CUET Mathematics 2026 PYQs18 May Shift 2. Free, no login required.

If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ? A. $|A| = 1$ B. $A$ is singular matrix. C. $|adj A| = 1$ D. $|adj.(adj A)| = 1$ Choose the correct answer from the options given below:

If $x^2y^2 = a^{\pi/2}$, then $\dfrac{d^2y}{dx^2} =$

If $\begin{vmatrix} x & 3 & x \\ x^2 & x & 7 \\ x & x & 7 \end{vmatrix} = ax^4+bx^3+cx^2+dx+e$, then the value of $6a+5b+4c+3d+2e$ is

$\int 3x^2 e^{x^3}\,dx$ is equal to : (where $C$ is an arbitrary constant)

If $P(A) = 0.4$, $P(B) = X$ and $P(\bar{A} \cap \bar{B}) = 0.4$, where A and B are independent event, then the value of X is:

If $x = 16at^{\frac{1}{4}}$ and $y = 8at^{\frac{3}{4}}$ then $\dfrac{dy}{dx}$ is equal to:

The area of the region bounded between the line $x=3$ and the parabola $y^2=6x$ is:

Match the LIST-I with LIST-II | LIST-I Differential equation | LIST-II Order and degree | |---|---| | A. $y'' = [1+(y')^2]^{3/2}$ | I. 3, 4 | | B. $y''' + y' + y = 2x$ | II. 2, 2 | | C. $2(y'')^3 - (y')^4 + y = 0$ | III. 3, 1 | | D. $(y''')^4 + (y'')^3 + y' + y = 0$ | IV. 2, 3 | Choose the correct answer from the options given below:

Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that $f(x)+f(y)=f\left(\dfrac{x+y}{1-xy}\right)$, Where $\mathbb{R}$ is set of real numbers then $\alpha+\int_{-\alpha}^{\alpha} f(x)\,dx$ is equal to:

For the function $f(x)=2x^3-21x^2+36x-100$; Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. Point of local maxima is | I. -208 | | B. Point of local minima is | II. -83 | | C. Local maximum value is | III. 6 | | D. Local minimum value is | IV. 1 | Choose the correct answer from the options given below:

Given the following L.P.P., in which objective function represents the maximum profit ($Z$) (in Rs.) such as Max. $Z=40x+30y$, subject to constraints: $x+3y \le 12,\ 3x+y \le 12,\ x,y \ge 0$ The value of the maximum profit is:

If $\alpha$ and $\beta$ are absolute maximum and absolute minimum values of a function $f(x)=\dfrac{x}{2}+\dfrac{2}{x}$ on the interval $[1,2]$, then the value of $\alpha+\beta$ is:

If $A=\begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}$ and I is indentity matrix of order 2, then which of following statements are TRUE? A. $A^2-6A-mI=0$ if $m=-5$. B. $A^2-6A+mI=0$ if $m=-5$. C. $A$ is a non-singular matrix. D. $A^2=A$ Choose the correct answer from the options given below:

If a matrix $A=\begin{bmatrix} 3 & -5 & 7 \\ 5 & 2 & 4 \\ -7 & -4 & 9 \end{bmatrix}$ is expressed as the sum of a symmetric matrix P and a skew symmetric matrix Q, then symmetric matrix P will be

The solution of the differential equation $9+y^2\dfrac{dy}{dx}=x^2$ is : [Where $C$ is an arbitrary constant]

Match the LIST-I with LIST-II | LIST-I Functions | LIST-II Principal value | |---|---| | A. $\sin^{-1}\left(\dfrac{1}{2}\right)$ | I. $\dfrac{\pi}{4}$ | | B. $\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$ | II. $\dfrac{\pi}{6}$ | | C. $\tan^{-1}(1)$ | III. $-\dfrac{\pi}{4}$ | | D. $\cos^{-1}\left(-\dfrac{1}{2}\right)$ | IV. $\dfrac{2\pi}{3}$ | Choose the correct answer from the options given below:

If the two lines given by $x=py+q, z=ry+s$ and $x=p'y+q', z=r'y+s'$ are perpendicular, then which of the following is equal to -1 ?

The angle between the two lines whose direction cosines are given by the equations $4l+m+n=0$ and $2mn+24nl+4lm=0$, is

The area of the smaller region in first quadrant bounded by $x^2+y^2=4$ and $x=\dfrac{3}{2}$ is:

Match the LIST-I with LIST-II | LIST-I Function $f(x)$ | LIST-II $f(x)$ is increasing in the interval | |---|---| | A. $f(x)=-x^2-2x+3$ | I. $(-\infty,2)$ | | B. $f(x)=x^2+4x+1$ | II. $(1,\infty)$ | | C. $f(x)=2x^2-4x+3$ | III. $(-\infty,-1)$ | | D. $f(x)=-3x^2+12x+1$ | IV. $(-2,\infty)$ | Choose the correct answer from the options given below:

A function defined as $f:R\to R$ satisfies $f(x+y)=f(x)f(y)$ and $f(x)\ne 0$ for all $x,y\in R$, where R is set of real numbers. If $f(x)$ is differentiable at $x=0$ and $f'(0)=2$, then $f'(x)$ is equal to

The function $f(x)=\sin^4(x)+\cos^4(x)$, on interval $\left(0,\dfrac{\pi}{2}\right)$, has

If $A=\begin{bmatrix} 0 & -\tan\alpha/2 \\ \tan\alpha/2 & 0 \end{bmatrix}$, then the value of $\begin{bmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$ for all $\alpha \in \mathbb{R}$(set of real numbers), is (I is identity matrix of order 2)

If the function $f(x)=\begin{cases} x^2, & x\le c \\ ax+b, & x>c \end{cases}$ is differentiable at $x=c$, then the relation between $b$ and $c$ is:

The value of $\int_{-1}^{1} \dfrac{x^6}{6^x+1}\,dx$ is

$A=\begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1 \end{bmatrix}$ and $2B=\begin{bmatrix} 1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & 2y & 1 \end{bmatrix}$. If $A=B^{-1}$ then $x+y$ is equal to

If A and B are independent events such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$, then value of p is:

One ticket is drawn from a purse containing four tickets with numbers 223, 133, 212, 322. Let $A_i$ be the event that i$^{th}$ digit of the number on drawn ticket is 2. Then which of the following events are independent ? A. $A_1$ and $A_2$ B. $A_2$ and $A_3$ C. $A_1$ and $A_3$ D. $A_1$, $A_2$ and $A_3$ Choose the correct answer from the options given below:

The integrating factor of the differential equation $y\log_e(10y).\dfrac{dx}{dy}+x=\dfrac{1}{[\log_e(10y)]^2}$, is

A farmer has a tubewell which works by connecting two switches $S_1$ and $S_2$. The probability that $S_1$ works is 9/10 and the probability that $S_2$ works is 8/10. The farmer connects them in series in 30% cases and in parallel in 70% cases. If it is known that the tubewell was working, what is the probability that it was a series connection.

If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$, where $m$ is a positive integer then which of the following are factors of $k$? A. $m!$ B. $(m+1)!$ C. $(m+2)!$ D. $(m+3)!$ Choose the correct answer from the options given below:

The feasible region of an LPP is a bounded region by vertices (4, 18), (6, 12), (40, 0) and (15, 0). Then the point (15, 15) lies in the A. open half plane of $x+2y<40$. B. closed half plane of $3x+y\ge 30$. C. closed half plane of $4x+3y\ge 60$. D. feasible region of the given LPP. Choose the correct answer from the options given below:

An alphabet has been selected from English alphabets. What is the probability that it is a vowel given that it precedes 'M' ?

The general solution of the differential equation $\tan\left(\dfrac{(1+x^2)y'+2xy}{2x}\right)=1+x^2$, is (Consider $\log_e x=\log x$) (where C is an arbitrary constant)

If $f(x)=\int e^x(\tan x+\tan^2 x)\,dx$ and $f(0)=0$, then $f\left(\dfrac{\pi}{4}\right)$ equals:

There are two unit vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}+\vec{b}|=\sqrt{3}$ and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert \vec{a} - \vec{b} \vert$ | I. | $0$ | | B. | $\cos\theta$ | II. | $1$ | | C. | $\theta$ | III. | $\dfrac{1}{2}$ | | D. | $\sin 3\theta$ | IV. | $\dfrac{\pi}{3}$ | Choose the correct answer from the options given below:

If a, b, c > 0 and $ax+by>c$, then its graph represents:

For the greatest integer function $f(x)=[x]$, which of the following statements are correct? A. It is continuous at all real numbers. B. It is continuous at $x=2$ and 3. C. It is continuous and differentiable for $x\in(2,3)$ D. It is continuous and differentiable at $x=4.5$ Choose the correct answer from the options given below:

The vector $\{(a^2+a-2)\hat{i}+(a^2-4)\hat{j}-(a^2-5a+6)\hat{k}\}$ makes acute angles with coordinate axes, then values of $a$ lies in :

If $\Delta$ represents the value of the determinant $\begin{vmatrix} 1 & \sin k\theta & 1 \\ -\sin k\theta & 1 & \sin k\theta \\ -1 & -\sin k\theta & 1 \end{vmatrix}$, where $k$ is any real number then the value of $\Delta$ belongs to

If $P(\vec{r})$ is a position vector of a point with scalar components $(x,y,z)$, then the value of $(\vec{r}.\hat{i})(-\hat{i})-(\vec{r}.\hat{j})\hat{j}+(\vec{r}.(-\hat{k}))\hat{k}$, is:

If $x,y,z$ are non-zero real numbers such that $\begin{vmatrix} 10+x & 10 & 10 \\ 10 & 10+y & 10 \\ 10 & 10 & 10+z \end{vmatrix}=0$, then the value of $x^{-1}+y^{-1}+z^{-1}$ is

The area bounded by $2x+y=8, y=a$ and $y=a+2$ with y-axis is 5 sq.units where $a>0$, then the value of $a$ is:

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|2\vec{a}+\vec{b}|=|\vec{b}|$ and $\vec{a}+\vec{b}\ne \vec{0}$, then the angle between $\vec{a}+\vec{b}$ and $\vec{a}$, is

For the relation R defined below, where $\mathbb{R}$ and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II | LIST-I Relation | LIST-II Properties of relation hold by R | |---|---| | A. $R=\{(a,b): a,b\in \mathbb{R}; a^2+b^2=4\}$ | I. Neither reflexive, nor symmetric, nor transitive | | B. $R=\{(a,b): a,b\in \mathbb{R}; 1+ab>0\}$ | II. Equivalence relation | | C. $R=\{(a,b): a,b\in N; a+2b=8\}$ | III. Symmetric but neither reflexive nor transitive | | D. On N×N, relation R defined by $(a,b)R(c,d) \Leftrightarrow a+d=b+c$ | IV. Reflexive and symmetric, but not transitive | Choose the correct answer from the options given below:

For the matrix $A=\begin{bmatrix} 0 & 0 & 5 \\ 0 & 6 & 0 \\ 7 & 0 & 0 \end{bmatrix}$, which of the following statement(s) is/are TRUE ? A. $A$ is a scalar matrix. B. $A$ is a diagonal matrix. C. $A$ is a square matrix. D. $A$ is a skew symmetric matrix. Choose the correct answer from the options given below:

Let $(\alpha, 0, \beta)$ be the coordinates of the point, which divides the line segment joining the points (1,2,-3) and (1,-1,-4) internally, then $(\alpha^2+\beta^2)$ equals:

If $f(x)=\int \sqrt{\dfrac{x+8}{x-8}}\,dx; f(8)=24\log_e 2$, then $f(10)$ is equal to:

For the function $(ex)^y=e^x$; Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $y$ is equal to | I. $\dfrac{1-\log_e x}{x(1+\log_e x)^3}$ | | B. value of $\dfrac{dy}{dx}$ | II. $\dfrac{x}{1+\log_e x}$ | | C. value of $\dfrac{d^2y}{dx^2}$ | III. $\dfrac{\log_e x}{(1+\log_e x)^2}$ | | D. $x^y$ is equal to | IV. $e^{x-y}$ | Choose the correct answer from the options given below:

The length of a rectangle is decreasing at 4 cm/minute and the width is increasing at 3 cm/minute. The rate of change of area when length is 10cm and width is 6cm, is:

If $\begin{bmatrix} x-2y & z \\ 3x+y & w \end{bmatrix}=\begin{bmatrix} 1 & 2 \\ -11 & 1 \end{bmatrix}$; then the value of $y-x$ is:-

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. Confidence interval | I. Sampling distribution of the sample mean approaches normal distribution as the sample size gets larger, no matter what the shape of the population distribution is. | | B. Hypothesis | II. A measurable characteristic of a sample. | | C. Central limit theorem | III. The amount of uncertainity associated with a sample estimate of a population parameter. | | D. Statistic | IV. An educated guess which needs to be tested. | Choose the correct answer from the options given below:

Suresh takes a loan of ₹ 4,00,000 with 10% annual interest rate for 5 years on flat rate basis. Which of the following statements are correct ? A. The total interest on the principal is ₹ 1,00,000. B. The number of months in loan period is 60. C. EMI under flat rate system is ₹ 12,000. D. EMI under flat rate system is ₹ 10,000. Choose the correct answer from the options given below:

A company has issued a bond having face value of ₹ 70,000, carrying an annual dividend rate of 8% and maturing in 15 years. If the bond is redeemed at par, then which of the following statements are true? A. The annual dividend is ₹ 5,600. B. The annual dividend is ₹ 6,300. C. Redemption price is ₹ 73,000. D. Redemption price is ₹ 70,000. Choose the correct answer from the options given below:

In a survey question for a sample of 340 people, 85 persons gave positive response, 145 people gave negative response and 110 people were neutral, gave no response. What is the point estimate of the proportion in the population who respond positive?

A lady invested ₹ 10,000 in a mutual fund and the value of investment at the time of redemption was ₹ 20,000. If the compound annual growth rate (CAGR) for this investment is 25.9 %, then the number of years for which she has invested the amount is:- [Given that : $2^{1/3}\approx 1.259$ ]

Mr. X runs 5 times as fast as Mr. Y. If Mr. X gives Mr. Y a start of 80 meters, how far must the goal on the race course be so that Mr. X and Mr. Y reach it at the same time?

A bank lent out ₹ 25,000 in two parts, one at 7% per annum and other at 11% per annum interest. The yearly average comes out to be 9.4%. The amount lent in two parts will be

The pattern of data in the time series is influenced by a large variety of factors. Which of the following are not the components of the time series? A. Regional component B. Irregular component C. Cyclone component D. Seasonal component Choose the correct answer from the options given below:

Let the speed of a boat in still water be $u$ km/hr and the speed of the water current in a river be $v$ km/hr. If a man rows distance $D$ down stream and same distance upstream, then average speed of total journey is

A car costing ₹ 5,00,000 has a useful life of 15 years. The estimated scrap value is ₹ 50,000. The annual depreciation using the straight line method is

$\int \dfrac{e^{7\log x}-e^{6\log x}}{e^{5\log x}-e^{4\log x}}\,dx$, $x>0$ and $x\ne 1$ is equal to (consider $\log x = \log_e x$)

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (0, 9), (2, 10), (6, 8), (10, 0). If the objective function is $Z=6x+5y$, then (Maximum value of $Z$ – Minimum value of $Z$) is equal to:

If $A=\begin{bmatrix} 2 & 1 \\ 7 & 5 \end{bmatrix}$, then the value of $|A(adj A)|$ is

If the cash equivalent of a perpetuity of ₹ 300 payable at the end of each quarter is ₹ 24,000, then the rate of interest per annum is:

Two pipes can fill a tank in 12 and 15 minutes respectively and a waste pipe can empty 3.4 litres per minute. All the three pipes working together can fill the tank in 18 minutes. The capacity of the tank is

A pair of dice is thrown 5 times. If getting a total of 7 is considered a success, then Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. Probability of no success | I. $26\left(\dfrac{1}{6}\right)^5$ | | B. Probability of 5 successes | II. $2\left(\dfrac{5}{6}\right)^5$ | | C. Probability of at least 4 successes | III. $\left(\dfrac{1}{6}\right)^5$ | | D. Probability of at most one success | IV. $\left(\dfrac{5}{6}\right)^5$ | Choose the correct answer from the options given below:

A father has setup a sinking fund in order to have ₹ 2,40,000 after 10 years for his daughter's marriage. How much amount should he set aside bi-annually into an account paying 5% per annum compounded half-yearly? [given : $(1.025)^{20}\approx 1.6$]

Which of the following points describe the concept of population in inferential statistics ? A. It is a collection of all elements having same characteristics. B. A survey done on the total population is not accurate. C. Population focuses on the identification of the characteristic. D. Population focuses on drawing inference about the sample. Choose the correct answer from the options given below:

The order and degree of the differential equation $\left[2+\left(\dfrac{dy}{dx}\right)\right]^{5/2}=7\dfrac{d^3y}{dx^3}$ is

For the function $f(x)=x^3-2x^2-4x-5$, which of the following statement is not correct ?

A value of $x$ satisfying $6x \equiv 5 \pmod{7}$ is

Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. All positive integral powers of a symmetric matrix are | I. Unit matrix. | | B. Positive odd integral powers of a skew-symmetric matrix are | II. Null matrix. | | C. All the matrices which are both symmetric and skew-symmetric, are | III. Skew - Symmetric matrix. | | D. All the square matrices whose each diagonal element is one and each non-diagonal element is equal to zero, are | IV. Symmetric matrix. | Choose the correct answer from the options given below:

For 6 trials of an experiment, let X be a binomial variate which satisfies the relation $9P(X=4)=P(X=2)$, then the probability of success is

The monthly salaries of workers in a garment factory are normally distributed. The mean salary is ₹ 10,000 and standard deviation is ₹ 625. If 2,500 workers are getting salary less than ₹ 10,000, then the total number of workers in the factory is:

If matrix $A=\begin{bmatrix} 5 & 2 & 3 \\ 4 & 1 & 2 \\ 7 & 6 & 0 \end{bmatrix}$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert A \vert$ | I. | $16$ | | B. | Minor of $a_{23}$ | II. | $27$ | | C. | Cofactor of $a_{32}$ | III. | $19$ | | D. | If $a_{23}$ is interchanged with $a_{32}$, then $\vert A \vert$ | IV. | $2$ | Choose the correct answer from the options given below:

The value of $\lambda$ for which the following system of equations has no solution is $x+y+2z=4$ $2x+y+3z=5$ $x+3y+\lambda z=7$

For the five values 12, $a$, 17, 21, 22, the three years moving averages are 13, 16, 20. The value of $a$ is

The total revenue received from the sale of $x$ units of a product is given by $R(x)=542+\dfrac{x^2+3}{4}$. What will be the marginal revenue when $x=24$ ?

Match the LIST-I with LIST-II | | LIST-I (Inequality) | | LIST-II (Solution set) | |---|---|---|---| | A. | $\vert x-3 \vert < 1$ | I. | $x \in \left(-\dfrac{2}{5}, \dfrac{8}{5}\right)$ | | B. | $\vert 3-5x \vert < 5$ | II. | $x \in \left(-\infty, -\dfrac{1}{2}\right)$ | | C. | $2x+1 < \vert 2x+1 \vert$ | III. | $x \in \left(-\dfrac{1}{3}, 5\right)$ | | D. | $\vert 7-3x \vert < 8$ | IV. | $x \in (2,4)$ | Choose the correct answer from the options given below:

If $y=\sqrt[5]{\log_e(5x^2)}$, then $\dfrac{dy}{dx}=$ (Take $\log_e x=\log x$)

If $x=\log_e t$ and $y=\dfrac{1}{t}$, then $\dfrac{d^2y}{dx^2}$ at $t=0.1$ is

Consider a LPP: Maximize $Z=22x+18y$ Subject to: $x+y\le 20$, $360x+240y\le 5760$, $x,y\ge 0$. Which of the following statements are correct ? A. The maximum value of $Z$ occurs at (0, 20). B. The maximum value of $Z$ occurs at (8, 12). C. The maximum value of $Z$ is 352. D. The maximum value of $Z$ is 392. Choose the correct answer from the options given below:

The interval in which the function $f(x)=x^4-\dfrac{x^3}{3}$ is increasing, is

If $X$ is a Poisson variate such that $P(X=3)=2P(X=4)$, then $P(X=2)$ equals: [given $e^{-2}=0.14$]