CUET Mathematics 2026 PYQs19 May Shift 2. Free, no login required.

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

The integral $I = \int \frac{(1+\log_e x)^3}{x} dx$ is equal to

Mr. Devendra invested ₹ 8,000 in 7% hundred rupee share at ₹ 80. After a year he sold these share at ₹ 75 each and invested in 18% twenty five-rupee shares at ₹ 41 each. Then his annual income from the second investement is:-

If $f(x) = \begin{vmatrix} 1 & x & x^2 \\ x & x^2 & 1 \\ x^2 & 1 & x \end{vmatrix}$, then the value of $f(\sqrt[3]{3})$ is

Which of the following matrices are diagonal matrices? A. $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$ B. $\begin{bmatrix} 1 & 2 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$ C. $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ D. $\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | LIST-I Inequality | | LIST-II Solution set | | |---|---|---|---| | A. | $4x + 3 \le 6x + 7$ | I. | $x \in (-\infty, -2)$ | | B. | $5x - 5 > 3x - 1$ | II. | $x \in (-\infty, 2]$ | | C. | $4x - 9 > 6x - 5$ | III. | $x \in [-2, \infty)$ | | D. | $3x - 1 \le 5$ | IV. | $x \in (2, \infty)$ | Choose the correct answer from the options given below:

A car hire firm has two cars, which is hire out day by day. The number of demands for cars on each day is distributed as a Poisson distribution with mean 1.5. Then which of the following is/are TRUE? (use $e^{-1.5} = 0.2231$) A. The probability of days when no car is required is 0.2231 B. The probability of days when some demand is refused is 0.1913 C. The probability of days when no car is required is 0.1913 D. The probability of days when some demand is refused is 0.2231 Choose the correct answer from the options given below:

If m and n are the order and degree of the differential equation $9\frac{d^3y}{dx^3} = \left\{1 + \left(\frac{dy}{dx}\right)^2\right\}^{5/2}$, then the value of $2m+3n$ is equal to

The demand function for a certain product is represented by $p = 35 + 5x - 3x^2$, where $x$ is the number of units demanded and $p$ is the price per unit. The marginal revenue when 2 units are sold is

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

Ram took a home loan of ₹ 45,00,000 at the rate of 6% per annum for 25 years. His EMI by using flat rate method is

The area (in sq. units) of region bounded by the curves $y^2 = 4x$ and $y = x$ is:

A person has invested ₹ 20,000 in hundred-rupees bond and redeemable at the end of 10 years at 110, and paying annual dividends at 4%. The yield rate is to be 5% effective. Then which of the following statements are TRUE? A. The annual dividend is ₹ 800. B. The annual dividend is ₹ 1200. C. Redemption price is ₹ 22000. D. Redemption price is ₹ 20000. Choose the correct answer from the options given below:

The value of $3^{16} \pmod 4$ is:

If A is a square matrix such that $A^2 = I$, then $(A+I)^3 + (A-I)^3 - 7A$ is equal to

In a LPP, Let R be the feasible region, then which of the following are TRUE? A. If R is bounded, then the objective function Z has both a maximum and minimum value on R. B. If R is unbounded, then the objective function Z may or may not have a maximum or minimum value. C. If a optimal solution exists. It must occur at atleast one corner point of R. D. If R is bounded, then maximum value will exist but minimum may or may not exist for an objective function Z. Choose the correct answer from the options given below:

The rise in prices of vegetables due to flood is an example of

If $X$ is a discrete random variable which assumes values $x_1, x_2, x_3, ..., x_n$ with the respective probabilities $p_1, p_2, ....., p_n$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\displaystyle\sum_{i=1}^{n} p_i =$ | I. | $E(X^2)$ | | B. | $\displaystyle\sum_{i=1}^{n} p_i x_i =$ | II. | $Var(X)$ | | C. | $\displaystyle\sum_{i=1}^{n} p_i x_i^2 =$ | III. | $1$ | | D. | $E(X^2) - \{E(X)\}^2 =$ | IV. | $E(X)$ | Choose the correct answer from the options given below:

Which of the following are true about the properties of transpose of appropriate matrices? A. $(A+B)^T = A^T + B^T$ B. $(A-B)^T = A^T - B^T$ C. $(AB)^T = A^TB^T$ D. $(kA)^T = k(A^T)$, where k is a scalar Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I<br>Criteria | | LIST-II<br>Types of biasness | |---|---|---|---| | A. | When individual has choice to choose to participate. | I. | Convenience | | B. | If sample gives less representation of the sample. | II. | Response bias | | C. | When a sample is taken from individual that are conveniently available. | III. | Voluntary response bias | | D. | Anything in a survey that influence responses. | IV. | Undercover | Choose the correct answer from the options given below:

If the cash equivalent of a perpetuity of ₹ 1200 payable at the end of each quarter is ₹ 96,000, then the rate of interest convertible quarterly is:

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours. The speed of the current is:

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:

Three pipes A, B and C can fill a tank together in 8 hours. After working at it together for 2 hours, B is closed and A and C can fill the remaining part in 9 hours. The time in which B alone can fill the tank is :

An electric scooter costs ₹ 36,000 and has a useful life of 15 years. If annual depreciation is ₹ 2,000, Its scrap value by using linear method of depreciation is:

If $x = 3t^2$ and $y = \sqrt{t}$, then the value of $\frac{d^2y}{dx^2}$ is

In a 1000 m race, Arun reaches the final point in 56 seconds and Pradeep reaches in 70 seconds. By how much distance does Arun beat Pradeep?

The interval in which the function $f(x) = -x^2 - 2x + 18$ is decreasing is :

The mean and variance of a Binomial distribution are 4 and 4/3 respectively. The number of trials is

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | Population | I. | A subgroup of members of the population. | | B. | Sample | II. | The measurable characteristic of population. | | C. | Parameter | III. | The measurable characteristic of sample. | | D. | Statistic | IV. | A collection of all elements having same characteristic. | Choose the correct answer from the options given below:

For the given five values 10, a, 13, b, 25, the 3-years moving averages are 15, 18, 19. The value of a+b is

Ravi rides his motor cycle at 25 km per hour, he has to spend ₹ 4 per kilometer on petrol, if he rides at a faster speed of 40 km per hour, the petrol cost increases to ₹ 10 per kilometer. He can spend ₹ 200 on petrol and wishes to maximize distance he can travel within one hour. Which of the following is/are TRUE? A. Maximum distance covered in one hour is 30 km B. The distance covered at speed of 25km/hr is 50/3 km C. The distance covered at speed of 25km/hr is $\frac{25}{2}$ km D. The distance covered at speed of 40km/hr is $\frac{75}{4}$ km Choose the correct answer from the options given below:

Amit invested ₹ 25,000 in a no-fee fund. After one year, the value of the fund rose to ₹ 30,000 then the nominal rate of return on the investment is

A 95% confidence interval for a population mean was reported to be 152 to 160. The margin of error is:

A coin is tossed 5 times, the probability of getting at least 3 heads is:

The number of points of the local maximum value of the function $f(x) = 3x^4 + 4x^3 - 12x^2 + 2$ is,