NDA MATHEMATICS QUIZ

Question 1:

$\cos 36^{\circ} \cdot \cos 72^{\circ} \cdot \cos 108^{\circ} \cdot \cos 144^{\circ}=\ldots$

$\frac{5}{16}$

$\frac{1}{16}$

$\frac{1}{32}$

$\frac{7}{16}$

Question 2:

$\tan 22 \frac{1}{2}^{\circ}$ equals:

$\sqrt{2}+1$

$\sqrt{2}-1$

$\frac{\sqrt{2}-1}{2 \sqrt{2}}$

$\sqrt{2}+1+2 \sqrt{2}$

Question 3:

$\frac{\sin 2 \theta-\sin \theta}{1+\cos 2 \theta-\cos \theta}=\ldots \ldots$

$\tan \theta$

$\cos \theta$

$\sin \theta \cdot \cos \theta$

$2 \sin \theta$

Question 4:

$(\cos \alpha-\cos \beta)^{2}+(\sin \alpha+\sin \beta)^{2}=\ldots \ldots$

$4 \sin ^{2} \frac{\alpha-\beta}{2}$

$4 \cos ^{2} \frac{\alpha+\beta}{2}$

$4 \sin ^{2} \frac{\alpha+\beta}{2}$

$4 \cos ^{2} \frac{\alpha-\beta}{2}$

Question 5:

$\frac{\sin A+\sin B-\sin (A+B)}{\sin A+\sin B+\sin (A+B)}$ = . . . . . .

$2 \tan \frac{A}{2} \cdot \tan \frac{B}{2}$

$\tan A \tan B$

$\tan ^{2} \frac{A}{2} \cdot \tan ^{2} \frac{B}{2}$

$\tan \frac{A}{2} \cdot \tan \frac{B}{2}$

Question 6:

$\sqrt{2+\sqrt{2+2 \cos 4 x}}$ is equal to.

$2 \cos x$

$\cos ^{2} x$

$2 \cos 2 x$

$2 \cos ^{2} x$

Question 7:

$\cos ^{2} 73^{\circ}+\cos ^{2} 47^{\circ}+\cos 73^{\circ} \cdot \cos 47^{\circ}=\ldots .$

$\frac{1}{4}$

$\frac{5}{4}$

$\frac{7}{4}$

$\frac{3}{4}$

Question 8:

If $\sin 5 \theta=a \sin ^{5} \theta+b \sin ^{3} \theta+c \sin \theta$ then

$a=16 ; b=-20 ; c=10$

$c=12 ; b=-10, c=5$

$a=16 ; b=-20 ; c=5$

$a=12, b=-20, c=10$

Question 9:

$\frac{4 \tan ^{3} \theta}{1-\tan ^{4} \theta}$ equals:

$\tan 2 \theta-\sin \theta+\cos \theta$

$\tan 2 \theta-\sin 2 \theta$

$\tan 2 \theta+\cos 2 \theta$

$\tan 2 \theta-\cos \theta$

Question 10:

If $\cos x=\frac{1}{2}\left(m+\frac{1}{m}\right)$ then $\cos 3 \theta$ equals

$\left(m^{3}-\frac{1}{m^{3}}\right)$

$\frac{1}{2}\left(m^{3}-\frac{1}{m^{3}}\right)$

$\frac{1}{2}\left(m+\frac{1}{m}\right)\left(m^{2}+\frac{1}{m^{2}}+1\right)$

None of these

NDA MATHEMATICS QUIZ - 22

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NDA MATHEMATICS QUIZ - 22

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