Class 12 Mathematics 2020 Board Exam

The relation $R$ in the set $\{1,2,3\}$ given by $R=\{(1,2),(2,1),(1,1)\}$ is

If $A$ is a square matrix of order $3$ and $|A|=5$, then the value of $|2A^{\prime }|$ is

If $A$ is a $3\times 3$ matrix and $|A|=-2$, then the value of $|A(\text{adj }A)|$ is

The matrix $\left[\begin{array}{ccc}2& -1& 3\\ \lambda & 0& 7\\ -1& 1& 4\end{array}\right]$ is not invertible for

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

${\tan }^{-1}\sqrt{3}+{\tan }^{-1}\lambda ={\tan }^{-1}\left(\frac{\sqrt{3}+\lambda }{1-\sqrt{3}\lambda }\right)$ is valid for what values of $\lambda$ ?

If $\cos \left({\sin }^{-1}\frac{2}{\sqrt{5}}+{\cos }^{-1}x\right)=0$, then $x$ is equal to

The domain of the function $f(x)={\sin }^{-1}(2x)$ is

The number of arbitrary constants in the particular solution of a differential equation of second order is (are)

(A) $0$

(B) $1$

(C) $2$

(D) $3$

The interval in which the function $f$ given by $f(x)=x^2{e}^{-x}$ is strictly increasing, is