CUET Mathematics 2025 PYQs19 May Shift 1. Free, no login required.

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then the value of $A^{20}$ is:

If $e^x + e^y = e^{x+y}$, then $\frac{dy}{dx}$ =

The value of $\int_0^1 x e^x dx$ is:

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below? <img src="https://balti.afterboards.in/BMA5vBPSyJrH2hF" width="300px"/>

The area (in sq. units) bounded by the parabola $y^2 = 4ax$, its latus rectum and the $x$-axis in the first quadrant is:

If $A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -3 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 3 \\ 4 & -5 \\ 1 & 2 \end{bmatrix}$, then which of the following statements are TRUE? (A) AB is defined (B) AB and BA both are defined and AB = I, where I is an identity matrix of order 2 (C) BA is defined (D) AB and BA both are defined and AB = BA Choose the correct answer from the options given below:

Consider the Linear Programming Problem Maximize $z = x + y$ Subject to the constraints $x - y \leq -1$, $x \geq y$, $x \geq 0, y \geq 0$ Then which one of the following is TRUE?

Function $f(x) = x^3 - 3x + 3$ is (A) Increasing in the interval $(-1, 1)$ (B) Increasing in the interval $(1, \infty)$ (C) Decreasing in the interval $(-1, 1)$ (D) Increasing in the interval $(-\infty, -1) \cup (1, \infty)$ Choose the correct answer from the options given below:

Let X denotes the number of hours a person uses a mobile and the probability distribution of X is as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | K | 2K | 2K | K | Then the value of K is

The maximum value of $\sin x \cdot \cos x$ is:

Match List-I with List-II | List-I | List-II | |---|---| | Differential Equation | Order and degree of differential equation | | (A) $\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^2 = e^{\frac{dy}{dx}} + 1$ | (I) Order = 1, Degree = 2 | | (B) $\left(\frac{d^2y}{dx^2}\right)^2 + 4\left(\frac{dy}{dx}\right)^3 = e^y - 1$ | (II) Order = 2, Degree = 1 | | (C) $3\left(\frac{dy}{dx}\right) + 4y + e^y = \frac{dx}{dy}$ | (III) Order = 2, Degree = 2 | | (D) $\frac{d^2y}{dx^2} + 3\left(\frac{dy}{dx}\right) = \left(e^y + \frac{dy}{dx}\right)^2$ | (IV) Order = 2, Degree = Not defined | Choose the correct answer from the options given below:

If A and B are square matrices of the same order 3, such that det (A) = 3 and AB = 3I, where I is an identity matrix of order 3. Then the value of det (B) is:

The general solution of the differential equation $\frac{dy}{dx} = e^{ax+by}$ is: (Here C is an arbitrary constant)

The difference of two different skew-symmetric matrices is:

Value of $\int \frac{2}{(x-3)\sqrt{x+1}} dx$ is: (Here C is an arbitrary constant)

Area of region bounded by the curves $x = y^3$, $x = 0$ between $y = -1$ and $y = 2$ is:

If $\vec{a} = 3\hat{i} - 6\vec{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - 4\vec{j} + \lambda\hat{k}$ are such that $\vec{a} \parallel \vec{b}$, then $3\lambda + 2 =$

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86$, then product of all values of $a$ is:

The function $f(x) = \sin 3x$, $x \in \left[0, \frac{\pi}{2}\right]$ (A) is increasing on $\left[0, \frac{\pi}{6}\right]$ (B) is decreasing on $\left[\frac{\pi}{6}, \frac{\pi}{2}\right]$ (C) is increasing on $\left[0, \frac{\pi}{2}\right]$ (D) is decreasing on $\left[0, \frac{\pi}{2}\right]$ Choose the correct answer from the options given below:

If $\vec{a} = \hat{i} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$ such that $\vec{r} \times \vec{b} = \vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a} = 0$, then $\vec{r}$ is:

Solution of the differential equation $\frac{dy}{dx} = \sqrt{1 + x^2 + y^2 + x^2y^2}$ is : (Here $C$ is an arbitrary constant)

The area (in square units) of the region bounded by the curves $3y^2 = ax$, $y = a$, $a > 0$ and $y$-axis is:

The semi vertical angle of a right circular cone of maximum volume of a given slant height is

If $y^{1/m} + y^{-1/m} = 2x$, then the value of $(x^2 - 1)\frac{d^2y}{dx^2} + x\frac{dy}{dx}$ is:

A function $f: \mathbb{R} \rightarrow \{x \in \mathbb{R}: -1 < x < 1\}$ is defined as $f(x) = \frac{x}{1+|x|}$, then $f$ is:

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probability, that both coins are unbiased is:

In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y-2x \leq 0$, $y \geq 0$, $0 \leq x \leq 5$. The feasible region of the above problem:

The value of k for which the function $f(x) = \begin{cases} \frac{1-\cos 8x}{16x^2}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}$ is continuous at $x = 0$ is:

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of $A^2 - 5A + 6I$ is

The shortest distance between lines $\frac{-x-3}{4} = \frac{y-6}{3} = \frac{z}{2}$ and $\frac{-x-2}{4} = \frac{y}{1} = \frac{z-7}{1}$ is:

If A and B are independent events, then which of the following statements are TRUE? (A) $P(A \cap B) = P(A).P(B)$ (B) $P(A \cap B) = P(A) - P(B)$ (C) $P(A \cup B) = P(A) + P(B) - P(A).P(B)$ (D) $P(A \cap B) = P(A). P(B|A)$ Choose the correct answer from the options given below:

If $2f(x) + f\left(\frac{1}{x}\right) = x^2 + 1$, then $\int f(x) dx$ is: (Here C is an arbitrary constant)

Distance of the point $(2, 4, -1)$ from the line $\frac{10+2x}{2} = \frac{y+3}{4} = \frac{6-z}{9}$ is

If a matrix P is both symmetric and skew-symmetric, then

Match List-I with List-II | List-I | List-II | |---|---| | Differential Equation | Integrating Factor | | (A) $y dx + (x - y^3)dy = 0$ | (I) $e^{-x}$ | | (B) $x\frac{dy}{dx} + y = x^2$ | (II) $\frac{1}{x}$ | | (C) $\frac{dy}{dx} - y = e^x$ | (III) $y$ | | (D) $x dy - y dx = x^3 dx$ | (IV) $x$ | Choose the correct answer from the options given below:

If matrix $A = \begin{bmatrix} p & -3 \\ -4 & p \end{bmatrix}$ and $|A^3| = 64$, then the value of p is:

Match List-I with List-II Let A and B be any two events | List-I | List-II | | --- | --- | | (A) $P(A')$ | (I) $\frac{P(A \cap B)}{P(A)}; P(A) \neq 0$ | | (B) $P(\phi)$ | (II) $\frac{P(A \cap B)}{P(B)}; P(B) \neq 0$ | | (C) $P(A\vert B)$ | (III) $1 - P(A)$ | | (D) $P(B\vert A)$ | (IV) 0 | Choose the correct answer from the options given below:

If $C_{ij}$ represents the cofactor of element $a_{ij}$ of the matrix $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & 0 \\ 4 & 1 & 5 \end{bmatrix}$ then the value of $C_{23} + C_{31} - C_{22}$ is

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\cos^{-1} x + \cos^{-1}(-x)$ | (I) $\frac{\pi}{3}$ | | (B) $\text{cosec}^{-1}(-x) + \sec^{-1}(-x)$ | (II) $-\frac{\pi}{3}$ | | (C) $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$ | (III) $\pi$ | | (D) $\tan^{-1}\left(\tan\frac{4\pi}{3}\right)$ | (IV) $\frac{\pi}{2}$ | Choose the correct answer from the options given below:

The minimum value of the function $f(x) = x^3 + (10-x)^3$ occurs at:

Match List-I with List-II | List-I | List-II | |---|---| | Mathematical Statement | Value | | (A) $\hat{i} \cdot (\hat{j} \times \hat{k})$ | (I) $-\hat{k}$ | | (B) $\hat{j} \cdot (\hat{i} \times \hat{k})$ | (II) 1 | | (C) $\hat{i} \times (\hat{j} \times \hat{k})$ | (III) -1 | | (D) $\hat{j} \times \hat{i}$ | (IV) $\vec{0}$ | Choose the correct answer from the options given below:

If the line $\frac{-x+1}{3} = \frac{-y-2}{-2k} = \frac{z+3}{2}$ and $\frac{-1+x}{3k} = \frac{-1 +y}{1} = \frac{-z+6}{5}$ are perpendicular, then the value of k is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\int_{-a}^a f(x) dx = 0$ | (I) 0 | | (B) $\int_0^{2a} f(x) dx = 2\int_0^a f(x) dx$ | (II) 1 | | (C) $\int_{-\pi}^{\pi} \cos x dx$ | (III) $f$ is an odd function | | (D) $\int_{-1}^1 x^{101} dx + 1$ | (IV) $f(2a-x) = f(x)$ | Choose the correct answer from the options given below:

The relation R in $\mathbb{R}$ (set of real numbers) is defined by $R = \{(a,b): a \leq b^3\}$, then R is

If $A = \begin{bmatrix} 2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0 \end{bmatrix}$, then the value of det (adj (2A)) is:

$\int \tan^{-1}\sqrt{x} $ $dx$ equals to: (Here C is an arbitrary constant)

If $x = e^{\cos 2t}$, $y = e^{\sin 2t}$, then $\frac{dy}{dx}$ equals to

If $|\vec{a}| = 1$, $|\vec{b}| = 2$, $|2\vec{a}+\vec{b}| = 2\sqrt{3}$ then $|\vec{a}-\vec{b}|$ is:

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0, 0)$, $(2, 4)$, $(0, 5)$ and $(4, 0)$. If the maximum value of $z = ax + by$, where $a, b > 0$ occurs at both $(2, 4)$ and $(4, 0)$, then

The value of the definite integral $I = \int_0^2 x\sqrt{2-x} dx$ is:

If X is a normal variate with mean 16 and standard deviation 4, then the value of standard normal variate Z corresponding to X = 17 is:

If a revenue function is given by $R(x) = 2027x - 1013x^2 - 675x^3$, then the marginal revenue function (MR) is:

A furniture trader deals in only two items - chairs and tables. He has Rs. 50,000 to invest and a space to store almost 35 items. A chair costs him Rs. 1000 and a table costs him Rs. 2000. The trader earns a profit of Rs. 150 and Rs. 250 on a chair and a table, respectively. Choose the correct option among following that describes the given linear programming problem (LPP) to maximize the profit ( where x and y are the number of chairs and tables that trader buys and sells)?

An automobile dealer wishes to buy four luxury cars of different brands given in the table below with some down payment and balance in equal monthly installments (EMI) for 10 years. The bank charges 9% interest per annum compounded monthly. $\left( {Given } \frac{0.0075 \times(1.0075)^{120}}{(1.0075)^{120}-1} = 0.01266\right)$ | Luxury Car | Price of the Car (in Rs.) | Down payment (in Rs.) | |---|---|---| | P | 25,00,000 | 5,00,000 | | Q | 35,00,000 | 12,00,000 | | R | 45,00,000 | 15,00,000 | | S | 42,00,000 | 15,00,000 | Match List-I with List-II | List-I | List-II | |---|---| | Luxury Car | EMI (in Rs.) | | (A) P | (I) 34,182 | | (B) Q | (II) 37,980 | | (C) R | (III) 29,118 | | (D) S | (IV) 25,320 | Choose the correct answer from the options given below:

A steamer can row at the speed of 16km/hr in still water. If the river is flowing at 8 km/hr and it takes 12 hours for a round trip, then the distance between the two places is:

If 95% confidence interval for the population mean was reported to be 140 to 150 and $\sigma = 25$, then size of the sample used in this study is: [Given: $Z_{0.025} = 1.96$]

The following data shows the percentage of urban Indian households who have a high speed 5G internet connection: | Year (x) | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---| | Urban house hold (y) | 9% | 18% | 21% | 29% | 38% | If a straight line trend by the method of least square for the above data is $y = 23 + 6.9(x - 2022)$, then the forecast for the year 2025 is:

Which of the following are types of "statistical inferences"? (A) Point estimation (B) Interval estimation (C) Marginal estimation (D) Hypothesis testing Choose the correct answer from the options given below:

The unit digit of $12^{12}$ is:

In what ratio a grocery shopkeeper mix two varieties of pulses worth Rs. 85 per kg and Rs. 100 per kg respectively, so as to get a mixture worth Rs. 92 per kg?

For the function $f(x) = x^{1/x}$, $x > 0$, which of the following are correct? (A) $x = 0$ is the only point where extremum may occur. (B) The given function is maximum at $x = e$. (C) The function has no extreme value for $x > 0$. (D) The maximum value of the function $f(x)$ is $e^{1/e}$. Choose the correct answer from the options given below:

For the given five values, 15, 24, 18, 33, 42, the three-year moving averages are

The area of the region bounded by the curves $y = x^2 + 2$ and $x$-axis, between $x = 0$ and $x = 3$ in the first quadrant is:

Which of the following statements are correct? (A) If A is a square matrix, then $|A^2| = |A|^2$. (B) If A and B are square matrices of the same order, then det (AB) = det (A) + det (B). (C) If A is a square matrix of order 3 and $|A|=2$, then the value of $|-3A|$ is 54. (D) If the matrix $\begin{bmatrix} 5 -x & x -1 \\ 3 &5 \end{bmatrix}$ is singular, then the value of x is 7/2. Choose the correct answer from the options given below:

In 5 trials of binomial distribution, the probability of 3 successes is 4 times the probability of 2 successes. The probability of success in each trial is:

Match List-I with List-II | List-I | List-II | | --- | --- | | (Inequality) | (Solution Set) | | --- | --- | | (A) $2x - 3 < x + 2 \le 3x + 5, x \in \mathbb{R}$ | (I) $x \in (-1, \infty)$ | | (B) $\vert 2x + 3\vert < 7, x \in \mathbb{R}$ | (II) $x \in (-\infty, 120]$ | | (C) $\frac{1}{2}\left(\frac{3}{5}x + 4\right) \ge \frac{1}{3}(x - 6), x \in \mathbb{R}$ | (III) $x \in (-5, 2)$ | | (D) $\frac{\vert x + 1\vert }{x + 1} > 0, x \in \mathbb{R} - \{-1\}$ | (IV) $x \in \left[-\frac{3}{2}, 5\right)$ | Choose the correct answer from the options given below:

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

If the slope of the tangent to the curve $y = y(x)$ at any point $(x, y)$ is $\frac{2x}{y^2}$ and the curve passes through the point $\left(\frac{1}{\sqrt3}, 1\right)$, then equation of curve is

Which of the following are examples of irregular trends in a time series? (A) Decrease in production due to a sudden strike. (B) The rise in prices before festivals (C) Unusual rise in income of the printing press due to the announcement of an election. (D) Fall in crop yield due to floods. Choose the correct answer from the options given below:

Three bad eggs are mixed with 7 good ones. If two eggs are drawn one by one without replacement, then the probability distribution of the number (X) of bad eggs drawn is: | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | 1/4 | 1/2 | 1/4 | | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | 15/61 | 20/61 | 26/61 | | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | 7/15 | 7/15 | 1/15 | | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | 1/8 | 1/4 | 5/8 |

Mr. Mittal invested Rs. 20,000 in a mutual fund in the year 2019. The value of the mutual fund increased to Rs. 32,000 in the year 2024. The compound annual growth rate of his investment is: [Given $(1.6)^{1/5} = 1.098$]

If the matrix $M = \begin{bmatrix} 0 & -1 & 3\alpha \\ 1 & \beta & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew-symmetric, then

Pipe A can fill the tank 3 times faster than pipe B. If both pipes A and B running together can fill the tank in 15 minutes, then the time taken by B alone to fill the tank is:

If $y = \sqrt{x + \sqrt{x + \sqrt{x + ...\ ...\ ...}}}$, then

Which of the following is NOT correct about "Sinking Fund"?

If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are A(0,2), B(3, 0), C(2, 3) and D(3, 1), then the maximum value of the objective function $Z = 4x + 2y$ occurs at

The value of a depreciable asset at the end of its useful life is called ____.

Consider the following hypothesis test: $H_0: \mu = 18$ $H_1: \mu \neq 18$ If a sample of 48 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $\sigma = 4.5$, then the value of the t-test statistic is:

If A is a non-singular matrix of order 3 such that $|adj(A)| = 121$, then $|AA^T|$ is equal to:

If the system of equations $2x + 3y = 10$, $x + ky = 4$ has a unique solution, then

What sum of money is needed to invest now, so as to get Rs. 5000 at the beginning of every month forever, if the money is worth 6 % per annum compounded monthly?

A person has taken a loan of Rs. 40,000 for 3 months from a lender who has deducted Rs.2,000 as interest at the time of lending. Then the effective rate of interest charged per annum by lender is (given:$(1.0526)^4 = 1.2275):$

In a 700 m race, the ratio of speeds of two participants A and B is 5:6. If A has a start of 150 m, then the distance by which A wins the race is:

Let $A = \begin{bmatrix} 0 & 2\alpha+1 \\ \ 1& \beta \end{bmatrix}$ and $B = \begin{bmatrix} b_{ij}\end{bmatrix}$ be a skew symmetric matrix of order 2 such that $b_{12} = 1$. If $AB = I_2$ where $I_2$ is identity matrix of order 2, then