NDA MATHEMATICS QUIZ - 9

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Question 1:

The function $y=x-\tan ^{-1} x$ decreases in the interval.

Question 2:

Value of $\int_{0}^{1}$ tan $^{-1} \sqrt{x} \cdot d x$ will be

Question 3:

Period of the function $f(\theta)=\sin ^{4} \theta+\cos ^{4} \theta$ is:

Question 4:

If $F(\theta)=5\left(\sin ^{4} \theta+\cos ^{4} \theta\right)$ then maximum value of $F(\theta)$ will be:

Question 5:

$\int_{0}^{1} \frac{\tan ^{-1} x \cdot e^{\tan ^{-1} x}}{\left(1+x^{2}\right)} $ is equals.

Question 6:

If $a, b, c$ are in H.P than $\sin ^{2} \frac{A}{2}, \sin ^{2} \frac{B}{2}$, $\sin ^{2} \frac{C}{2}$ are in

Question 7:

If $\tan \alpha, \tan \beta$ are the roots of $x^{2}-5 x+6=0$ then  $(\alpha+\beta)$ equal to:

Question 8:

If ${ }^{\mathrm{A}} \mathrm{n}_{1}$ be the area bounded by the curve $y=(\tan \theta)^{n}$ and the lines $y=0 ; x=0$ and $\theta=\pi / 4$ then the value of ${ }^{\mathrm{A}} \mathrm{n}_{1}$ + ${ }^{\mathrm{A}} \mathrm{n}_{1}-2$ for n>2 will be:

Question 9:

The number of solutions of the equation $\sin 2 \theta-12(\sin \theta-\cos \theta)+12=0$

$\theta\in[0,2 \pi]$ are possible?

Question 10:

If $\mathrm{ABC}$ be a triangle than

a secB $\sec C+b \sec A \sec C+c \sec A \sec B$ is equal to:

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