NDA MATHEMATICS QUIZ - 18

Attempt now to get your rank among 4 students!

Question 1:

If $\sum_{k=1}^{2 k} \sin ^{-1} x_{k}=k \pi$ then $\sum_{k=1}^{2 k} x_{k}$ is

Question 2:

Value of $\cot \left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)$ is

Question 3:

$\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}$ then

Question 4:

If $x=\tan ^{-1} \frac{1}{7}+\tan ^{-1} \frac{1}{8}+\cot ^{-1} 18$ then $\cot x$ is equal to

Question 5:

The number of solutions of $\sin ^{-1} x=2 \tan ^{-1} x $ is

Question 6:

$\tan ^{-1}\left(\frac{\cos \theta}{1+\sin \theta}\right)=\ldots . . ;-\frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{2}$


Question 7:

If $\cos ^{-1} \frac{a}{2}+\cos ^{-1} \frac{b}{3}=\mathrm{t}$ then $9 a^{2}-12 a b \cos t+4 b^{2}$ is equal to

Question 8:

If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=\pi$; then $\alpha^{2}+\beta^{2}+\gamma^{2}+2 \alpha \beta \gamma$ equals

Question 9:

The number of solution for which the equation $\sin ^{-1} x=\cos ^{-1} x+\sin ^{-1}(5 x-3)$ holds is

Question 10:

If $\cot ^{-1} \frac{x-2}{x-1}+\cot ^{-1} \frac{x+2}{x+1}=\cot ^{-1}(1)$ then $x=......$