NDA MATHEMATICS QUIZ-1

If $A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3\end{array}\right]$ then $A^{5}$ equals $ \mathrm{}$.

In a class of 110 students 65 students passed in English and 57 students passed in Hindi . then the number of students who passed only in English is-

In a triangle $\mathrm{ABC}$, if $\mathrm{C}=90^{\circ}$, then $\frac{a^{2}+b^{2}}{a^{2}-b^{2}} \sin (A-B)=\ldots \ldots .$

If $4 \cos ^{-1} x+\sin ^{-1} x=2 \pi$ then $x$ equals

Value of the integral $\int \frac{\tan ^{-1} x \cdot d x}{\left(1+x^{2}\right)^{\frac{3}{2}}}$ is

If $\cos \theta+\sin \theta=\sqrt{2} \cos \theta$ then $\cos \theta-\sin \theta=k \sin \theta$ where

Value of $\tan 105^{\circ}$ will be

Value of the integral $\int_{1}^{\sqrt{e}} t \log d t$ is

If $y=e^{\tan x}$ then the value of $\cos ^{2} x \frac{d^{2} y}{d x^{2}}-$ $(1+\sin 2 x) \frac{d y}{d x}=\ldots . .$

$\operatorname{Lt}_{x \rightarrow \infty}\left(\frac{x+4}{x+1}\right)^{x+3}=\ldots \ldots$