CUET Mathematics 2026 PYQs21 May Shift 1. Free, no login required.

Solution of differential equation $\frac{dy}{dx} = \frac{1+x^2}{1+y^2}$ is

If $y = \log_x(x^2+1).\log_{(x^2+1)} x$, then $\frac{dy}{dx}$ is

The points of local maxima and local minima of the $f(x) = x^3 - 6x^2 + 9x + 27$ are

For a matrix $A = \begin{bmatrix} 1 & 4 & 5 \\ 3 & 2 & 6 \\ 0 & 1 & 0 \end{bmatrix}$, where $I$ is identity matrix of order 3 Match List-I with List-II | List-I | List-II | |---|---| | (A) $\left\vert A \right\vert$ | (I) $72$ | | (B) $(\text{adj}A)A$ | (II) $18$ | | (C) $\left\vert 2A \right\vert$ | (III) $9$ | | (D) $2\left\vert A \right\vert$ | (IV) $9I$ | Choose the correct answer from the options given below:

For any 3 ×3 matrix $A$, if $A(adj\,A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then $2|A|$ is equal to

The function $f(x) = 4x + \frac{1}{x}$ is (A). Increasing in the interval $\left(-\infty, -\frac{1}{2}\right)$ (B). Increasing in the interval $\left(-\frac{1}{2}, 0\right)$ (C). Decreasing in the interval $\left(0, \frac{1}{2}\right)$ (D). Decreasing in the interval $\left(\frac{1}{2}, \infty\right)$ Choose the correct answer from the options given below:

The feasible region for a LPP is shown in the figure. The minimum value of Z = 2x - 3y is <img src="https://balti.afterboards.in/DRY9mOZGxffoEdj" width="400px"/>

If $A = \begin{bmatrix} 4 & -1 & \lambda \\ 2 & 0 & 6 \\ 1 & -2 & 7 \end{bmatrix}$, then $\frac{1}{2}A^{-1}$ exist if

Match List-I with List-II | List-I (Differential Equation) | List-II (Degree) | |---|---| | (A) $2(y'')^2 + 3y = 6$ | (I) 4 | | (B) $2y + 5(y')^4 = 7$ | (II) 1 | | (C) $\log x + (y'')^3 = e^x$ | (III) 2 | | (D) $\sqrt{1-2y'} = 5(y'')^{\frac{1}{4}}$ | (IV) 3 | Choose the correct answer from the options given below:

The value of $\int_{-2}^{3} |x-1|\, dx$ is

If $P(A \cap B) = \frac{1}{2}$, $P(A' \cap B') = \frac{1}{3}$, $P(A) = p$ and $P(B) = 2p$, then value of $p$ is

If $[1 \quad 2 \quad 1] \begin{bmatrix} -1 & 0 & 1 \\ 1 & 2 & -1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} 2x \\ x \\ -7 \end{bmatrix} = [0]$, then the value of $x$ is

The area in the first quadrant bounded by $y = 9x^2$, $x = 0$, $y = 1$ and $y = 4$ is :

If $A = [a_{ij}]_{3 \times 3}$ and $a_{ij} = i - j$, then which of the following statements are TRUE? (A). $A$ is scalar matrix (B). $A$ is skew symmetric matrix (C). $|A| = 0$ (D). $a_{21} + a_{12} = 0$ Choose the correct answer from the options given below:

$\int e^x \left(\frac{x-1}{2x^2}\right) dx$ is equal to ( where $C$ is an arbitrary constant)

A man is known to speak the truth 3 out of 4 times. He throw a die and reports that it is five then the probability that it is actually five is

$\int \frac{dx}{\sin^2 x \cos^2 x} =$

If $x = 3\sin\theta - \sin 3\theta$, $y = 3\cos\theta - \cos 3\theta$, then $\frac{d^2y}{dx^2}$ at $\theta = \frac{\pi}{3}$ is

Given a function $f(x) = ax + \frac{b}{x}$; $a > 0, b > 0$, then Match List-I with List-II | List-I | List-II | |---|---| | (A) $f(x)$ has local maxima at $x$ is equal to | (I) $\sqrt{\frac{b}{a}}$ | | (B) $f(x)$ has local minima at $x$ is equal to | (II) $2\sqrt{ab}$ | | (C) Local Maxima of $f(x)$ | (III) $-\sqrt{\frac{b}{a}}$ | | (D) Local Minima of $f(x)$ | (IV) $-2\sqrt{ab}$ | Choose the correct answer from the options given below:

Value of $\int (e^{2\log x} + e^{x\log 2} + e^{2\log 2})dx$ is

If the lines $\frac{x-1}{2} = \frac{y+1}{\lambda-3} = \frac{z-2}{2}$ and $x = 0, \frac{2y-4}{-2} = \frac{z+1}{2-\lambda}$ are perpendicular, then value of $\lambda$ is

Value of $\int_{1}^{4} \frac{\log_e x}{x^2}\, dx$ is

If $f(x) = \begin{cases} \frac{x^2+3x-10}{x-2}, & x \neq 2 \\ 2k+1, & x = 2 \end{cases}$ is continuous at $x = 2$, then the value of $k$ is

Let A and B be independent events such that $P(A) = \frac{3}{7}$ and $P(B) = \frac{1}{7}$, Then Match List-I with List-II | List-I | List-II | |---|---| | (A) P(A and B) | (I) $\frac{24}{49}$ | | (B) P(A or B) | (II) $\frac{18}{49}$ | | (C) P(A and not B) | (III) $\frac{25}{49}$ | | (D) P(neither A nor B) | (IV) $\frac{3}{49}$ | Choose the correct answer from the options given below:

A problem is given to 3 students A,B and C, whose probabilities of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, then (A). P(Problem solved) = $\frac{3}{4}$ (B). P(Problem not solved) = $\frac{1}{4}$ (C). P(Problem solved by exactly one student) = $\frac{7}{24}$ (D). P(Problem solved by at least 2 students) = $\frac{17}{24}$ Choose the correct answer from the options given below:

The maximum value of $z = 3x + 4y$ subject to the constraints $x + y \geq 2, 2x + 3y \leq 6, x \geq 0, y \geq 0$ is

The number of corner points of the feasible region determined by the constraints $2x - y \geq 0, x - 3y + 3 \geq 0, x \geq 0, y \geq 0$ is

A pair of dice is thrown. If the two numbers appearing on them are different then the probability that the sum of the number is 6, is.

If $\begin{vmatrix} 2+x & y & z \\ x & 2+y & z \\ x & y & 2+z \end{vmatrix} = 0$, then the value of $x+y+z$ is

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$. The value of $\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}$ is

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$; $y(0)=5$ is

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 2 & 3 & -1 \end{bmatrix}$, then $A^2$ is equal to

If $\vec{a} = 2\hat{i} - 2\hat{j} + \hat{k}$, then which of the following statements are TRUE? (A) unit vector along $\vec{a}$ is $\frac{1}{3}(2\hat{i}+2\hat{j}-\hat{k})$ (B) $|3\vec{a}| = 9$ (C) $\vec{a}$ is perpendicular to $2\hat{i}+3\hat{j}+2\hat{k}$ (D) Direction Ratios of $\vec{a}$ are 2,-2,1 Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$, then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

The number of symmetric relations on set $A = \{1,2,3\}$ is

Let $f(x) = |x-1| + |x-2|, x \in R$. Then which of the following statements is/are TRUE? (A) $f$ is continuous everywhere. (B) $f$ is continuous everywhere except at $x = 1$ and $x = 2$ (C) $f$ is not differentiable at $x = 1$ and $x = 2$ (D) $f$ is differentiable at $x = 1$ and $x = 2$ Choose the correct answer from the options given below:

Match List-I with List-II | List-I (Straight Lines) | List-II (Direction Ratios) | |---|---| | (A) $\vec{r} = (\hat{i}+\hat{j}) + \lambda(2\hat{i}-\hat{j}+3\hat{k})$ | (I) 2,1,-3 | | (B) $\frac{x}{2} = \frac{1-y}{-1} = \frac{z+1}{3}$ | (II) -2,1,3 | | (C) $\frac{1-2x}{4} = \frac{y+1}{1} = \frac{2z+3}{6}$ | (III) 2,-1,3 | | (D) $\vec{r} = (2\hat{i}-\hat{k}) + \lambda(2\hat{i}+\hat{j}-3\hat{k})$ | (IV) 2,1,3 | Choose the correct answer from the options given below:

For any invertible matrix $A$, which of the following is NOT true.

General solution of the Differential equation $\frac{dy}{dx} + ay = e^{mx}$ is

Let $\vec{a}$ be any vector such that $\vec{a}.\hat{i} = \vec{a}.(\hat{i}+\hat{j}) = \vec{a}.(\hat{i}+\hat{j}+\hat{k}) = 1$, then $\vec{a}$ is

Area bounded by the curves $y = x|x|$, $x = -1$, $x = 1$ is

If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$, then $f$ is

If $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$, Then Match List-I with List-II | List-I | List-II | |---|---| | Values of $a, b$ & $c$ | value of $\Delta$ | | (A). $a=b=c=1$ | (I). 2 | | (B). $a=-1,b=1,c=1$ | (II). 0 | | (C). $a=-1,b=-1,c=1$ | (III). -2 | | (D). $a=-1,b=-1,c=-1$ | (IV). 4 | Choose the correct answer from the options given below:

The function $f(x) = \sin x + \cos x$; $0 \leq x \leq 2\pi$ is (A) Increasing in $\left(0, \frac{\pi}{4}\right)$ (B) Decreasing in $(0, \pi)$ (C) Increasing in $\left(\frac{5\pi}{4}, 2\pi\right)$ (D) Decreasing in $\left(\frac{\pi}{4}, \frac{5\pi}{4}\right)$ (E) Neither increasing Nor decreasing in $\left(0, \frac{\pi}{4}\right)$ Choose the correct answer from the options given below:

For the differential equation $\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} = k, k \neq 0$, which one of the following is TRUE ?

If $A$ and $B$ are matrices of the same order, then $AB^T - BA^T$ is a

A balloon which always remains spherical is being inflated by pumping in 900 cubic cm of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm is

Value of $\cot\left\{\frac{\pi}{4} - 2\cot^{-1}3\right\}$ is

If $\vec{r} = \vec{a_1} + \lambda\vec{b_1}$ and $\vec{r} = \vec{a_2} + \mu\vec{b_2}$ are two skew lines such that $\vec{b_1} \times \vec{b_2} = 2\hat{i}+3\hat{j}+2\hat{k}$, $\vec{a_1} = \hat{i}+\hat{j}+\hat{k}$ and $\vec{a_2} = 2\hat{i}+3\hat{j}+\hat{k}$, then the shortest distance between the lines is

Let us consider vector $\vec{a} = (c\log_2 x)\hat{i} - 6\hat{j} + 3\hat{k}$ and $\vec{b} = (\log_2 x)\hat{i} + 2\hat{j} + (2c\log_2 x)\hat{k}$, then which of following statements are TRUE? (Where $x \in \mathbb{R}$ (set of real numbers)) (A) Vector $\vec{a}$ and $\vec{b}$ make obtuse angle for any $x \in (0,\infty)$ if $c \in (-1,0)$ (B) Vector $\vec{a}$ and $\vec{b}$ makes obtuse angle for any $x \in \mathbb{R}$ if $c > 0$ (C) Vector $\vec{a}$ and $\vec{b}$ makes obtuse angle for any $x \in (0,\infty)$ if $c \in \left(-\frac{4}{3}, -1\right]$ (D) Vectors $\vec{a}$ and $\vec{b}$ makes obtuse angle for $x \in \mathbb{R}$ if $c \in (1,2)$ Choose the correct answer from the options given below:

If $x = 2t^2$ and $y = 3t^3$, then the value of $\frac{d^2y}{dx^2}$ at $t = 3$ is :

3 types of rice, A, B and C, are mixed together in the ratio 1 : 1 : 3 respectively. The price of rice A is ₹120 per kg and that of rice B is ₹130 per kg. If the price of the mixture is ₹150 per kg, then the price of rice C is:

Time series helps to (A) derive conclusions after arranging the time series in a systematic manner. (B) predict the future behavior of a variable. (C) study the past behavior of data. (D) plan future operations. Choose the correct answer from the options given below:

A fair coin is tossed until a head or five tails occur. The probability distribution of the number of tosses is,

For the nominal rate of 18 % p.a. [given that : $(1.09)^2 = 1.1881, (1.045)^4 = 1.1925, (1.015)^{12} = 1.1956$] Match List-I with List-II | List-I | List-II | |---|---| | Nominal rate Compounded | Effective rate | | (A) Annually | (I) 18.81% | | (B) Semi-annually | (II) 19.56% | | (C) Quarterly | (III) 18% | | (D) Monthly | (IV) 19.25% | Choose the correct answer from the options given below:

Which one of the following inequalities are satisfied by $x = 10$?

Which of the following systems has only a trivial solution?

A bike costs ₹85,000 and has a useful life of 15 years. If the scrap value of the bike after 15 years is ₹10,000, then the book value of the bike at the end of the tenth year is

Which of the following is not a rejection rule for one sample t-test: (Where α is the level of significance) (A) Reject null hypothesis $H_0$ : if $t \leq -t_\alpha$. (B) Reject null hypothesis $H_0$ : if $t \geq -t_\alpha$. (C) Reject null hypothesis $H_0$ : if $t \geq t_\alpha$. (D) Reject null hypothesis $H_0$ : if $t \leq -t_{\alpha/2}$ or $t \geq t_{\alpha/2}$. Choose the correct answer from the options given below:

A person invested ₹5,00,000 in a fund. At the end of the year, the value of the fund is ₹6,50,000. The nominal rate of return, if the market price is the same at the end of the year is:

If $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + \begin{vmatrix} 3 & 2 \\ 4 & 5 \end{vmatrix} = 0$, then the value of $x$ is

A pipe can fill a tank in 6 hours. Due to a leak in its bottom, it is filled in 7 hours. If the tank is full, then the time it will take to empty it because of the leak is:

The feasible region of inequality $2x + 3y > 6$ is

The integral $I = \int \frac{(1+\log x)^3}{x}\, dx$ equals:

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

Two dice are thrown then the probability of the sum of numbers appearing to be prime is :

The points on the ellipse $4x^2 + y^2 = 4$ that are farthest from the point (1,0) are;

If 18, Q, 19.2, T, 19.8 are the 5-year moving averages of the following series of observations: 16, P, 20, 18, R, 17, 19, S, 20, then Match List-I with List-II | List-I | List-II | |---|---| | (A) $3P + 2R$ | (I) 11.4 | | (B) $2R - (P+S)$ | (II) 86 | | (C) $\frac{1}{5}(P+R+S)$ | (III) 37.6 | | (D) $Q+T$ | (IV) 9 | Choose the correct answer from the options given below:

In a 100 m race, A gives a start of 10 m to B but still beats B by 5 seconds. If the speed of B is 4.5 km/hr, then the speed of A is:

$3^{16}$ (mod 4) is equal to

A function $f(x) = \begin{cases} \frac{kx^3}{4} & \text{if } x \leq 1 \\ 8 & \text{if } x > 1 \end{cases}$ for some constant $k$, then $\frac{d^2f(x)}{dx^2}$ at $x = -1$ is

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---|---|---| | P(X) | K | 3K | 7K | 5K | 4K | K | 2K | The value of K is

A bond is not characterized by which of the following terms? (A) Face value (B) Coupon rate (C) Redemption price (D) Equated monthly installment. Choose the correct answer from the options given below:

As per the concept of inferential statistics, population stands for:-

Max (z) = 5x + 10y subject to constraints: $x + 2y < 120$ $x + y > 60$ $x - 2y > 0$ $x, y \geq 0$ Which of the following points do not lie in the feasible region of the above LPP ? (A) (90, 15) (B) (30, 15) (C) (60, 20) (D) (90, 10) Choose the correct answer from the options given below:

During a season change, a pathologist observed that out of 10,000 people tested for viral fever, 1000 people were tested positive. Then the standard deviation for the distribution of positive reports is_______

Match List-I with List-II | List-I | List-II | |---|---| | (A) The interval in which $f(x) = x^2 - 4x + 17$ is increasing. | (I) $(-5,\infty)$ | | (B) The interval in which $f(x) = x^2 - 4x + 17$ is decreasing. | (II) $(-\infty,-5)$ | | (C) The interval in which $f(x) = 3x^2 + 30x - 7$ is increasing. | (III) $(2,\infty)$ | | (D) The interval in which $f(x) = 3x^2 + 30x - 7$ is decreasing. | (IV) $(-\infty,2)$ | Choose the correct answer from the options given below:

A motorboat can travel 10 km against the stream in 30 minutes and returns back at the same point in 10 minutes. The speed of the stream is,

A sample of size 9 from a normal population with sample mean $\bar{X} = 15.8$ and population estimated standard deviation $\sigma = 3.21$, then 99% confidence interval for population mean is : $(Use: t_8(0.01) = 3.335)$

Ravi borrowed ₹15,00,000 from a bank to purchase a plot and decided to repay the loan in equal monthly installments (EMI) in 10 years. If bank charges interest at 10% per annum, then EMI using a flat rate method is

Which of the following matrices are invertible? (A) $\begin{bmatrix} 2 & 2 \\ 3 & 3 \end{bmatrix}$ (B) $\begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}$ (C) $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix}$ (D) $\begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix}$ Choose the correct answer from the options given below:

The supply function of a producer is given by $p = \frac{3}{5}e^{3x}$, where $x$ denotes a thousand units. If sales are 4000 units, then the producers' surplus is

The maximum and the minimum value of the function $f(x) = -||x+3|-5| + 2$ are :

The present value of a sequence of payments of ₹3000 made at the end of every 6 months and continuing forever, if money is worth 9% per annum compounded semi-annually, is

If A is a square matrix $\begin{bmatrix} 5 & -5 \\ -5 & 5 \end{bmatrix}$ such that $A^2 = p\,A$, then the value of p is,