CUET Mathematics 2022 23 Aug Shift 1 PYQs

The number of all different possible matrices of order $2 \times 2$ with each entry $-1$, $0$ or $1$ is :

If A and B are square matrices of same order, then $A'B - B'A$ is a:

Let the matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}$ and $AB = \begin{bmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix}$ then order of B is :

The interval in which $f(x) = \frac{x}{2} + \frac{2}{x}$ is a decreasing function of $x$ is :

If $x = at^2$ and $y = 2at$, then the value of $\frac{d^2y}{dx^2}$ is ( where t is a parameter )

The tangent to the curve $y = e^{3x}$ at the point $(0, 1)$, meets the x-axis at :

$\int \frac{dx}{(e^x - 1)} =$

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

If $\int (1 + e^{-x} + e^{-2x} + ...)dx = \log\phi(x) + C$, then $\phi(x)$ is equal to :

Let $\int \frac{dx}{\left(\sqrt{x} - \sqrt{x-1}\right)^2} = \alpha u(x) + \beta v(x) + C$, where $u(x) = x^2 - x + \left(x - \frac{1}{2}\right)\sqrt{x^2 - x}$ and $v(x) = \log\left|x - \frac{1}{2} + \sqrt{x^2 - x}\right|$. The value of $\alpha + \beta$ is :

$\int \frac{x^2 - 4}{(x+2)(x-1)(x-3)} dx =$

The solution of differential equation $y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)$ is :

If a fair coin is tossed 10 times, then the probability of getting all heads or all tails, is :

If the objective function for an LPP is max.$(z) = 300x + 700y$ and the corner points for the bounded feasible region are $(6,0)$ $(5,0)$ $(0,6)$ $(4,4)$ and $(0,4)$, then the maximum values of z occurs at :

If an unbiased coin is tossed 10 times, probability of obtaining more head than tail is :

Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :

If $n(A) = 3$, $n(B) = 2$, then number of all possible surjective function from set A to set B are :

If $A^2 - A + I = O$, where O is the zero matrix and I is the identity matrix, then $A^{-1}$ is

If $A = \begin{bmatrix} 6 & -8 \\ -2 & 5 \end{bmatrix}$ and $A^2 - 10A = C$ then C is equal to

Choose the correct statement A. If any two rows or any two columns are identical or proportional, then value of determinant is Zero. B. Minor of an element $a_{ij}$ of the determinant of matrix A is the determinant obtained by deleting $i^{th}$ row and $j^{th}$ column C. If $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$, then A is Skew-symmetric matrix D. If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$, then $(A + A')$ is Symmetric matrix E. If $|A| = 0$, then A is non-singular matrix

$\int_{-\pi/2}^{\pi/2} \sin^7 x \, dx =$

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

$\int \frac{dx}{\sin^2 x \cos^2 x} =$

$\int \sqrt{x^2 - 4x + 5} \, dx =$

Match List I with List II | List - I | List - II | |---|---| | A. $\int \frac{dx}{x^2 - a^2} =$ | I. $\log_e\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$ | | B. $\int \frac{dx}{a^2 - x^2} =$ | II. $\frac{1}{2a}\log_e\left\lvert\frac{x-a}{x+a}\right\rvert + C$ | | C. $\int \frac{dx}{\sqrt{x^2 - a^2}} =$ | III. $\frac{1}{2a}\log_e\left\lvert\frac{a+x}{a-x}\right\rvert + C$ | | D. $\int \frac{dx}{\sqrt{x^2 + a^2}} =$ | IV. $\log_e\left\lvert x + \sqrt{x^2 - a^2}\right\rvert + C$ | Choose the correct answer from the options given below:

Match list I with list II | List - I | List - II | |---|---| | A. Slope of tangent to the curve $y = x^3 - x$ at $x = 2$ | I. $-2$ | | B. Slope of tangent to the curve $y = 3x^3 - 4x$ at $x = 0$ | II. $11$ | | C. Slope of normal to the curve $y = \sin\theta$ at $\theta = \frac{\pi}{3}$ | III. $2$ | | D. Slope of normal to the curve $y = \cos\theta$ at $\theta = \frac{\pi}{6}$ | IV. $-4$ | Choose the correct answer from the option given below :

$\sin^{-1}(\cos x) = \frac{\pi}{2} - x$ is valid for :

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :

Match List - I with List - II | List - I (Differential Equation) | List - II (Degree) | |---|---| | A. $\left[1 + (y')^2\right]^2 = y''$ | I. $2$ | | B. $\left[1 + (y'')^3\right]^{\frac{1}{2}} = (y')^3$ | II. $4$ | | C. $(y''')^2 + y'' + 3y' + 5y = e^x$ | III. $1$ | | D. $\left[1 + (y')^3\right]^{\frac{1}{2}} = (y'')^2$ | IV. $3$ | Choose the correct answer from the option given below:

Choose the correct statements: A. The order and degree (if defined) of a differential equation are always positive integrals B. The order of a differential equation is the highest order derivative of the dependent variable with respect to the independent variable involved in a differential equation C. If $\frac{dy}{dx} + P(x)y = Q(x)$ then Integrating factor $= e^{\int P(x)dx}$ D. The sum of order and degree of differential equation $1 + (y'')^5 = (y''')^3$ is $8$ E. If the solution of a differential equation of order $n$, contains $n$ arbitrary constant, then it is called a general solution Choose the correct answer from the options given below:

The reflection of the point $(\alpha, \beta, \gamma)$ in the xz plane is

The angle between the planes $2x + y + 3z - 2 = 0$ and $x - 2y + 5 = 0$ is :

If $-3 \leq k \leq 1$ and $|\vec{a}| = 2$ then $|k\vec{a}|$ is

The angle between the pairs of lines $\vec{r} = (3\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(\hat{i} + 2\hat{j} + 2\hat{k})$ $\vec{r} = (5\hat{i} - 2\hat{j}) + \mu(3\hat{i} + 2\hat{j} + 6\hat{k})$ is :

A vector perpendicular to a plane containing a triangle ABC having vertices as $A(1,1,0)$, $B(2,1,1)$ and $C(0,3,2)$, is:

The area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a} = \hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = 2\hat{i} - 7\hat{j} + \hat{k}$ is :

If $\vec{a}$ is a unit vector and $(\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 8$ then $|\vec{x}|$ is

The feasible region and optimal solution of a LPP with objective function, max.$(z) = 600x + 400y$, subject to : $x + 2y \leq 12$, $2x + y \leq 12$, $x + 1.25y \geq 5$, $x \geq 0$ and $y \geq 0$, is:<img src="https://balti.afterboards.in/qaJVYwB0zdE2O4c" width="400px"/> The feasible region and optimal solution is _____

Consider an experiment of tossing 3 coins simultaneously. Define the following events: $E$ = [Three heads or three tails appear] $F$ = [At least two heads appear] and $G$ = [At most two heads appear] Choose the correct option:

In the family mother, father and son stand up at random for a family picture. Define following two events : $E$ = [Son stands at one of the two ends in the picture] $F$ = [Father stands in the middle of the picture] The value of $P(F/E)$ is :