CUET Mathematics 2026 PYQs29 May Shift 1. Free, no login required.

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:

Match List-I with List-II | List-I (Function) | List-II (Critical point) | |---|---| | (A) $f(x)=x^3-3x$ | (I) $x=3$ | | (B) $f(x)=x^3-12x$ | (II) $x=0$ | | (C) $f(x)=x^2-6x$ | (III) $x=1$ | | (D) $f(x)=x^2$ | (IV) $x=2$ | Choose the correct answer from the options given below:

Ram invested ₹10,000 in a stock of a company for 6 years. The value of his investment at the end of each year is given below: | | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |---|---|---|---|---|---|---| | | ₹10,000 | ₹11,500 | ₹13,000 | ₹11,800 | ₹12,200 | ₹14,000 | Then CAGR % of his investment is: (Given $(1.4)^{1/6}=1.058$)

Which of the following are correct? (A) The central limit theorem (CLT) states that the sampling distribution of the sample approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution. (B) The measurable characteristic of population is called parameter. (C) The population focuses on the identification of the characteristic. (D) The sample makes inference about the population. Choose the correct answer from the options given below:

The mean of the number of tails in three tosses of a coin is :

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | 0.15 | 0.30 | 0.30 | 0.15 | Which of the following are correct? (A) $P(X \le 1)=0.25$ (B) $P(X>3)=0.15$ (C) $P(X=2)=0.30$ (D) $P(X \le 2)=0.55$ Choose the correct answer from the options given below:

If 35, 70, 36, 59, 62 is the given annual time series, then 3-yearly moving averages are

If an edge of a variable cube is increasing at the rate of 0.8 cm/sec, at what rate its surface area is increasing when its edge is 10 cm?

If X is a Poisson variate such that $3P(X=2)=2P(X=1)$, then $P(X=0)$ is equal to: (Given $e^{-4/3}=0.264$)

In what ratio water must be added to dilute honey costing ₹300 per litre so that the resulted syrup would be worth ₹250 per litre?

If A is a non-singular matrix of order 3, then Match List-I with List-II | List-I | List-II | |---|---| | Determinant of A | $\left\vert \text{adj}(\text{adj } A) \right\vert =$ | | (A) $\left\vert A \right\vert = 3$ | (I) $1$ | | (B) $\left\vert A \right\vert = 4$ | (II) $16$ | | (C) $\left\vert A \right\vert = 2$ | (III) $81$ | | (D) $\left\vert A \right\vert = 1$ | (IV) $256$ | Choose the correct answer from the options given below:

If $A=\begin{bmatrix}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{bmatrix}$ and $A(adjA)=xI$, where $I$ is an identify matrix of order 3, then $x$ is equal to

Which of the following are correct? (Where $R$ is set of real numbers) (A) If $x \le 8$, then $-x \ge -8$ (B) If $x \in R, |x| \le 3$, then $-3 \le x \le 3$ (C) If $x \in R, |x|<-4$, then $x \in \phi$ (D) $x=|x|$ iff $x \ge 0$ Choose the correct answer from the options given below:

A person has an initial investment of ₹50,000 in an investment plan. After 2 years, it has grown to ₹60,000, then his rate of return is:

The corner points of the bounded feasible region for an LPP are (0, 0), (6, 0), (4, 3) and (0, 8). The objective function $Z=px+qy$, $p,q>0$ has maximum value 360 at points (6, 0) and (4, 3). The value of $Z$ at (0, 8) is :

Consider the following hypothesis test: $H_o: \mu \le 12$ $H_a: \mu > 12$ A sample of 25 provided a sample mean $\bar x=14$ and a sample standard deviation $s=4.32$. The degree of freedom is

The speed of a boat in still water is 12 km/hr. It takes twice as long to go upstream to a point as to return downstream to the starting point, then the speed of the stream is :

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\displaystyle\int_{-1}^{1}(2x^5+3x^3+4x+1)dx=$ | (I) 2 | | (B) $\displaystyle\int_{-2}^{2}(4x^3+2)dx=$ | (II) 12 | | (C) $\displaystyle\int_{-1}^{1}x^3dx=$ | (III) 8 | | (D) $\displaystyle\int_{-3}^{3}(3x^5+2)dx=$ | (IV) 0 | Choose the correct answer from the options given below:

If for the following data: | Year | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | |---|---|---|---|---|---|---|---| | Production (in lakh tonnes) | 30 | 35 | 36 | 32 | 37 | 40 | 36 | Using straight line trend by the method of least squares, the trend value for the year 2009 is :

Let X denote the number of scores in a test. If X is normally distributed with mean 100 and standard deviation 15, then the probability that X does not exceed 130 is, (Given $P(0 \le Z \le 2)=0.4772$, where $Z$ be the standard normal variate)

Match List-I with List-II | List-I (Singular matrix) | List-II (A value of $x$) | |---|---| | (A) $A=\begin{bmatrix}x & 4 \\ 2 & 2x\end{bmatrix}$ | (I) 3 | | (B) $A=\begin{bmatrix}3 & x \\ 3x & 9\end{bmatrix}$ | (II) 4 | | (C) $A=\begin{bmatrix}x & 1 \\ 1 & x\end{bmatrix}$ | (III) 2 | | (D) $A=\begin{bmatrix}x & 1 \\ 16 & x\end{bmatrix}$ | (IV) 1 | Choose the correct answer from the options given below:

If $A=\begin{bmatrix}2 & -1 & 3 \\ -3 & 4 & 5\end{bmatrix}$ and $B=\begin{bmatrix}2 & 1 \\ 3 & 5 \\ 2 & 3\end{bmatrix}$ and $BA=(b_{ij})$, then $b_{22}+b_{31}$ is :

The revenue function is given by $R(x)=150x-2x^2-x^3$, where $x$ is the number of units demanded, then the marginal revenue when 5 units are sold, is :

In a game of 100 points, A can give 20 points to B and 28 points to C. How many points can B give C?

A simple random sample of 64 items from a population with standard deviation $\sigma=4$ resulted in a sample mean of 35. What is the margin of error for the population mean at a 95% confidence level? (Given $Z_{0.025}=1.96$)

Match List-I with List-II | List-I (Parametric function) | List-II ($\dfrac{dy}{dx}$) | |---|---| | (A) $x=\log t, y=\dfrac{1}{t}$ | (I) $-\dfrac{1}{4t^2}$ | | (B) $x=t^2, y=2t$ | (II) $\dfrac{1}{t}$ | | (C) $x=4t, y=\dfrac{1}{t}$ | (III) $t^2$ | | (D) $x=2t^2, y=t^4$ | (IV) $-\dfrac{1}{t}$ | Choose the correct answer from the options given below:

If the objective function for an LPP is $Z=4x+5y$ and the corner points for bounded feasible region are (10, 0), (5, 3), (2, 5) and (0, 6), then the minimum value of $Z$ occurs at

Which of the following are correct? (A) Sinking fund is a fixed term account. (B) Sinking fund is set-up for a particular upcoming expense. (C) In sinking fund any amount, any time can be deposited. (D) Sinking fund can be used only for the purpose it was created. Choose the correct answer from the options given below:

Which of the following are correct? (A) The order of the differential equation $\left(\dfrac{dy}{dx}\right)^2+3y^2-5y=0$ is 2. (B) The degree of the differential equation $x\dfrac{d^2y}{dx^2}=\left(3+2\left(\dfrac{dy}{dx}\right)^2\right)^3$ is 3. (C) The differential equation representing the curve $y=cx$, $c$ being an arbitrary constant is $ydx-xdy=0$. (D) The general solution of an ordinary differential equation of $n^{th}$ order contains $n$ independent arbitrary constants. Choose the correct answer from the options given below:

The area (in sq. units) of the region bounded by $x^2=4y, y=1, y=9$ and $x=0$ in the first quadrant is :

Ram takes a loan of ₹5,00,000 from a bank at an interest rate of 6% per annum for 10 years. He wants to pay back the loan in equated monthly installments, then his EMI by using flat rate method is :

The last digit of $12^{13}$ is :

Which of the following are correct? (A) If $A=\begin{bmatrix}7 & 5 \\ 4 & 3\end{bmatrix}$, then $A^{-1}=\begin{bmatrix}3 & -5 \\ -4 & 7\end{bmatrix}$ (B) If $A=\begin{bmatrix}3 & 5 \\ 6 & 10\end{bmatrix}$, then $A$ is a non-singular matrix (C) $A=\begin{bmatrix}0 & -5 \\ 5 & 3\end{bmatrix}$ is a symmetric matrix (D) If $A=\begin{bmatrix}6 & x \\ y & 0\end{bmatrix}$ and $A=A^T$, then $x=y$ Choose the correct answer from the options given below:

The real value of $a$ for which the system of equations $x+ay=0, y+az=0, z+ax=0$ has infinitely many solutions, is :

Two pipes can fill a tank in 20 minutes and 24 minutes respectively, and a waste pipe can empty 3 gallons of water per minute. If all the three pipes working together can fill the tank in 15 minutes, then the capacity of the tank is :

A machine costing ₹55,000 is expected to have a useful life of 10 years and a final scrap value of ₹5,000. The annual depreciation charge using the straight line method is :