CUET Mathematics 2026 PYQs30 May Shift 2. Free, no login required.

If $f(x) = (x+3)e^{-x}$, then which of the following statements are True? (A) Function $f(x)$ is increasing on $(-2, \infty)$. (B) Function $f(x)$ is decreasing on $(-2, \infty)$. (C) Function $f(x)$ is increasing on $(-\infty, -2)$. (D) Function $f(x)$ is decreasing on $(2, 3)$.

If $a_{ij}$ and $A_{ij}$ represents the elements and cofactors of the matrix $A = \begin{bmatrix}2 & 1 & 3\\3 & 2 & 1\\1 & 2 & 3\end{bmatrix}$, then which of the following statements are True? (A) $|A| = 28$ (B) $A_{23} = -3$ (C) $a_{11}A_{12} = -16$ (D) $\frac{A_{21}}{A_{13}} = \frac{3}{4}$ Choose the correct answer from the options given below:

If $x = at^2$ and $y = 4at$, then the value of $\frac{d^2y}{dx^2}$ at $t = 1/a$, is

Match **List-I** with **List-II** | List-I | List-II | |---|---| | Curve $y=f(x)$ (where C is an arbitrary constant) | The curve $y=f(x)$ satisfies the differential equation | | (A) $y = \log x + C$ | (I) $x\frac{dy}{dx} - y = 0$ | | (B) $y = e^x + C$ | (II) $x\frac{dy}{dx} - 1 = 0$ | | (C) $y = cx$ | (III) $x^2\frac{dy}{dx} + 1 = 0$ | | (D) $y = \frac{1}{x} + C$ | (IV) $\frac{d^2y}{dx^2} - \frac{dy}{dx} = 0$ | Choose the correct answer from the options given below:

Probability of solving a specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively, then which of the following are True? [where P(X) denotes the probability of an event X] (A) P(Problem is solved) = $\frac{2}{3}$ (B) P(Exactly one of them solves the problem) = $\frac{1}{2}$ (C) P(Both of them solve the problem) = $\frac{5}{6}$ (D) P(Atmost one solves the problem) = $\frac{5}{6}$ Choose the correct answer from the options given below:

If $y = x\frac{dy}{dx} + \sqrt{a^2\left(\frac{dy}{dx}\right)^2 + b^2}$, then the order and degree of the differential equation are

The local minimum value of $f(x) = x^3 + \frac{243}{x}$ is

If $A = \begin{bmatrix}0 & a & 1\\-1 & b & 1\\-1 & c & 0\end{bmatrix}$ is a skew symmetric matrix, then the value of $(a+b-c)^2$ is

A is a square matrix of order 3 x 3, then Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) $\left\vert \text{adj}A \right\vert$ | (I) $\dfrac{1}{\left\vert A \right\vert}$ | | (B) $\left\vert A^{-1} \right\vert$ | (II) $\left\vert A \right\vert^{4}$ | | (C) $\left\vert A.\text{adj}A \right\vert$ | (III) $\left\vert A \right\vert^{3}$ | | (D) $\left\vert \text{adj}(\text{adj}A) \right\vert$ | (IV) $\left\vert A \right\vert^{2}$ | Choose the correct answer from the options given below:

If $\int_0^1 (4x^3 + 3x^2 + 2x + k)dx = 0$, then the value of 'k' is

$\int e^{x\log_e a}.e^x dx$ is: [where C is an arbitrary constant]

The area bounded by the curve $y^2 = 2x$, $y$-axis and the line $y=1$, is

The general solution of the differential equation $x(x^2-1)\frac{dy}{dx} = 1$ is: [Where C is an arbitrary constant]

If A and B are two square matrices of the same order such that $(A+B)^2 = A^2+B^2$, then

The point/points which provides the optimal solution of the linear programming problem maximum $z = 3x+y$, $x+3y \le 12, 3x+y \le 12, x,y \ge 0$, is/are

The shortest distance between lines whose vector equations are: $\vec{r} = (1-t)\hat{i} + (t-2)\hat{j} + (3-2t)\hat{k}$ and $\vec{r} = (s+1)\hat{i} + (2s-1)\hat{j} - (2s+1)\hat{k}$, is:

The side of an equilateral triangle is increasing at the rate of 2 cm/sec. The rate at which the area of the triangle is increasing, when the side of the triangle is 5 cm, is

If $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$, then which of the following statements are correct? (A) $\vec{a}$ and $\vec{b}$ are perpendicular to each other. (B) $\vec{a}$ and $\vec{b}$ are parallel. (C) $|\vec{a}\times\vec{b}| = 2\sqrt{21}$. (D) Projection of $\vec{a}$ on $\vec{b}$ = 0. Choose the correct answer from the options given below:

The value of $\begin{vmatrix}x & a & a\\a & x & a\\a & a & x\end{vmatrix}$ is equal to:

If $A = \begin{bmatrix}\cos\alpha & \sin\alpha\\-\sin\alpha & \cos\alpha\end{bmatrix}$, then the value of $1000|A^n| + 2|A|$ for a positive integer $n$, is equal to

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|\vec{a}\times\vec{b}|^2 + |\vec{a}.\vec{b}|^2 = 100$ and $|\vec{a}| = 5$ then the value of $|\vec{b}|$ is

If A is square matrix of order 3 x 3 such that $a_{ij} = j - i$, then which of the following statements are correct? (A) A is a symmetric matrix. (B) A is a skew symmetric matrix. (C) $|A| = 0$. (D) A is a diagonal matrix. Choose the correct answer from the options given below:

The equation of line passing through the points (2, -1, 3) and (4, 2, 1) is (A) $\frac{x-2}{2} = \frac{y+1}{3} = \frac{z-3}{-2}$ (B) $\frac{x-4}{3} = \frac{y-2}{-2} = \frac{z-1}{2}$ (C) $\vec{r} = (2\hat{i}-\hat{j}+3\hat{k}) + \lambda(2\hat{i}+3\hat{j}-2\hat{k})$ (D) $\frac{x-4}{-2} = \frac{y-2}{-3} = \frac{z-1}{2}$ Choose the correct answer from the options given below:

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true? (A) The value of p is $\frac{2}{5}$ (B) $P(A\cap B) = \frac{2}{15}$ (C) $P(B/A) = \frac{1}{3}$ (D) $P(A/B) = \frac{3}{5}$ Choose the correct answer from the options given below:

The area (in square units) bounded by the curve $y = x^2|x|$, x-axis and the lines $x=-2$ and $x=2$, is

If $f(x) = \begin{cases}\lambda x+5, & if\ x\le 2\\x+3, & if\ x>2\end{cases}$ is continuous at $x=2$, then, the value of $\lambda$ is

For the function $f(x) = x^5 - 5x^4 + 5x^3 - 1$, which of the following are true? (A) $f(x)$ has local minimum value equal to -28. (B) $f(x)$ has point of inflection at $x=1$. (C) $f(x)$ has point of local maxima at $x=1$. (D) $f(x)$ has the local maximum value equal to 2. Choose the correct answer from the options given below:

A pair of dice is thrown, then the probability of getting a sum of 7, is

A closed right circular cylinder has a volume of 2156 cm³. The radius of its base so that its total surface area may be minimum, is equal to:

The value of integral $\int_{-\pi/2}^{\pi/2} \frac{1}{1+e^{\sin x}}dx$ is

The greatest integer function $f: R\to R$ defined by $f(x) = [x]$, then which of the following are true? (A) $f(x)$ is one - one and onto. (B) Domain of $f(x) = R$ (the set of real numbers). (C) $f(x)$ is neither one-one nor onto. (D) Range of $f(x) = Z$ (The set of integers). Choose the correct answer from the options given below:

A man is known to speak truth 4 out of 5 times. A coin is tossed. He reports that a head appears. The probability that actually there was a head, is

The corner points of the bounded feasible region of a linear programming problem are A(15,0), B(40,0), C(4, 18), D(6, 12) and objective function is $z = 20x+10y$, then which of the following are TRUE? (A) Value of z at point A(15, 0) = 300. (B) Value of z at point B(40, 0) = 800. (C) Value of z at point C(4, 18) = 340. (D) Maximum value of z = 800. Choose the correct answer from the options given below:

If two cards are drawn at random without replacement from a pack of 52 playing cards, then the probability that both the cards are red, is

If $0 < x < \frac{\pi}{4}$, then $\int\sqrt{1-\sin2x}\,dx$ is: [where C is an arbitrary constant]

Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Domain of $\sin^{-1}(2x-3)$ | (I) [-1, 0] | | (B) Domain of $\sin^{-1}(1+2x)$ | (II) [-1, 1] | | (C) Domain of $\cos^{-1}(2x-1)$ | (III) [1, 2] | | (D) Domain of $\sin^{-1}(x^2)$ | (IV) [0, 1] | Choose the correct answer from the options given below:

Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) $\frac{d}{dx}(\sqrt{\sin x})$ | (I) $\frac{-\sin x}{2\sqrt{\cos x}}$ | | (B) $\frac{d}{dx}(\sqrt{\cos x})$ | (II) $-\sin 2x$ | | (C) $\frac{d}{dx}(\sin^2 x)$ | (III) $\frac{\cos x}{2\sqrt{\sin x}}$ | | (D) $\frac{d}{dx}(\cos^2 x)$ | (IV) $\sin 2x$ | Choose the correct answer from the options given below:

The solution set of the inequality $3x+4y<12$ is

Match **List-I** with **List-II** | List-I | List-II | |---|---| | Definite integral | Value | | (A) $\int_2^3 x^2 dx$ | (I) $-\frac{1}{2}$ | | (B) $\int_{-1}^1 (x+1)dx$ | (II) $\frac{19}{3}$ | | (C) $\int_0^1 (x-1)dx$ | (III) $\frac{16}{3}$ | | (D) $\int_0^4 \sqrt{x}\,dx$ | (IV) 2 | Choose the correct answer from the options given below:

Match **List-I** with **List-II** | List-I | List-II | |---|---| | Differential equation | Integrating factor | | (A) $\frac{dx}{dy}+\frac{2x}{y}=y^2$ | (I) $e^x$ | | (B) $\frac{dy}{dx}+y=e^{-x}$ | (II) $\frac{1}{\sqrt{y}}$ | | (C) $\frac{dy}{dx}-\frac{y}{2}=x$ | (III) $y^2$ | | (D) $\frac{dx}{dy}-\frac{1}{2}\frac{x}{y}=\sin y$ | (IV) $e^{-x/2}$ | Choose the correct answer from the options given below:

If A and B are invertible matrices of the same order, then Match **List-I** with **List-II** | List-I (Determinant) | List-II (Equal to) | |---|---| | (A) $\left\vert A^{-1}B \right\vert$ | (I) $\dfrac{1}{\left\vert A \right\vert \left\vert B \right\vert}$ | | (B) $\left\vert AB^{-1} \right\vert$ | (II) $\dfrac{\left\vert B \right\vert}{\left\vert A \right\vert}$ | | (C) $\left\vert A^{-1}B^{-1} \right\vert$ | (III) $\left\vert A \right\vert \left\vert B \right\vert$ | | (D) $\left\vert AB \right\vert$ | (IV) $\dfrac{\left\vert A \right\vert}{\left\vert B \right\vert}$ | Choose the correct answer from the options given below:

If $y = \log_3(\log x)$, (Consider $\log_e x = \log x$) then the value of $\frac{dy}{dx}$ is

The area lying between the curves $x^2=4y$ and $x=2y$ is

The particular solution of the differential equation $\sec^2x\tan y\,dx - \sec^2y\tan x\,dy = 0$, $y=\frac{\pi}{4}$ when $x=\frac{\pi}{4}$, is

Direction ratios of the line perpendicular to the lines $\frac{x-3}{2}=\frac{y+7}{-3}=\frac{z-2}{1}$ and $\frac{x+2}{1}=\frac{y+3}{2}=\frac{z-5}{-2}$ are

If $A = \begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x) = x^2-2x-3$, then $f(A)$ is

If $A = \begin{bmatrix}\frac{1}{4} & 2\\0 & 2x-3\end{bmatrix}$, $B = \begin{bmatrix}4 & 8\\0 & -1\end{bmatrix}$ and AB = $I_2$ (Identity matrix of order 2), then the value of $x$ is

If n(A) = 3 and n(B) = 2, then number of non-empty relations from A to B is

If $\vec{a}$ and $\vec{b}$ are two unit vectors inclined at an angle $\theta$, then the value of $|\vec{a}-\vec{b}|$ is

A unit vector $\vec{a}$ makes angles $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with x-axis and y-axis respectively and an acute angle $\theta$ with z-axis, then the value of $\theta$ is

Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) The value of $I=\int_0^1 \frac{1}{\sqrt{x}}dx$ is | (I) 1 | | (B) The value of $I=\int_0^1 (5x^2+1)dx$ is | (II) $\frac{1}{2}$ | | (C) The value of $I=\int_0^\infty e^{-x}dx$ is | (III) $\frac{8}{3}$ | | (D) The value of $I=\int_1^e \frac{\log x}{x}dx$ is | (IV) 2 | Choose the correct answer from the options given below:

A man wants to get ₹10,000 forever at the beginning of each quarter, if the money is worth 8% per annum compounded quarterly, then the money he needed to invest now is

It is 7:00 P.M. currently. What time will be in next 536 hours?

For a straight line trend $y_t = a+bx$ for $n$ data by the method of least squares if, $n=8, \sum y=47.8, \sum xy=4.3$ and $\sum x^2=42$, then $y_t$ at $x=-3.5$ is _____. [where $y_t$ represents trend value of y]

The following data are from a simple random sample: 8, 11, 13, 10, 13, 17. The point estimate of the population mean is:

A bond sells at discount. Which of the following is feasible? [YTM = yield to maturity]

If $A = \begin{bmatrix}\alpha & \beta\\r & \Delta\end{bmatrix}$, such that $|A| = 25$, then the value of $\left|\frac{1}{5}A\right|$ is.

Consider the linear programming problem (LPP): Max Z= 4x + 3y subject to the constraints: $x\le 8, y\le 4, x\ge 0, y\ge 0$. At what coordinates will the objective function have optimal solution?

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

Shyamaji takes a loan of ₹20,00,000 with 10% annual interest rate for 10 years. What will be her EMI under flat rate system?

The area (in sq. units) bounded between the curves $x=e^y$, $x=e$ and x-axis in the first quadrant is

There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---|---|---| | P(X) | z | 2z | 2z | 3z | $z^2$ | $2z^2$ | $7z^2+z$ | Which of the following are TRUE? (A) P(X < 3) = 0.8 (B) P(X > 4) = 0.2 (C) The value of z is 0.1 (D) $P(3\le X<5) = 0.31$ Choose the correct answer from the options given below:

If A and B are symmetric matrices of same order, then which of the following statements are true? (A) $AB^T+B^TA$ is a skew-symmetric matrix. (B) $AB^T-BA^T$ is a skew-symmetric matrix (C) $(AB)^T(A^T)^{-1}=B$ (D) $(AB)^{-1}(BA)^T=A$ Choose the correct answer from the options given below:

A trader has two varieties of rice, type A & type B whose selling prices are ₹100 per kg and ₹180 per kg respectively. The possible quantities of type A rice to be mixed with 500 kg of type B rice, such that the selling price of the resulting mixture is ranging between ₹120 per kg to ₹150 per kg, are: (A) 1400 kg (B) 200 kg (C) 1000 kg (D) 800 kg Choose the correct answer from the options given below:

For which of the following real functions, $x=0$ is a point of local maxima? (A) $f(x)=4x^4-3x^3-2x^2+1$ (B) $f(x)=3x^5+\sqrt{2}x^4-7x^2+4$ (C) $f(x)=5x^4-3x^2+e$ (D) $f(x)=-3x^3+2x^2-9$ Choose the correct answer from the options given below:

If the average rainfall in a given area is 8 inches and the following table represents the average rainfall for four consecutive years, then the value of test statistic 't' is_____. | Year | year 1 | year 2 | Year 3 | year 4 | |---|---|---|---|---| | Rainfall (inches) | 8 | 5 | 6 | 5 |

Let A be a square matrix of order 3 such that $|A|=3$, then the value of $\frac{|adj(adjA)|}{|A|}$ is

In a company, the cost of producing one item is ₹100, if the item is sold at ₹150 and ₹50,000 is the fixed cost of the company, then the break-even point is:

Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Snowball sampling | (I) Statistic | | (B) A measurable characteristic of a sample | (II) Parameter | | (C) Stratified sampling | (III) Non-probability sampling | | (D) A measurable characteristic of a population | (IV) Probability sampling | Choose the correct answer from the options given below:

Scrap value of a machine is one-tenth of its actual cost. If the estimated life of the machine is ten years and the annual depreciation under linear method is ₹45000, then the cost of the machine is

The fomula for calculating compound annual growth rate of an investment is: [F.V = final value of the investment, P.V = starting value of the investment, n = investment period]

Three pipes A, B, and C can fill a tank together in 2 hours. Pipes B and C take 3 hours to fill the tank, while pipes A and C take 4 hours to fill the tank. Which of the following statements are correct? (A) Pipe A alone takes 6 hours to fill the tank. (B) Pipe B alone takes 5 hours to fill the tank. (C) Pipe B alone takes 4 hours to fill the tank. (D) Pipe C alone takes 12 hours to fill the tank. Choose the correct answer from the options given below:

A motorboat completes a round trip of 150 km between two places A and B in 8 hours. If downstream speed of the motorboat is 25 km/hr, then the upstream speed of the motorboat is

Let C = C(x) be the total cost of producing x units of a product and AC is the average cost and MC is the marginal cost, then Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) AC decreases with x | (I) when MC = AC | | (B) AC increases with x | (II) when MC < AC | | (C) AC doesn't change with x | (III) when MC = 0 | | (D) C is constant. | (IV) when AC < MC | Choose the correct answer from the options given below:

Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Mean of a normal variate X is 12 and standard deviation is 4, then the Z-score of data point 20 is | (I) 1 | | (B) If X is Poisson variate such that P(X=1) = 2P(X=2), then the mean of X is | (II) 8 | | (C) In a binomial distribution, if mean is 5 and variance is 4, then the number of trials is | (III) 2 | | (D) In a binomial distribution, if n = 20 and q = 0.6, then its mean is | (IV) 25 | Choose the correct answer from the options given below:

Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) The solution set of the inequation $3x-6\le 0$ is | (I) $(3,\infty)$ | | (B) The solution set of the inequation $-5x+20<0$ is | (II) $[3,\infty)$ | | (C) The solution set of the inequation $3x-9\ge 0$ is | (III) $(-\infty,2]$ | | (D) The solution set of the inequation $8x+11>35$ is | (IV) $(4,\infty)$ | Choose the correct answer from the options given below:

If the following table represents the three yearly moving averages of a data, then the value of $\frac{a+b+c+d}{3}$ is- | Year | Value | 3-yearly moving average | |---|---|---| | 1 | 2 | | | 2 | a | 4 | | 3 | 6 | b | | 4 | 8 | 7 | | 5 | c | 9 | | 6 | 12 | d | | 7 | 11 | |

If the objective function for a LPP is $Z=3x+5y$ and the corner points of the bounded feasible region are (0, 0), (6, 0), (3, 5) and (0, 3), then the value of $|max(Z) - min(Z)|$ is:

Which of the following is correct about the sinking fund?

The differential equation representing family of circles with centre at origin and radius r units is-

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

If A and B are square matrices of order n, such that AB = A and BA = B, then $A^2$ =

In a printing press of a publication house, there is a small chance $\frac{1}{1000}$ for any typing error in 20 pages, then the number of pages containing no error in printing two volumes of an Encyclopedia containing total 10000 pages are: [Given: $e^{-0.02}=0.9802$]

In a race of 1000 metres, X gives Y a start of 175 m and defeats him by 50 seconds. If speed of X is 5 m/s, then the speed of Y is