CUET Mathematics 2026 PYQs29 May Shift 2. Free, no login required.

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

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$]

The interval in which the function $f(x)=x^3-12x^2+36x+20$ is increasing, is

The determinant of which of the following matrices is a perfect square ? A. $\begin{bmatrix}5&29\\-1&6\end{bmatrix}$ B. $\begin{bmatrix}5&26\\1&6\end{bmatrix}$ C. $\begin{bmatrix}10&3\\17&10\end{bmatrix}$ D. $\begin{bmatrix}8&5\\-3&-8\end{bmatrix}$ Choose the correct answer from the options given below:

The solution to the inequality $-12 < \frac{2x-1}{3} < 12$ is

With reference to the matrix $A=\begin{bmatrix}5&0&0\\0&5&0\\0&0&-5\end{bmatrix}$, which of the following are TRUE ? A. |A|=125 B. A is a scalar matrix. C. A is a diagonal matrix. D. |A|=-125 Choose the correct answer from the options given below:

Ten cards are numbered from 1 to 10. A and B are playing a game by drawing a card, alternately, with replacement, till one gets a prime number then the probability of B's winning if A started the game is

For the function $f(x)=2x^3-9x^2+12x-5, x \in [0,3]$, which of the following statements are correct ? A. The point of absolute maxima is x=3. B. The absolute minimum value is -1. C. The critical points are x=1 and x=2. D. The absolute maximum value is 3. Choose the correct answer from the options given below:

For the given five values, 17, 25, 21, 35, 43, the three-year moving averages are:

The area of the region bounded by the curve $y=|x|$, x-axis and the lines $x=-5$ and $x=5$ is

Which of the following shaded regions represents the solution to the inequation $|x|+|y| \leq 1$ ?

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $\begin{vmatrix} x+2 & 3 \\ x+5 & 4 \end{vmatrix} = 3$ | I. $x = 10$ | | B. $\begin{vmatrix} x+2 & x+5 \\ 3 & 4 \end{vmatrix} = 13$ | II. $x = 60$ | | C. $\begin{vmatrix} x+4 & x-4 \\ 8 & 7 \end{vmatrix} = 0$ | III. $x = 0$ | | D. $\begin{vmatrix} x+4 & 8 \\ x-4 & 7 \end{vmatrix} = 60$ | IV. $x = 20$ | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | The measurable characteristic of a population is called | I. Statistic | | B. | The measurable characteristic of a sample is called | II. Confidence level | | C. | The percentage of all possible samples that can be expected to include the true population parameter is called | III. Confidence interval | | D. | A range that could be expected to contain the population parameter of interest is | IV. Parameter | Choose the correct answer from the options given below:

The effective rate that is equivalent to a nominal rate of 8 % compounded continuously is :

The marginal cost (MC) of producing x units of an item in a factory is given by $MC=0.006x^2-0.001x+4$. If the fixed cost is ₹1000, then the cost of producing 200 units will be :

The bounded feasible region of an LPP is shown in the diagram given below. The objective function $z=3x+10y$ attains optimum values at : <img src="https://balti.afterboards.in/gJcms7Bb2ql0aVM" width="400px"/> A. Point (0,0) B. Point (0,4) C. Point (6,3) D. Point (5,6) Choose the correct answer from the options given below:

A person invested ₹y in a mutual fund and the value of the investment at the time of redemption was ₹x. If he invested the amount for 3 years and the compound annual growth rate of his investment is 10 %, then the value of $\frac{y}{x}$ is:

Which of the following is true about the sinking fund ?

If $77 \equiv x(mod\ 4)$, then the least positive value of $x$ is :

In reference to the differential equation : $y''+y=(e)^{y'}$, which of the following statements are correct ? A. The order of the differential equation is 1. B. The degree of the differential equation is 1. C. The order of the differential equation is 2. D. The degree of the differential equation is not defined. Choose the correct answer from the options given below:

Ms Rajni takes a loan of ₹25,00,000 at an interest of 10% per annum for a period of 20 years. Her EMI using a flat rate method is:

If matrix $A=\begin{bmatrix}0&3a&-4\\2&1&2\\2b&2&-1\end{bmatrix}$ is a symmetric matrix, then the values of $a$ and $b$ are

Pure milk costs ₹80 per litre. A milkman adds water to 24 litres of pure milk and sells the mixture at ₹60 per litre without extra gain or loss. How many litres of water does he add?

$\int \frac{dx}{x(x^{10}+1)}$ is equal to

A simple random sample consists of five observations: 2, 4, 6, 7,11, then which of the following are true ? A. Sample mean = 7.5 B. Sample mean = 6 C. Sample standard deviation = $\sqrt{11}$ D. Sample standard deviation = $\sqrt{11.5}$ Choose the correct answer from the options given below:

In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

The probability distribution of a discrete random variable is given below : | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | 1/5 | m | 2/5 | 2m | 3m | Which of the following are correct? A. $P(2)=\frac{1}{15}$ B. $P(4)=\frac{2}{15}$ C. $P(X<2)=\frac{1}{5}$ D. $P(X\geq4)=\frac{1}{5}$ Choose the correct answer from the options given below:

Mr. B.M. Wadhwa purchased a car costing ₹20 lakh. It has a useful life of 15 years. The depreciation follows the straight line trend. If the annual depreciation is ₹1,20,000, what is the scrap value of the car ?

Every gram of wheat provides 0.15 g of proteins and 0.24 g of carbo hydrates. The corresponding values of proteins and carbo hydrate of rice are 0.05g and 0.48g respectively. Wheat costs ₹40 per kg and rice costs ₹60 per kg. The minimum daily requirements of proteins and carbohydrates for an average child are 50g and 200 g respectively. Which of the following options describes the LPP to minimize the total cost of wheat and rice that provide minimum daily requirements of proteins and carbohydrates ?

Consider the following hypothesis test: $H_0: \mu \leq 35$ $H_a: \mu > 35$ A sample of 25 provided a sample mean of 34.65. The population standard deviation is 4. The value of the t-test statistic is

A boat goes 24 km upstream in 4 hours and 32 km downstream in 4 hours. The speed of the boat in still water is:

Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | Rise and fall of the share market | I. Seasonal Component | | B. | Continuous increase in the population of India | II. Cyclical Component | | C. | The rise in prices of woolen clothes in winter | III. Irregular Component | | D. | Increase in prices of goods due to strikes of transporters | IV. Trend Component | Choose the correct answer from the options given below:

At what rate of interest will the present value of a perpetuity of ₹600 payable at the end of each quarter be ₹40,000 ?

Given that $[a_{ij}]$ is a square matrix of order n. Match the LIST-I with LIST-II | LIST-I | | LIST-II | |---|---|---| | A. | $A=[a_{ij}]; a_{ij}=\begin{cases}1, & \forall i=j\\0, & \forall i\neq j\end{cases}$ | I. Identity Matrix | | B. | $B=[a_{ij}]; a_{ij}=\begin{cases}2i-3j, & \forall i=j\\0, & \forall i\neq j\end{cases}$ | II. Diagonal Matrix | | C. | $C=[a_{ij}]; a_{ij}=\begin{cases}k, & \forall i=j\\0, & \forall i\neq j\end{cases}$ | III. Scalar Matrix | | D. | $D=[a_{ij}]; a_{ij}=\begin{cases}2i-3j, & \forall i\leq j\\0, & \forall i>j\end{cases}$ | IV. Upper Triangular Matrix | Choose the correct answer from the options given below:

One pipe can fill a tank five times as fast as another pipe. If, together, two pipes can fill the tank in 30 minutes, how much time does the faster pipe alone take to fill the tank ?

If $x=4t^3$ and $y=6t^2$ then $\frac{d^2y}{dx^2}$ at $t=1$ is