CUET Mathematics 2026 19th May Shift 2 PYQs

The area bounded by the curve defined by $x = 2\cos\theta$ and $y = 3\sin\theta$; is [where $\theta$ is a parameter]

If A is a square matrix of order $n$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert A(\text{adj }A) \vert$ | I. | $\vert A \vert^{n-1}$ | | B. | $\text{adj}(\text{adj }A)$ | II. | $\vert A \vert I$, where $I$ is the identity matrix of order $n$ | | C. | $\vert \text{adj }A \vert$ | III. | $\vert A \vert^{n-2} A$ | | D. | $A(\text{adj }A)$ | IV. | $\vert A \vert^n$ | Choose the correct answer from the options given below:

Refer to the LPP given by $Z = 2.5x + y$, subject to constraints $3x + y \le 12; 3y + x \le 12; x, y \ge 0$: In the given figure, If $Z_A$ = value of Z at A, $Z_C$ = value of Z at C and Max.(Z) = maximum value of Z, then which of the following relations between $Z_A$, $Z_C$ and Max.(Z) are correct? <img src="https://balti.afterboards.in/NicbC8snv3eouyH" width="400px"/> A. $2Z_A = 5$ Max.(Z) B. $5Z_A = 2Z_C$ C. $Z_A = 6 + Z_C$ D. $6+Z_A = Z_C$ Choose the correct answer from the options given below:

A die is thrown thrice. If the first throw is a four, then the chance of getting 11 as total sum, is

Which of the following statements are TRUE? A. Order of the differential equation is the order of highest differential appearing in the differential equation. B. Degree of a differential equation is a real number. C. Order of a differential equation is whole number. D. Degree of a differential equation is the degree of the highest order derivative, when differential coefficients are free from radicals and fractions. Choose the correct answer from the options given below:

Solution of differential equation $\frac{dy}{dx} = e^{x-y} + 3x^2 e^{-y}$ is: (where C is an arbitrary constant)

The derivative of $|x|$ with respect to $x$, where $x \in R \sim \{0\}$ is

If A and B are two square matrices of order 'n', where $AB \neq BA$, then

A matrix which is both symmetric and skew symmetric is a

Let A be a square matrix of order 3 and I is an identity matrix of order 3. If $|A| = 3$, the value of $|A(4I)|$ is

The value of $\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}$ is:

The area bounded by the curve $|-x|+|-y|=2$ is

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then $A^{26}$ is equal to

$\int 5^x dx$ is (where C is an arbitrary constant)

Function $f(x) = x + \frac{1}{x}, x \neq 0$ is increasing in the interval

Match the LIST-I with LIST-II [Where R and Z denotes set of real numbers and set of integers respectively] | | LIST-I<br>Function | | LIST-II<br>Nature | |---|---|---|---| | A. | $f: R \to R, f(x) = \sin^2 x + \cos^2 x$ | I. | Bijective | | B. | $f: Z \to Z, f(x) = x^3$ | II. | Surjective but not injective | | C. | $f: R \to R, f(x) = x^3 - x$ | III. | Injective but not surjective | | D. | $f: R \to R, f(x) = 3 - 4x$ | IV. | Neither injective nor surjective | Choose the correct answer from the options given below:

The angle between two lines whose direction ratio are proportional to $(-\theta, -2\theta, \theta)$ and $(-2\theta, \theta, \theta)$, where $\theta \in \mathbb{R} \sim \{0\}$, is

The absolute maximum value of the function $f(x) = \frac{x}{2} + \frac{2}{x}$ in the interval $[-3, 3]$, is

$\int_1^4 \frac{\{x\}}{[x]} dx$ is equal to [Where $\{x\}$ = fractional part function and $[x]$ = greatest integer function]

Let X be a non-empty set and let P be the collection of all subsets of X. Let R be a relation in P, defined by $R = \{(A, B): A \text{ is subset of } B\}$. Then, R is A. Reflexive relation B. Symmetric relation C. Not a transitive relation D. Transitive relation Choose the correct answer from the options given below:

For the constriants $x + y \le 60$, $5x + y \le 100$ and $x \ge 0, y \ge 0$, the feasible region is: <img src="https://balti.afterboards.in/gfreR046lrZ4WWe" width="400px"/>

A coin is tossed thrice, and events E and F are defined as: E : "The first throw results in a head" F : "The last throw results in tail" Then, which of the following statements is true for events E and F?

A coin is tossed four times. The probability of getting atleast 1 head before getting the first tail is

The equation of the curve that passes through $(-1, 1)$ and the slope of line touching to the curve at any point $(x, y)$ is $\frac{3x^2}{y}$, is:

$\int \frac{\log x - 3}{(\log x)^4} dx$ is equal to (where C is an arbitrary constant and $\log_e x = \log x$)

Which one of the following is TRUE?

Match the LIST-I with LIST-II | | LIST-I<br>Characteristic of square matrix | | LIST-II<br>Type of matrix | |---|---|---|---| | A. | A is a square matrix such that $A + A^T = 0$. | I. | Identity matrix or scalar matrix | | B. | B is a square matrix such that $B^2 = B$ | II. | Diagonal matrix | | C. | C is a square matrix with all equal diagonal element and all the non-diagonal elements are zero. | III. | Skew symmetric matrix | | D. | D is a matrix such that all the non-diagonal elements are zero. | IV. | Idempotent matrix | Choose the correct answer from the options given below:

The value of $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is negative, if

If A and B are square matrices of same order such that, $AB=BA$, $A^{-1} = A^2$ and $B^{-1} = B^3$, then the value of $(AB)^{2040}$, is

Observe the graph of a function $y = f(x)$ and identify the correct statements (s): <img src="https://balti.afterboards.in/yTiOrT3AAuhsTbm" width="400px"/> A. Function is continuous but not differentiable at $x = a$ B. Function is not defined at $x = a$ C. Function is defined at $x = a$ but not differentiable. D. Given that at $x = a, y = b$. Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I<br>Curve $y = f(x)$, where $f(x)$ is | | LIST-II<br>Nature / derivative / value of $y = f(x)$ | |---|---|---|---| | A. | $x\vert x \vert$ | I. | $y'$ is 2 for all $x \in R^+$ (set of positive real numbers) | | B. | $x + \vert x \vert$ | II. | $y'$ is 2 for all $x \in R^-$ (set of negative real numbers) | | C. | $x - \vert x \vert$ | III. | $f(-5) = -1$ | | D. | $\dfrac{x}{\vert x \vert}$ | IV. | $(0, 0)$ is the point of inflection | Choose the correct answer from the options given below:

Let $\vec{a}$ and $\vec{b}$ be two vectors, such that $|\vec{a}| = 3, |\vec{b}| = 5$ and the angle between them is $60°$, then the value of $|\vec{a} + \vec{b}|$ is

If $\theta$ is angle between $\vec{a}$ & $\vec{b}$, then for vectors $\vec{a}, \vec{b}$ and $\vec{c}$, Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}, \vec{a} \neq 0, \vec{b} \neq \vec{c}$ | I. | $\theta = \dfrac{\pi}{4}$ | | B. | $\vec{a} \times \vec{b} = 0$ | II. | $\vec{a} \parallel (\vec{b} - \vec{c})$ | | C. | $\vert \vec{a}.\vec{b} \vert = \vert \vec{a} \times \vec{b} \vert$ | III. | $\vec{b} = \vec{c}$ | | D. | $\vec{a}.\vec{b} = \vec{a}.\vec{c}$ and $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$, $\vec{a} \neq 0$ | IV. | $\vec{a} = 0, \vec{b} = 0$ or $\vec{a} \parallel \vec{b}$ | Choose the correct answer from the options given below:

Two linear programming problems (LPPs) have same bounded feasible region with three corner points $(0, 3), (4, 4), (7, 0)$. If $Z_1 = x - 3y$ and $Z_2 = 2x + y$ are objective functions of LPPs, then which of the following is/are correct? A. only $Z_1$ maximizes at $(7, 0)$. B. both $Z_1, Z_2$ minimize at $(0, 3)$. C. both $Z_1, Z_2$ maximize at $(7, 0)$. D. $Z_2$ maximizes at $(4, 4)$. Choose the correct answer from the options given below:

Area bounded by the curves $y = \cos^2 x, x = 0, y = 0$ and $x = \pi$, is:

Let $f(x) = x^3 - 3ax$, where $a > 0$, then the values for which $f(x)$ is decreasing, are

If $\begin{vmatrix} 1+x^2 & 1 & 1 \\ 1 & 1+y^2 & 1 \\ 1 & 1 & 1+z^2 \end{vmatrix} = k\left(1 + \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right)$ then $k$ is equal to

Area bounded by the curves $y = 3^x, y = x$ and $x = 1, x = 2$ is:

If $f(x+y) = f(x) + f(y)$ for all $x, y \in R$ (set of real numbers) and $f(x)$ is continuous at $x = 0$, then identify the correct statement ?

A beg contains 4 white and 6 red balls. Four balls are drawn at random, then match the probability of the numbers of white balls drawn. Where P(E) denotes the probability of an event E. Then Match List-I with List-II | LIST-I | | LIST-II | | |---|---|---|---| | A. | P (no white ball) | I. | $\frac{8}{21}$ | | B. | P (all white balls) | II. | $\frac{1}{14}$ | | C. | P (one white ball) | III. | $\frac{6}{14}$ | | D. | P (two white balls) | IV. | $\frac{1}{210}$ | Choose the correct answer from the options given below:

If the lines $\frac{x-1}{2} = \frac{y-m}{3} = \frac{z-3}{4}$ and $\frac{x-4}{5} = \frac{y-1}{2} = z$ are interesecting, then the value of $m$, is

If the sum of the length of the hypotenues and a side of a right angled triangle is L cm then the angle between hypotenuse and other side of the triangle for which the area of the triangle is maximum, is:

4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is:

If $\vec{a}$ and $\vec{b}$ are two perpendicular vector whose direction ratios are $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$, then which of the following is a true statement?

Points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ at a distance of 5 units from the point $(1, 3, 3)$, are

The general solution of the given differential equation $dy + (2y - e^{-2x})dx = 0$, is: [where c is an arbitrary constant]

Vectors $\vec{a}, \vec{b}, \vec{c}$ are such that $\vec{a} + \vec{b} + \vec{c} = 0$ and $|\vec{a}| = |\vec{b}| = |\vec{c}|$ then, the angle between any two of them, is

The value of $\begin{vmatrix} \log_3 512 & \log_4 3 \\ \log_3 8 & \log_4 9 \end{vmatrix}$ is:

For the function $f(x) = -2|\log_e|x||$, which of the following is true?

If $x \in N$(Set of Natural Numbers) and $\begin{vmatrix} x+3 & -2 \\ -3x & 2x \end{vmatrix} = 8$, then the value of $x$ is