CUET Mathematics 2022 25 May Shift 1 PYQs

If A is a square matrix of order 3, B = kA and |B| = $x$|A| then,

The area enclosed by the ellipse $\frac{x^2}{9^2} + \frac{y^2}{6^2} = 1$ is:

The programming problem Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

The differential equation $\frac{dy}{dx} + \frac{x}{y} = 0$, represents the family of curves:

Match List I with List II | LIST I | LIST II | |---|---| | A. Maximum value of $f(x) = -\lvert x+1 \rvert + 3$ | I. 6 | | B. Minimum value of $f(x) = (2x-1)^2 + 5$ | II. 5 | | C. Maximum value of $f(x) = 6 - x^2$ | III. no maximum value | | D. Maximum value of $f(x) = x^3 + 1$ | IV. 3 | Choose the correct answer from the options given below:

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Then, E (X) is :

$\int_{0}^{1.5} [x] dx$, where $[x]$ denotes the greatest integer function $\leq x$, is equal to :

The solution of a LPP with basic feasible solutions (0, 0), (10, 0), (0, 20), (10, 15) and objective function Max $Z = 2x + 3y$ is :

The degree of the differential equation $\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is:

If $y = \frac{1}{x+1}$, then $\frac{d^2y}{dx^2}$ at $x = 2$ is:

If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then

The matrix $A = \begin{bmatrix} 0 & 1 & -3 \\ -1 & 0 & 0 \\ 3 & 0 & 0 \end{bmatrix}$ is a

If $f(x) = \frac{1}{1-x}$, then for $x > 1, f(x)$ is:

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:

If $\begin{vmatrix} 2 & 3-x \\ x & 1 \end{vmatrix} = 0$, then the values of $x$ are:

Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is

A manufacturer can sell $x$ items at a price of Rs $3x+5$ each. The cost price of $x$ items is Rs $x^2 + 5x$. If x is the number of items she should sell to get no profit and no loss, then:

The angle between the line $\frac{x+2}{3} = \frac{y-3}{2} = \frac{z+5}{6}$ and the plane $2x + 10y - 11z = 5$ is:

Solution of $\frac{dy}{dx} = (1+x^2)(1+y^2)$ is:

If the matrix $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$, then $A^2$ is equal to:

Particular solution of the differential equation $\log\left(\frac{dy}{dx}\right) = x + y$, given that when $x = 0, y = 0$ is:

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :<img src="https://balti.afterboards.in/uuDFz7SlhIgJEH7" width="400px"/>

The derivative of $\sin(\tan^{-1} e^{2x})$ with respect to $x$ is:

The approximate volume of a cube of side a meters on increasing the side by 4% is:

The feasible region of an LPP Max $Z = 3x + 2y$ subject to $x \geq 0, y \geq 0, x - 2y \leq 3$ is:

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

The area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum is:

Match List I with List II | LIST I | LIST II | |---|---| | A. $\sin^{-1} x + \cos^{-1} x, x \in [-1,1]$ | I. $-\frac{\pi}{2}$ | | B. $\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})$ | II. $-\frac{\pi}{6}$ | | C. $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$ | III. $\frac{\pi}{2}$ | | D. $\sin^{-1}\left(-\frac{1}{2}\right)$ | IV. $\frac{\pi}{6}$ | Choose the correct answer from the options given below:

If the matrix $A = \begin{bmatrix} 0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0 \end{bmatrix}$ is skew-symmetric, then :

A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector $3\hat{i} + 2\hat{j} - 2\hat{k}$ is $\frac{x-1}{3} = \frac{y-2}{2} = \frac{y-3}{-2}$. B. Equation of line passing through (1, 2, 3) and parallel to the line given by $\frac{x+3}{3} = \frac{4-y}{5} = \frac{z+8}{6}$ is $\frac{x-1}{3} = \frac{y-2}{5} = \frac{z+3}{6}$. C. Equation of line passing through the origin and (5, -2, 3) is $\frac{x}{5} = \frac{y}{-2} = \frac{z}{3}$. D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is $2(x-1)+3(y-2)-1(z-3) = 0$. E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is $2x + 3y + 4z = 1$. Choose the correct answer from the options given below:

If $f: R \to R$ is defined by $f(x) = \sin x + x$, then $f(f(x))$ is:

If $A = \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and B is a square matrix of order 3, then |AB| is equal to:

Match List I with List II | LIST I | LIST II | |---|---| | A. The area of parallelogram determined by vectors $2\hat{i}$ and $3\hat{j}$ | I. 2 | | B. The value of $(\hat{i} \times \hat{j}) \cdot \hat{k} + (\hat{j} \times \hat{k}) \cdot \hat{i}$ | II. 4 | | C. The value of a for which the vectors $2\hat{i} - 3\hat{j} + 4\hat{k}$ and $a\hat{i} - 6\hat{j} + 8\hat{k}$ are collinear. | III. 0 | | D. The value of $\lambda$ for which the vectors $2\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} - 4\hat{j} + \lambda\hat{k}$ are perpendicular | IV. 6 | Choose the correct answer from the options given below:

If three points $A(a_1, b_1), B(a_2, b_2)$ and $C(a_3, b_3)$ are collinear and $D = \begin{vmatrix} a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ a_3 & b_3 & 1 \end{vmatrix}$, then:

The area of the region bounded by the lines $x = 2y + 3, x = 0, y = 1$ and $y = -1$ is:

$\int \left(\frac{1+x+x^2}{1+x^2}\right) e^{\tan^{-1} x} dx =$

Value of $\frac{e^{\sin(\tan^{-1} x + \cot^{-1} x)}}{e^{\sin(\sin^{-1} x + \cos^{-1} x)}}, x \in [-1, 1]$, is:

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

If A is a square matrix of order 3, then |adj A| is equal to:

The maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is:

Match List I with List II | LIST I | LIST II | |---|---| | A. $\int \frac{\sin x}{1 + \cos x} \, dx$ | I. $e^{\tan^{-1} x} + C$ | | B. $\int \frac{1}{1 - \tan x} \, dx$ | II. $\log(\log x + 1) + C$ | | C. $\int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx$ | III. $-\log\lvert 1+\cos x \rvert + C$ | | D. $\int \frac{1}{x + x \log x} \, dx$ | IV. $\frac{x}{2} - \frac{1}{2}\log\lvert \cos x - \sin x \rvert + C$ | Choose the correct answer from the options given below:

The function $f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1$, is discontinuous at

Probabilities to solve a specific problem by A, B and C are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Probability that at least one will solve the problem is:

Which of the following statements is NOT CORRECT.

If a line makes angles 90 degree, 60 degree and $\theta$ with $x, y$ and $z$ axis respectively, where $\theta$ is acute, then value of $\theta$ is:

The range of the function $f(x) = \frac{1}{3 - \sin 4x}$ is:

The equation of the tangent, to the curve $y = x^2 - 2x - 3$ which is perpendicular to the line $x + 2y + 3 = 0$, is

The solution of the differentiable equation $2x\frac{dy}{dx} + y = 14x^3, x > 0$, is

Let the vectors $\vec{a} = \hat{i} - 3\hat{j} + 2\hat{k}, \vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{c} = 3\hat{i} + 5\hat{j} - 2\lambda\hat{k}$ be coplanar. Then $\lambda$ is equal to

A coin is tossed 7 times. The probability of getting at least 4 heads is:

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is

The price relatives and weights of a set of commodities are given as: | Commodity | A | B | C | |---|---|---|---| | Price Relative | 150 | 130 | 180 | | Weight | $x$ | $3x$ | $y$ | If the sum of weights is 30 and the index for the set is 144, then the values of $x$ and $y$ are:

The point on the straight line $3x + 4y = 8$, which is closest to the origin is:

Given the data for the sales of a product in a state is as follows: | Year | 2005 | 2006 | 2007 | 2008 | 2009 | |---|---|---|---|---|---| | Sales (In lakh Rs) | 150 | 130 | 160 | 170 | 200 | The equation of the straight-line trend by method of least squares is:

Between 3 p.m. and 5 p.m. the average number of phone calls per minute coming into the helpline desk of a bank is 5. The probability that during one particular minute there will be only one phone call is :

The maximum value of $Z = 3x + y$ subject to the constraints $x + y \leq 30, 2x + y \leq 40, x, y \geq 0$ is

Match List I with List II | LIST I | LIST II | |---|---| | A. The variance of a Poisson distribution with mean $\lambda$ is | I. $\sqrt{\lambda}$ | | B. The standard deviation of a Poisson distribution with mean $\lambda$ is | II. 4 | | C. In a Poisson distribution, if mean is 4, then the standard deviation is | III. $\lambda$ | | D. In a Poisson distribution, if mean is 4, then the variance is | IV. 2 | Choose the correct answer from the options given below:

A person takes a car loan of Rs 9,00,000 at the rate of 12% per annum for 5 years from a bank. The EMI under flat rate system is:

Match List I with List II | LIST I | LIST II | |---|---| | A. A special characteristic of a population is known as a: | I. statistic | | B. A special characteristic of a sample is known as a: | II. Confidence interval | | C. The uncertainty of a sampling process is expressed by: | III. Estimation | | D. The process by which one makes the inferences about a population based on the information obtained from a sample is known as: | IV. Parameter | Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

Match List I with List II | LIST I | LIST II | |---|---| | A. The solution of $3x + 7 > 12$ is | I. $[-1, \infty)$ | | B. The solution of $\frac{3x+5}{2} \geq 1$ is | II. $\left[\frac{17}{8}, \infty\right)$ | | C. The solution of $2x + 5 < 7x + 9$ is | III. $\left(\frac{5}{3}, \infty\right)$ | | D. The solution of $6x - 5 \geq -2x + 12$ is | IV. $\left(-\frac{4}{5}, \infty\right)$ | Choose the correct answer from the options given below:

If $\begin{bmatrix} 2x + 3 & y + 1 \\ 2x - z & 3y \end{bmatrix} = \begin{bmatrix} 7 & -2 \\ -4 & -9 \end{bmatrix}$, then matrix $\begin{bmatrix} 3z + 1 & 4 \\ -2 & 4 \end{bmatrix}$ is equal to:

The longest side of a triangle is 4 times the shortest side and the third side is 3 cm shorter than the longest side. If the perimeter of the triangle is at least 69 cm, then the minimum length of the shortest side is:

If the probability distribution of a discrete random variable $X$ is given as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.5 | 2k | 3k | 3k | 2k | Then the value of $k$ is:

Match List I with List II | LIST I | LIST II | |---|---| | A. A matrix that has unequal number of rows and columns is called | I. Non-singular matrix | | B. A matrix whose determinant is non-zero is called | II. Null matrix | | C. A diagonal matrix whose diagonal elements are equal is called | III. Rectangular matrix | | D. A matrix that is both symmetric and skew-symmetric is | IV. Scalar matrix | Choose the correct answer from the options given below:

If the sum of two positive numbers is 25 and their product is maximum when divided in the ratio of cubes of one and squares of the other, then the numbers are:

A, B and C entered in a partnership business. They invested their capitals in the ratio of $\frac{4}{3} : \frac{5}{2} : \frac{6}{5}$. After 5 months, B invested 40% more than what he had invested earlier. If the total profit at the end of one year was Rs 50,550, then how much profit did A earn?

A shopkeeper has 10 litres of pure honey. He sells honey at the cost price of Rs. 300 per litre. After mixing some quantity of water in pure honey he sells the syrup of pure honey and water at Rs. 250 per litre. The quantity of water mixed in pure honey is

If $f(x) = a \log x + \frac{b}{x} + x$ has its extreme values at $x = -1$ and $x = 3$, then $(a, b)$ is equal to:

Match List I with List II | LIST I | LIST II | |---|---| | A. A solution that does not satisfy all the constraints is called | I. Linear | | B. The objective function in an LPP is | II. Convex polygon | | C. Linear inequalities or equations on the variables of LPP are called | III. Infeasible solution | | D. The feasible region in an LPP, formed by the convex combinations of the corner points, is called | IV. Constraints | Choose the correct answer from the options given below:

If the cost function $C(x)$ of producing $x$ units of a commodity is given as $C(x) = x^3 - 60x^2 + 13x + 50$, then the level of output for which the marginal cost is minimum is

From the data given below the Laspeyre's price index for the year 2016 with year 2010 as base year is | Commodity | Price year 2010 | Price year 2016 | Quantity Year 2010 | Quantity Year 2016 | |---|---|---|---|---| | A | 1 | 2 | 10 | 13 | | B | 5 | 10 | 12 | 16 | | C | 6 | 10 | 15 | 18 |

The minimum value of $Z = 30x + 10y$ subject to the constraints $x + 2y \leq 30, 3x + y \geq 30, 4x + 3y \geq 60, x, y \geq 0$ is

If $57 \equiv x (\bmod 5)$, then the least positive value of $x$ is:

If $x = \log t$ and $y = \frac{1}{t^2}$, then $\frac{d^2 y}{d x^2}$ is equal to

From a population having a mean of 20 and standard deviation 2, a random sample of size 64 is taken and its mean is found to be 19.5. The test statistic to test that the sample is taken from the population is

From a sample of 5 items having values 2, 4, 6, 7, 6, the unbiased estimates of the population mean and the standard deviation are:

A boat takes 6 hr 25 minutes to row upstream a certain distance with a speed which is 14.4 times that of the river current. The time taken by the boat to row down the same distance with same speed is:

An asset costing Rs 2,00,000 has a useful life of 10 years and scrap value of Rs 40,000. Its book value at the end of year 6 by Straight Line Method, is :

The present value of a perpetuity of Rs 1,200 payable at the beginning of each year, if the money is worth 5% effective, is:

In a 1000 m race P beats Q by 100 m and in the same race Q beats R by 200 m. By what distance does P beat R?

If $y = \log_e \left(\frac{x^3}{e^3}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to

If the probability distribution of a random variable X is given as | $x_i$ | 0 | 1 | 2 | 3 | |---|---|---|---|---| | $p_i$ | $2k^2$ | $k^2$ | $3k^2$ | $k$ | Then the mean of X is

A consumer in 2015, paid Rs 20 per kg for a particular variety of rice. The wholesale price index number for this variety of rice for the year 2018, with the year 2015 as the base year is 125. Then the cost per kg of rice in the year 2018 will be:

If the objective function $Z = px + qy$ ($p, q > 0$) of an LPP has minimum value 7p, at the corner points (2, 3) and (7, 0), then