Class 12 Mathematics 2023 Board Exam

If $P(A|B)=0.3$, $P(A)=0.4$ and $P(B)=0.8$, then $P(B|A)$ is equal to :

If $|A|=2$, where $A$ is a $2\times 2$ matrix, then $|4A^{-1}|$ equals :

If $f(x)=a(x-\cos x)$ is strictly decreasing in $\mathbb{R}$, then '$a$' belongs to

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

The value of $p$ for which the vectors $2\hat{i}+p\hat{j}+\hat{k}$ and $-4\hat{i}-6\hat{j}+26\hat{k}$ are perpendicular to each other, is :

Direction cosines of the line $\frac{x-1}{2}=\frac{1-y}{3}=\frac{2z-1}{12}$ are :

A relation $R$ is defined on a set of real numbers $\mathbb{R}$ as

$$R=\{(x,y):x\cdot y\text{ is an irrational number}\}$$

Check whether $R$ is reflexive, symmetric and transitive or not.

Assertion (A): The range of the function $f(x)=2{\sin }^{-1}x+\frac{3\pi }{2}$, where $x\in [-1,1]$, is $\left[\frac{\pi }{2},\frac{5\pi }{2}\right]$.

Reason (R): The range of the principal value branch of ${\sin }^{-1}(x)$ is $[0,\pi ]$.

If for a square matrix $A$, $A^2-3A+I=O$ and $A^{-1}=xA+yI$, then the value of $x+y$ is :

The value of $k$ for which $f(x)=\{\begin{array}{ll}3x+5,& x\ge 2\\ k{x}^2,& x<2\end{array}$ is a continuous function, is :