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

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,