CUET Mathematics 2026 PYQs18 May Shift 1. Free, no login required.

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$, $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$, when $z$ is maximum at $D(4,10)$ and $C(6,8)$, is: <img src="https://balti.afterboards.in/F4sq6T1IDmhbV95" width="400px"/>

Which of the following differential equations are of order 2 and degree 1? (A). $\frac{d}{dx}\left(\frac{dy}{dx}\right) + x\frac{dy}{dx} = y$ (B). $\frac{d^2y}{dx^2} + x = \sqrt{\frac{dy}{dx} - y}$ (C). $\left(\frac{dy}{dx}\right)^2 + \frac{d^2y}{dx^2} = \log x$ (D). $\left(\frac{dy}{dx}\right)^2 + \frac{dy}{{dx}} = 3$ Choose the correct answer from the options given below:

If $y = a\log x + bx^2 + x$ has extreme values at $x = 1$ and $x = 2$, then

Area bounded by the curve $y^2 = 4x$ and the lines $y = 2$ and $x = 0$ is

The solution of the differential equation $x\frac{dy}{dx} = 2x^2 + 1$; $x \neq 0$ with $y = 1$ when $x = 1$, is

The value of $\int \frac{dx}{1+\sqrt{x}}$ is

If $A$ is a square matrix of order $3 \times 3$ and $|adj\ A| = 4$, then Match List-I with List-II | List-I | List-II | |---|---| | (A) $\left\vert A^{-1} \right\vert$ | (I) $108$ | | (B) $\left\vert 3\,\text{adj}A \right\vert$ | (II) $\pm\dfrac{1}{2}$ | | (C) $\left\vert 2A \right\vert$ | (III) $\pm8$ | | (D) $\left\vert A.\text{adj}A \right\vert$ | (IV) $\pm16$ | Choose the correct answer from the options given below:

Solution of differential equation $\frac{dy}{dx} = e^{x+y} - xe^y$ is

A die is thrown and a coin is tossed. The probability that the outcome will be a number greater than 4 or a head or both is

If $A$ is a square matrix of order 3 such that $A(adj\ A) = \begin{bmatrix}-2 & 0 & 0\\ 0 & -2 & 0\\ 0 & 0 & -2\end{bmatrix}$, then $|adj\ A|$ is equal to

The sum of a matrix $A$ and its transpose is $\begin{bmatrix}6 & -1\\ -1 & 4\end{bmatrix}$. Which of the following statements is true?

Match List-I with List-II | List-I | List-II | |---|---| | **Integral** | **Value of the integral** | | (A) $\displaystyle\int_{1}^{2} e^{2\log x} \, dx$ | (I) $\log 2$ | | (B) $\displaystyle\int_{-1}^{1} \left\vert x \right\vert \, dx$ | (II) $\dfrac{1}{2}$ | | (C) $\displaystyle\int_{0}^{1} \log e^x \, dx$ | (III) $\dfrac{7}{3}$ | | (D) $\displaystyle\int_{1}^{2} \dfrac{1}{x} \, dx$ | (IV) $1$ | Choose the correct answer from the options given below:

If a matrix has 7 elements, then it can be a (A) Scalar matrix (B) Symmetric matrix (C) Column matrix (D) Row matrix Choose the correct answer from the options given below:

If $y = (1+x)(1+x^2)(1+x^4)$, then $\frac{dy}{dx}$ at $x = -1$ is

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

Match List-I with List-II | List-I Differential equation | List-II Order and degree | |---|---| | (A) $\frac{d^4y}{dx^4} + \sin\left(\frac{d^3y}{dx^3}\right) = 0$ | (I) order = 2, degree = 1 | | (B) $\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} = 0$ | (II) order = 3, degree = 1 | | (C) $\frac{d^3y}{dx^3} + y^2 + \frac{dy}{dx} = 0$ | (III) order = 2, degree = 2 | | (D) $3y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^4 = 0$ | (IV) order = 4, degree not defined | Choose the correct answer from the options given below:

If the area bounded by curves $y = 2^{kx}$, $x = 0$, $x = 2$ in first quadrant is $\frac{3}{\log 2}$, then $k$ is ($k \neq 0$)

The area of the region bounded by curves $y = |x-4|$, $x = 1$, $x = 5$ and the x-axis is

Let A and B be two independent events. Then which of following statements is not true?

The cartesian equation of a line is $x = ay+b$, $z = cy+d$. It's direction ratios are

Equation of a line passing through (1, 2, -3) which is parallel to the line $\frac{x+2}{3} = \frac{y-3}{-4} = \frac{z+5}{5}$ is

Let $A$ and $B$ be two symmetric matrices of same order, then Match List-I with List-II | List-I | List-II | |---|---| | (A). $AB - BA$ | (I). Neither symmetric nor Skew symmetric | | (B). $BA - 2AB$ | (II). Skew symmetric | | (C). $AB + BA$ | (III). Null matrix | | (D). $(AB)^T - BA$ | (IV). Symmetric | Choose the correct answer from the options given below:

A solid sphere of gold of radius 5 cm, is being melted in a furnace such that the radius is decreasing uniformly. When the radius is 1cm, the rate at which surface area (A) is decreasing w.r.t. time ($t$) is equal to ($\frac{dv}{dt}$ = rate at which volume is decreasing w.r.t. $t$)

If $|\vec{a}| = 2$, $|\vec{b}| = 3$ and $|2\vec{a} - \vec{b}| = 5$, then $|2\vec{a} + \vec{b}|$ equals to

If $f(x) = \sin^{-1}\left(\dfrac{2^{x+1}}{1+4^x}\right)$, then Match List-I with List-II | List-I | List-II | |---|---| | Value of $x$ | $\dfrac{1}{2}f(x)$ | | (A) $x = 0$ | (I) $\tan^{-1}\sqrt{2}$ | | (B) $x = \dfrac{1}{2}$ | (II) $\tan^{-1}4$ | | (C) $x = 1$ | (III) $\dfrac{\pi}{4}$ | | (D) $x = 2$ | (IV) $\tan^{-1}2$ | Choose the correct answer from the options given below:

$\int \frac{1}{x^2+4x+8}dx$ is equal to (Where C is an arbitrary constant)

Match List-I with List-II | List-I | List-II | |---|---| | (A) $\displaystyle\int_{\pi/6}^{\pi/3} \cos x \, dx$ | (I) $0$ | | (B) $\displaystyle\int_{-\pi}^{\pi} (\sin^{61}x + x^{123}) \, dx$ | (II) $4$ | | (C) $\displaystyle\int_{0}^{\pi/2} \dfrac{1}{1+\tan^3 x} \, dx$ | (III) $\dfrac{\sqrt{3}-1}{2}$ | | (D) $\displaystyle\int_{-2}^{2} (2 - \left\vert x \right\vert) \, dx$ | (IV) $\dfrac{\pi}{4}$ | Choose the correct answer from the options given below:

If $A$ is a square matrix of order $n \times n$, then which of the following are correct? (A) $|kA| = k^n|A|$, $k$ is a constant (B) $|k\ adjA| = k^n|adjA|^{n-1}$, $k$ is a constant (C) $|adj\ adjA| = |A|^{(n-1)^2}$ (D) $A(adjA) = |A|I$, $I$ is an identity matrix of order $n$ Choose the correct answer from the options given below:

Let a relation $R$ be defined on a set $A = \{1,2,3,4,5\}$ as $R = \{(a,b): |a-b| \text{ is even or zero}\}$. Then which of the following statements is not TRUE?

The corner points of the bounded feasible region determined by $2x+y \leq 10$, $x+3y \leq 15$, $x,y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px+qy$, $p,q > 0$, then the relation between $p$ and $q$ so that the maximum of $z$ occurs at both (3, 4) and (0, 5), is

If $\begin{vmatrix}6 & 7\\ 3 & 8\end{vmatrix} = \begin{vmatrix}3x & 6\\ -1 & x\end{vmatrix}$, then the sum of values of $x$ is equal

If $|\vec{a}| = 5$, $|\vec{b}| = 6$ and $\vec{a}.\vec{b} = 18$, then value of $|\vec{a} \times \vec{b}|$ is

For the function $f(x) = \sqrt{x}$, which of the following statements are true? (A) $f(x)$ is continuous for $x \geq 0$. (B) $f(x)$ is continuous for $x \in R$ (Set of real numbers). (C) $f(x)$ is differentiable for $x > 0$. (D) $f(x)$ is differentiable for $x \in R$ (Set of real numbers). Choose the correct answer from the options given below:

If $\int \frac{1}{\tan x + \cot x}dx = k\cos 2x + C$, where C is an arbitrary constant, then the value of $k$ is

The position vector of the point which divides the join of the points $2\vec{a}-3\vec{b}$ and $3\vec{a}-2\vec{b}$ externally in the ratio 2:3, is:

If $P = \begin{bmatrix}0 & 1\\ 1 & 1\end{bmatrix}$ and $Q = \begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}$, then which of the following are correct? (A) $P+Q$ is a singular matrix. (B) $P-Q$ is a symmetric matrix. (C) $P$ and $Q$ are non-singular matrices. (D) $(P+Q)(P-Q) \neq P^2 - Q^2$ Choose the correct answer from the options given below:

If the corner points of the bounded feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function $z = 2x+3y$ occurs at

Match List-I with List-II | List-I Differential equation | List-II Curve satisfying the differential equation | |---|---| | (A) $\frac{d^2y}{dx^2}+y=0$ | (I) $x^2+y^2=C$: Where C is an arbitrary constant | | (B) $\frac{dy}{dx}+y=\frac{x^2+y}{x}$ | (II) $3e^{-4y}+4e^{3x}=C$: Where C is an arbitrary constant | | (C) $\frac{dy}{dx}+\frac{x}{y}=0$ | (III) $y=\sin x+\cos x+C$: Where C is an arbitrary constant | | (D) $\log(dy/dx)=3x+4y$ | (IV) $y=x+Cxe^{-x}$: Where C is an arbitrary constant | Choose the correct answer from the options given below:

If P and Q are symmetric matrices, then QP-PQ is

If $x = \sqrt{a^{\tan^{-1}t}}$ and $y = \sqrt{a^{\cot^{-1}t}}$, then $\frac{d^2y}{dx^2}$ is

The maximum value of $\Delta = \begin{vmatrix}1 & \sin\theta & 1\\ -\sin\theta & 1 & \sin\theta\\ -1 & -\sin\theta & 1\end{vmatrix}$ is ($\theta$ is real number)

If the function $f(x) = x^2-2kx+7$ is increasing on [1, 5] then $k$ belongs to

The shortest distance between the lines $\vec{r} = 2\hat{i}+3\hat{j}+4\hat{k}+\lambda(\hat{i}-\hat{j}+\hat{k})$ and $\vec{r} = 5\hat{i}+5\hat{j}+5\hat{k}+\mu(-\hat{i}+\hat{j}-\hat{k})$ where $\lambda,\mu \in R$ (set of real numbers) is:

Consider the system of equation $x+y+3z=8$, $2x+y+bz=24$, $x+ay+3z=10$, then which of the following statements are True? (A) The system of equations has a unique solution if $a=2, b=3$ (B) The system of equations is inconsistent if $a=1, b \in R$ be any real number. (C) The system of equations is inconsistent if $a \neq 1$, and $b \neq 6$ (D) The system of equations has a unique solution if $a=4$ and $b=3$. Choose the correct answer from the options given below:

Which of the following statements are correct? (A) $\hat{i} \times (\hat{j} \times \hat{k}) = \vec{0}$. (B) If $|\vec{a}\times\vec{b}|=2$, $\vec{a}.\vec{b}=4$, then $|\vec{a}|^2|\vec{b}|^2=6$. (C) The number of vectors of unit length perpendicular to $\vec{a}$ and $\vec{b}$ are 2. (D) If $\vec{a}$ and $\vec{b}$ represent the diagonals of the rhombus, then $\vec{a}.\vec{b}=0$ Choose the correct answer from the options given below:

A bag contains 3 white and 2 black balls, another bag contains some white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. If the probability of getting a black ball from the selected bag is 8/15, then the number of white balls in the second bag is

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

The value of '$\lambda$' for which the function $f(x) = \begin{cases}\frac{1-\cos 4x}{4x^2}, & \text{if } x \neq 0 \\ \lambda, & \text{if } x = 0\end{cases}$ is continuous at $x=0$, is:

For any two events A and B, which of the following are correct? (A) $P(A\cup B) = P(A)+P(B)-P(A\cap B)$ (B) $P(A) = P(A\cup B)+P(A\cap B)$ (C) $P(A/B) = P(A)/P(B)$ (D) $P(A) = P(A\cap B)+P(A\cap \bar{B})$ Choose the correct answer from the options given below:

If A and B are two events such that $P(A) \neq 0$, $P(B) \neq 1$ and $P(\bar{A}/\bar{B}) = \frac{1-k}{P(\bar{B})}$, then the value of $k$ is

The interval in which the function $f(x) = x^3-3x^2+3x-20$ is increasing, is

The mean of the number of heads in a simultaneous toss of three coins is

Which of the following statements are true? (A) The break-even point is the level of production where the revenue from sales is equal to the cost of production and marketing. (B) If R is the total revenue collected by a company when it sells $x$ units of a product at a price of p per unit, then R is given by $R=px$. (C) Let $C=C(x)$ be the total cost of producing and marketing $x$ units of a product, then marginal cost, $MC=\frac{dC}{dx}$. (D) If AC is the average cost, then $AC=\frac{x}{C}$. Choose the correct answer from the options given below:

The corner points of the bounded feasible region for an L.P.P are (0, 10), (5, 5), (15,15), and (0, 20). If the objective function is $Z=px+qy, p,q>0$, then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at (15, 15) and (0, 20) is

A pump can fill a tank with water in 2 hours. Because of a leak, it took $2\frac{1}{3}$ hours to fill the tank. In how many hours can the leak drain all the water from the tank?

For the inequality $3-2x \geq x-32$, which of the following are true? (A) When $x \in N$ (set of natural numbers), the solution set is $\{1,2,3,\dots,11\}$. (B) When $x \in I$ (set of integers), the solution set is $\{-\infty,\dots,-3,-2,-1,0,1,2,3,\dots 10,11\}$. (C) When $x \in W$ (set of whole numbers), the solution set is $\{0,1,2,3,\dots,11\}$. (D) When $x \in R$ (set of real numbers), the solution set is $(-\infty,\infty)$. Choose the correct answer from the options given below:

There are 50 telephone lines in an exchange. If the probability that any one of them will be busy is 0.1, then the probability that all the lines are busy is

The differential equation satisfied by the equation $y = ae^{bx}$, where $a$ and $b$ are arbitrary constants, is

If $\int e^{3\log x}(x^4+1)^{-1}dx = \frac{m}{n}\log(x^4+1)+C$, where C is an arbitrary constant, $m$ and $n$ are positive integers such that g.c.d $(m,n)=1$, then $(4m^2+n^2)$ is equal to

A company has issued a bond having face value of ₹ 100,000, carrying an annual dividends at 8% and maturing in 12 years. If the prevailing market rate of interest is 9%, then annual dividend is

Match List-I with List-II | List-I | List-II | |---|---| | A is given matrix | $\left\vert \text{adj}(\text{adj}A) \right\vert$ | | (A) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 3$ | (I) $3$ | | (B) Order of A $= 3 \times 3$ and $\left\vert A \right\vert = 2$ | (II) $1$ | | (C) Order of A $= 4 \times 4$ and $\left\vert A \right\vert = 1$ | (III) $16$ | | (D) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 4$ | (IV) $4$ | Choose the correct answer from the options given below:

If the matrix $A = \begin{bmatrix}a & 3 & b\\ c & 0 & -1\\ -2 & 1 & 0\end{bmatrix}$ is skew-symmetric, then $4a+3b+2c$ is equal to

The least non-negative remainder when 64 x 65 x 66 is divided by 67, is

A man can row a boat in still water at the rate of 4 km/hr. He finds that it takes him twice as long to row upstream of a river as to row downstream of the same river, then the speed of the current of the river is

The area (in sq. units) bounded by a parabola $y^2=4x$ and its latus rectum, is

A machine costing ₹ 1,00,000 has a useful life of 5 years. The estimated scrap value is ₹ 20,000. Using linear method, the annual depreciation is

Match List-I with List-II | List-I | List-II | |---|---| | Matrix A | $\left\vert \text{adj}A \right\vert$ | | (A) $\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$ | (I) $2$ | | (B) $\begin{bmatrix} 3 & 0 \\ 1 & 5 \end{bmatrix}$ | (II) $5$ | | (C) $\begin{bmatrix} 6 & -1 \\ 5 & 3 \end{bmatrix}$ | (III) $15$ | | (D) $\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ | (IV) $23$ | Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | Parametric Curve | $\dfrac{dy}{dx} =$ | | (A) $x = t, y = t^2$ | (I) $\dfrac{3}{2}t$ | | (B) $x = t^2, y = t^3$ | (II) $2t$ | | (C) $x = t^3, y = t^2$ | (III) $\dfrac{1}{2t}$ | | (D) $x = t^2, y = t$ | (IV) $\dfrac{2}{3t}$ | Choose the correct answer from the options given below:

The function $f(x) = 2x^3-15x^2+36x+4$ has local maxima at $x=$

Which of the following statements are correct? (A) The mean of a binomial distribution is always greater than the variance. (B) The mean of a Poisson distribution is always greater than the variance. (C) If $f(x)$ is the probability density function of a random variable $X$, then $P(a \leq X \leq b) = \int_a^b f(x)dx$. (D) If $X$ is a random variable and $a,b$ are real numbers, then $Var(aX+b)=a^2Var(X)$. Choose the correct answer from the options given below:

Ram takes a personal loan of ₹ 5,00,000 at the rate of 12% per annum for 3 years. His EMI using a flat rate method is

Match List-I with List-II | List-I | List-II | |---|---| | **Differential equation** | **Order and degree** | | (A) $y''' + x^2(y'')^3 + y = 0$ | (I) $3, 2$ | | (B) $y''' + y^2 + e^{y'} = 0$ | (II) $3, 3$ | | (C) $(y''')^2 + x^2(y'')^3 + xy = 0$ | (III) $3, 1$ | | (D) $(y''')^3 + x(y'')^2 + y = 0$ | (IV) $3, \text{Not defined}$ | Choose the correct answer from the options given below:

If for the following data: | Year ($x_i$) | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |---|---|---|---|---|---|---|---| | Sales (in ₹ crores) ($y_i$) | 6 | 8 | 9 | 11 | 13 | 17 | 20 | If the equation of the straight line trend is $y=a+b(x_i-2013)$, then the trend value for the year 2018 is

If we reject the null hypothesis when it is true, we might be making

Consider the following hypothesis test: $H_0: \mu \leq 25$ $H_a: \mu > 25$ A sample of 25 provided a sample mean of 27.80. The population standard deviation is 5, then the value of the test statistic is

If $A=\begin{bmatrix}1 & 0\\ -1 & 7\end{bmatrix}$, $I=\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}$ and $A^2=8A+kI$, then $k$ is equal to:

Which of the following statements are correct? (A) A sample size of 30 or more is considered to be sufficient to hold the central limit theorem. (B) A survey done using a sample of the population has no margin of error. (C) The measurable characteristic of a population is called parameter. (D) The sample makes an inference about the population. Choose the correct answer from the options given below:

For the given six values 17, 22, 21, 35, 40, 51, the three years moving averages are

The cost of Type 1 rice is ₹ 15 per kg and Type 2 rice is ₹ 20 per kg. If both Type 1 and Type 2 are mixed in the ratio 2:3, then the price per kg of the mixed variety is

For what values of $x$ and $y$, are the following matrices equal? $A=\begin{bmatrix}2x+1 & 3y\\ 0 & y^2-5y\end{bmatrix}$, $B=\begin{bmatrix}x+3 & y^2+2\\ 0 & -6\end{bmatrix}$

Which of the following statements are correct about the compound annual growth rate (CAGR)? (A) CAGR is calculated by using the final and beginning value of an investment. (B) CAGR is compounded annual return of an investment. (C) CAGR describes the effect of compounding. (D) CAGR can be used to demonstrate and compare the performance of investment advisors. Choose the correct answer from the options given below:

If the objective function for an L.P.P is $Z=2x+5y$ and the corner points for bounded feasible region are (8, 0), (2, 3), (3, 5), and (0, 7), then the minimum value of $Z$ occurs at

In a 600 m race, A beats B by 37.5 m or by 10 seconds, then the time taken by B to finish the race is

Which of the following statements are correct about the sinking fund? (A) It is a fixed term account. (B) It is set-up for a particular upcoming expense. (C) In the sinking fund a fixed amount at regular intervals is deposited. (D) It can be used in any emergency. Choose the correct answer from the options given below:

Let $X$ be a discrete random variable whose probability distribution is defined as follows; $P(X=x)=\begin{cases}k(x+1), & x=1,2,3,4\\ 2kx, & x=5,6,7\\ 0, & \text{otherwise}\end{cases}$ where $k$ is constant, then $P(X=5)$ is equal to