CUET (UG) Mathematics Medium Questions

Let A = $[a_{ij}{]}_{nXn}$ be a matrix. Then Match List-I with List-II

Choose the correct answer from the options given below:

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Which of the following inequalities holds true?

(A) $\sqrt{5}+\sqrt{3}>\sqrt{6}+\sqrt{2}$.

(B) If $a>b$ and $c<0$, then $\frac{a}{c}<\frac{b}{c}$.

(C) $\frac{1}{x^2}>\frac{1}{x}>1$, if $0<x<1$

(D) If $a$ and $b$ are positive integers and $\frac{a-b}{6.25}=\frac{4}{2.5}$, then $b>a$

Choose the correct answer from the options given below:

Let $f:\mathbb{R}\to \mathbb{R}$ be defined as $f(x)=10x$. Then (Where $\mathbb{R}$ is the set of real numbers)

1. f is both one-one and onto
2. f is onto but not one-one
3. f is one-one but not onto
4. f is neither one-one nor onto

Let $A=[a_{ij}{]}_{2\times 3}$ and $B=[b_{ij}{]}_{3\times 2}$, then $|5AB|$ is equal to

${\int }_1^4|x-2|dx$ is equal to

Consider the LPP: Minimize $Z=x+2y$ subject to $2x+y\ge 3,x+2y\ge 6,x,y\ge 0$. The optimal feasible solution occurs at

For $|x|<1$, $\sin ({\tan }^{-1}x)$ equal to

Let $A=$ $\left[\begin{array}{ccc}1& 2& 1\\ -1& 3& 2\\ 2& 4& 1\end{array}\right]$ and $M_{ij},A_{ij}$ respectively denote the minor, co-factor of an element $a_{ij}$ of matrix $A$, then which of the following are true?

(A) $M_{22}=-1$

(B) $A_{23}=0$

(C) $A_{32}=3$

(D) $M_{23}=1$

(E) $M_{32}=-3$

Choose the correct answer from the options given below:

If $A=\left[\begin{array}{ccc}0& 0& \sqrt{3}\\ 0& \sqrt{3}& 0\\ \sqrt{3}& 0& 0\end{array}\right]$, then $|\mathrm{adj}A|$ is equal to

The area (in sq. units) of the region bounded by the parabola $y^2=4x$ and the line $x=1$ is

Which of the following are linear first order differential equations?

(A) $\frac{dy}{dx}+P(x)y=Q(x)$

(B) $\frac{dx}{dy}+P(y)x=Q(y)$

(C) $(x-y)\frac{dy}{dx}=x+2y$

(D) $(1+x^2)\frac{dy}{dx}+2xy=2$

If the maximum value of the function $f(x)=\frac{{\log }_{e}x}{x},x>0$ occurs at $x=a$, then $a^2{f}^{\prime \prime }(a)$ is equal to

If $y=3e^{2x}+2e^{3x}$, then $\frac{d^{2}y}{d{x}^2}+6y$ is equal to

The solution of the differential equation ${\log }_e\left(\frac{dy}{dx}\right)=3x+4y$ is given by

Let A = $\{1,2,3\}$. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is

If $A$ is a square matrix and $I$ is the identity matrix of same order such that $A^2=I$, then $(A-I{)}^3+(A+I{)}^3-3A$ is equal to

If $a>0$, then $P(0<x\le 2)$ is equal to

The integral $I=\int \frac{e^{5{\log }_{e}x}-e^{4{\log }_{e}x}}{e^{3{\log }_{e}x}-e^{2{\log }_{e}x}}dx$ is equal to

The unit place digit of the number $(37{)}^2$ is:

If $A=$ $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$ and $B=$ $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ then the matrix $AB$ is equal to