=(2\hat{i}+\hat{k})+\mu(-2\hat{i}+\hat{j})$ | | C. | $\frac{x}{-2}=\frac{y-1}{1}=\frac{z-1}{-2}$ in vector form | III. $\vec{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu(2\hat{i}-2\hat{j}+4\hat{k})$ | | D. | $\frac{2-x}{2}=y, z=1$ in vector form | IV. $\frac{x-1}{2}=\frac{y+1}{4}=\frac{z}{3}$ | Choose the correct answer from the options given below:

The value of $\int_0^{\pi/2} \frac{\cos x}{\cos\frac{x}{2}+\sin\frac{x}{2}}\,dx$ is

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is

If $\begin{vmatrix}2a & 2a & 3b+c\\3b & 2a+c & 3b\\2a+3b & c & c\end{vmatrix} = 48$, then abc is equal to

Match the LIST-I with LIST-II (Consider N and R as set of natural numbers and set of real numbers respectively) | | LIST-I<br>Function | | LIST-II | |---|---|---|---| | A. | $f: N \to N, f(x) = x^2$ is | I. | Neither one-one nor onto | | B. | $f: R \to R, f(x) = 3 - 2x$ is | II. | one-one but not onto | | C. | $f: R \to R, f(x) = x^2$ is | III. | onto but not one-one | | D. | $f: \{-1,1\} \to \{1\}, f(x) = \vert x \vert$ is | IV. | one-one and onto | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I<br>Differential equations | | LIST-II<br>Integrating factor | |---|---|---|---| | A. | $(x+y)\dfrac{dy}{dx} = 1$ | I. | $e^{-x}$ | | B. | $x\dfrac{dy}{dx} - y = x^2$ | II. | $x$ | | C. | $\dfrac{dy}{dx} - y = \sin x$ | III. | $\dfrac{1}{x}$ | | D. | $x\dfrac{dy}{dx} + y = \tan x$ | IV. | $e^{-y}$ | Choose the correct answer from the options given below:

The number of feasible solutions of the linear programming problem as Maximum $z=15x+30y$ subject to the constraints $3x+y \leq 12$ $x+2y \leq 10$ $x \geq 0, y \geq 0$ is

Which of the following statements is/are TRUE ? A. The sine of the angle between the vectors $\vec{a}=\hat{i}+3\hat{j}-2\hat{k}$ and $\vec{b}=-2\hat{i}+2\hat{j}-4\hat{k}$ is $\frac{2}{\sqrt{7}}$ B. The area of the parallelogram PQRS is $\frac{1}{2}|\vec{PR}\times\vec{QS}|$ C. If $\vec{a}=5\hat{i}-4\hat{j}+3\hat{k}$ then $|\vec{a}\times\hat{i}|^2+|\vec{a}\times\hat{j}|^2+|\vec{a}\times\hat{k}|^2=100$ D. Vectors perpendicular to the vectors $\vec{a}=2\hat{i}-\hat{j}+2\hat{k}$ and $\vec{b}=-\hat{i}+4\hat{j}-3\hat{k}$ are given by $\lambda(-\hat{i}+2\hat{j}+2\hat{k})$ where $\lambda$ is a scalar. Choose the correct answer from the options given below:

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$, then x equals:

If $\int \frac{\sin^6 x}{\cos^{10} x}\,dx = -2a\tan^9 x + b\tan^7 x + c$, (where c is an arbitrary constant), then which one of the following is TRUE?

If A, B and C are three independent events such that P(A)=P(B)=P(C)=x, then P(at least two of A, B, C occur) =

For the differential equation $\frac{d}{dx}\left(\frac{d^3y}{dx^3}\right)+\left(\frac{dy}{dx}\right)^3+y+x=7$, which of the following statements are True? A. Order of differential equation is 4 B. Number of arbitrary constants in the particular solution of differential equation are 4 C. Number of arbitrary constants in the general solution of the differential equation are 4 D. Degree of differential equation is 3 Choose the correct answer from the options given below:

If $\vec{a}=2\hat{i}+\hat{j}$, and $\vec{b}=\hat{j}-\hat{k}$, then which of the following statements is/are TRUE ? A. $|\vec{a}+\vec{b}|=3$ B. Unit vector along $\vec{a}+\vec{b}$ is $2\hat{i}+2\hat{j}-\hat{k}$ C. Direction ratio of $\vec{a}+\vec{b}$ are 2, 2, -1 D. unit vector perpendicular to $\vec{a}$ and $\vec{b}$ is $-\frac{1}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$ Choose the correct answer from the options given below:

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE: A. $P(B/A)=P(A).P(B)$ B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$ C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$ D. $P(B/A).P(A/B)=2$ Choose the correct answer from the options given below:

Let $A=[a_{ij}]_{3\times3}$, where $a_{ij}=i-j$, then which of the following statements is/are TRUE ? A. A is diagonal matrix B. A is square matrix C. A is symmetric matrix D. A is skew symmetric matrix Choose the correct answer from the options given below:

$\int \frac{1}{x(x^6+1)}\,dx =$ (consider $\log_e x = \log x$)

The function $f(x)=\begin{cases}\frac{e^{3x}-e^{-5x}}{x}, & x\neq 0\\ \lambda, & x=0\end{cases}$ is continuous at x=0 for the value of '$\lambda$' as:

The value of $\lambda$ for which the vectors $3\hat{i}+6\hat{j}-\hat{k}$ and $-2\hat{i}+4\hat{j}-\lambda\hat{k}$ are perpendicular is

P is a point on the line segment joining the points (3, 2, -1) and (6, 2, -2) internally. If x coordinate of P is 5, then its z-coordinate is

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is $\tan^{-1}\left(\frac{2}{3}\right)$. Water is poured into it at a constant rate 6 cubic metre per hour. The rate at which the level of the water is rising at the instant when the depth of water in the tank is 5 meter is

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | If $\cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi$ then $\alpha(2\beta+\gamma) + \beta(2\gamma+\alpha) + \gamma(2\alpha+\beta)$ equals | I. | $1$ | | B. | The value of $\tan^2(\sec^{-1}4) + \cot^2(\text{cosec}^{-1}5)$ is | II. | $9$ | | C. | If $\sin\left(\cos^{-1}\dfrac{2}{5} + \sin^{-1}x\right) = 1$ then $10x$ equals | III. | $4$ | | D. | The length of the interval of domain of $\sin^{-1}2x$ is | IV. | $39$ | Choose the correct answer from the options given below:

A function $f(x)=\sin x(1+\cos x), x \in [0,\pi]$ has a local maxima at $x=$

The area of the region bounded by the curve $y=\sqrt{9-x^2}$ and x-axis is

The area of the region bounded by the curve $x^2=4y$, the line $x=4y-2$ and x-axis is

For linear programming problem maximize $z=2x+3y$ Subject to the constraints $x+y \leq 4$ $x \leq 2$ $x \geq 0, y \geq 0$ Maximum value of z is

An insurance company insured 200 scooter drivers, 400 car drivers and 600 Truck drivers. The probability of an accident involving scooter driver, car driver and truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured person meets an accident, then the probability that he is a truck driver is:-

Function $f(x)=\sin3x, x \in \left[0,\frac{\pi}{2}\right]$ is decreasing in the interval

A function f(x) is defined by $f(x)=\begin{cases}x^2+\alpha x+\beta: & 0\leq x<2\\3x+2 : & 2\leq x\leq4\\2\alpha x+5\beta :& 4<x\leq8\end{cases}$. If function f(x) is continuous on [0, 8], then value of $2\alpha+3\beta$ is

If A is a skew symmetric matrix, then $A^2$ is a

Let $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}|=2, |\vec{b}|=1, |\vec{c}|=3$. If projection of $\vec{a}$ on $\vec{b}$ is equal to projection of $\vec{c}$ on $\vec{b}$ and $\vec{a}\perp\vec{c}$, then value of $|2\vec{a}+3\vec{b}-2\vec{c}|$ is

A box contains 3 red and 2 black balls and another box contains 2 red and 4 black balls. One box chosen at random. From the selected box one ball is drawn. The probability of getting a red ball is