NDA MATHEMATICS QUIZ

Question 1:

If $\tan x, \cos x$ and $\sin x$ are in G.P. then value of $\cot ^{6} x-\cot ^{2} x$ is equal to

0.0

1.0

2.0

3.0

Question 2:

If $\alpha$ and $\beta$ be the acute angles such that ( $\alpha$ $+\beta$ ) and $(\alpha-\beta)$ satisfy the equation $\tan ^{2} x-$ $4 \tan x+1=0$ then

$\alpha<\beta$

$\beta<\alpha$

$\alpha=\beta$

$\alpha+\beta=\frac{7 \pi}{12}$

Question 3:

If $\sec (A-B), \sec A$, and $\sec (A+B)$ are in A.P. then

$\cos A \cdot \operatorname{Sec} \frac{B}{2}=\pm 1$

$\cos A \cdot \sec \frac{B}{2}=\pm \sqrt{3}$

$\cos A \cdot \sec B=\pm \sqrt{2}$

Question 4:

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

$k=\sqrt{3}$

$k=\sqrt{5}$

$k=\sqrt{2}$

None of these

Question 5:

If $\alpha+\beta+\gamma=\alpha \beta \gamma$ ,then value of $\frac{\alpha}{1-\alpha^{2}} + \frac{\beta}{1-\beta^{2}}+\frac{\gamma}{1-\gamma^{2}}$ is

$\frac{4 \alpha \beta \gamma}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

$\frac{8 \alpha \beta \gamma}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

$\frac{4 \alpha^{2} \beta^{2} \gamma^{2}}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

$\frac{\alpha \beta \gamma}{\left(1-\alpha^{2}\right)\left(1-\beta^{2}\right)\left(1-\gamma^{2}\right)}$

Question 6:

If $\mathrm{A}+\mathrm{B}+\mathrm{C}=\frac{\pi}{2}$ then $\sin ^{2} A+\sin ^{2} B+\sin ^{2} C$ equals

$1+2 \sin A \cdot \sin B \sin C$

$4 \sin A \cdot \sin B \sin C$

$1-2 \sin A \cdot \sin B \cdot \sin C$

$2 \sin A \cdot \sin B \cdot \sin C$

Question 7:

If $\alpha+\beta+\gamma=\pi$ and $\cos \alpha=\cos \beta \cdot \cos \gamma$ , then $\cot \beta \cdot \cot \gamma$ equal is

2

$\frac{1}{2}$

1

$\frac{1}{3}$

Question 8:

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

$(2+\sqrt{3})$

$-(2-\sqrt{3})$

$-(2+5 \sqrt{3})$

$-(2+\sqrt{3})$

Question 9:

Value of $\tan 855^{\circ} \cdot \cot 495^{\circ}$ is equal to

1.0

$-1$

2.0

$-2$

Question 10:

If $\cot \theta \cdot \cot \phi=3$ then $\cos (\theta-\phi)$ equals to.

$2 \cos \theta \cos \phi$

$\quad \cos (\theta+\phi)$

$2 \cos (\theta+\phi)$

$\quad \cos \theta \cos \phi$]

NDA MATHEMATICS QUIZ - 25

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