CUET Mathematics 2022 4 Aug Shift 1 PYQs

Let A be a non singular square matrix of $2 \times 2$. Then, $|adj\ A|$ is equal to

Value(s) of $x$ for which, $\begin{vmatrix} x & 1 \\ 5 & x \end{vmatrix} = \begin{vmatrix} 8 & 2 \\ 2 & 1 \end{vmatrix}$ is:

If the area of a triangle with vertices A(1,3), B(0,0) and C(k,0) is 3 sq. units, then k is:

If $y = \frac{\log_e x}{x}$, then $\frac{d^2y}{dx^2} =$

The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing is -

If $y = \frac{\sqrt{x+1} + \sqrt{x-1}}{\sqrt{x+1} - \sqrt{x-1}}$, then $(x^2-1)^{3/2} \frac{d^2y}{dx^2} =$

If x is real, then minimum value of $x^2 - 8x + 17$ is :

$\int \frac{x}{(x^2+3)(x^2+4)} dx =$

$\int e^x \left(\frac{1}{x} - \frac{2}{x^3}\right) dx =$

The area of the region bounded by the curve $x^2 = 4y$ and the straight line $x = 4y - 2$ is:

The sum of order and degree of differential equation $2x^2 \cdot \left(\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\frac{dy}{dx}\right)^3 + y = 0$ is

Match List I with List II | List I | List II : Order and degree respectively | |---|---| | A. $\frac{dy}{dx} - (x^2+3) = 0$ | I. 2 and 1 | | B. $2x^2 \frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0$ | II. 2 and 3 | | C. $y''' + y^2 + e^{y'} = 0$ | III. 1 and 1 | | D. $\left(\frac{ds}{dt}\right)^4 + 3s\left(\frac{d^2s}{dt^2}\right)^3 = 0$ | IV. 3 and not defined | Choose the correct answer from the options given below:

The probability distribution of a discrete random variable X is given as : | x | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X=x) | 0.1 | k | 2k | 2k | k | The value of K is:

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. The probability distribution of the number of kings will be:

The objective function for a L.P.P. is $Z = 5x + 7y$ and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at

A function f: R $\to$ R is given by $f(x) = x^3 + 3$. If $f(x) = -24$, then the value of x is:

If R is a relation on $A = \{a, b, c\}$ such that $R = \{(a,a), (b,b)\}$, which element/elements should be included to make R an equivalence relation. A. (c, c) B. (c, c), (a, c), (c, a) C. (a, b), (b, c), (a, c) D. (b, c), (c, c), (c, a), (b, a) Choose the correct answer from the options given below:

If A and B are square matrices of same order n, then identify correct statements from the statements given below: A. $|adj\ A| = |A|^{n-1}$ B. $|A \cdot B| = |B| \cdot |A|$ C. $adj\ A' = (adj\ A)'$ D. $adj\ AB = (adj\ A) \cdot (adj\ B)$ E. $|A^n| = |A|^n$ Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 6 & 4 \\ 5 & 3 \end{bmatrix}$ and $B = adj(A)$, then $|B|$ is equal to:

Match List I with List II: Given that A and B are invertible matrices of size $3 \times 3$ | List I | List II | |---|---| | A. $\lvert AB \rvert$ | I. $\frac{1}{\lvert A \rvert}$ | | B. $\lvert \operatorname{Adj} A \rvert$ | II. $\lvert A \rvert \lvert B \rvert$ | | C. $\lvert A^{-1} \rvert$ | III. $B^{-1} \cdot A^{-1}$ | | D. $(AB)^{-1}$ | IV. $\lvert A \rvert^2$ | Choose the correct answer from the options given below:

Match List I with List - II | List - I | List - II | |---|---| | A. An even function | I. $x^2 + \cos x$ | | B. For an even function, $\int_{-a}^{a} f(x)dx =$ | II. 0 | | C. If $f(2a-x) = -f(x)$, then $\int_{0}^{2a} f(x)dx =$ | III. $2\int_{0}^{a} f(x)dx$ | | D. An odd function | IV. $x^3 + \sin x$ | Choose the correct answer from the options given below:

$\int_{0}^{\pi} \frac{e^{\cos x}}{e^{\cos x} + e^{-\cos x}} dx =$

Match List - I with List - II | List - I | List - II | |---|---| | A. $\tan^{-1}\left(\tan\frac{7\pi}{6}\right)$ | I. $\frac{5\pi}{6}$ | | B. $\tan^{-1}\left(\tan\frac{8\pi}{6}\right)$ | II. $\frac{\pi}{2}$ | | C. $\tan^{-1}\frac{1}{\sqrt{3}} + cosec^{-1}\frac{2}{\sqrt{3}}$ | III. $\frac{\pi}{6}$ | | D. $\cos^{-1}\left(\cos\frac{5\pi}{6}\right)$ | IV. $\frac{\pi}{3}$ | Choose the correct answer from the options given below:

The value of $\sec^2(\tan^{-1}2) + cosec^2(\cot^{-1}3)$ is:

If $f(x) = \begin{cases} \frac{\tan(\pi/4 - x)}{\cot 2x}, & x \neq \pi/4 \\ k, & x = \pi/4 \end{cases}$ is continuous at $x = \pi/4$, then the value of k is

The derivative of $\sin^{-1}\left(\frac{2x}{1+x^2}\right)$ w.r.t. $\tan^{-1}\left(\frac{2x}{1-x^2}\right)$ is

The tangent to the curve $y^2 + 2x - 5 = 0$ at the point (h, k) is parallel to the line $x + 2y = 4$, then the value of 'k' is:

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' is

Solution of the differential equation $\frac{dy}{dx} = x + xy - (1 + y)$ is:

The solution of the differential equation $\frac{dy}{dx} = \frac{\lambda^2}{(x+y)^2}$ ($\lambda$ is constant) is:

The points of trisection of the segment joining the points (1, 0, 2) and (1, 3, 2) are: A. $(1, \frac{3}{2}, \frac{4}{3})$ B. (1, 1, 2) C. (1, 2, 2) D. $(1, \frac{3}{2}, 2)$ Choose the correct answer from the options given below:

The equation of line of intersection of the planes $x + y + 3z = 7$ and $x - y + 2z = 3$ is:

The distance of the point (1, 2, 0) from the line $\frac{x-3}{2} = \frac{y+4}{3} = \frac{z+6}{5}$ measured parallel to the plane $x + y + z = 3$ is

The line $\frac{x+2}{3} = \frac{y+3}{5} = \frac{z-6}{4}$ passes through (a, 2, c). The value of a and c are:

The equation of the line passing through (-2, 3, 4) and parallel to the vector $2\hat{i} - \hat{j} + \hat{k}$ is:

If $\vec{a}$ and $\vec{b}$ are two perpendicular vectors such that $|\vec{a}| = 3$, $|\vec{b}| = 4$ and $\theta$ is the angle between $\vec{a}$ and $(\vec{a} - \vec{b})$, then $\cos\theta$ is equal to:

$[\vec{a} + \vec{b},\ \vec{b} + \vec{c}, \vec{a} + \vec{b} + \vec{c}]$ is equal to

The maximum value of $z = 4x + 3y$, if the feasible region for an LPP is as shown below is:<img src="https://balti.afterboards.in/yaqRTNOpRch3l7q" width="400px"/>

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$, then $P(A'/B)$ is:

If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is: