SSC CHSL MATHS QUIZ

Question 1:

If $\sin \theta+\cos \theta=\frac{\sqrt{5}}{2}$ , then Find the value of $\sin ^{6} \theta+\cos ^{6} \theta+$ $5 \sin ^{2} \theta \cdot \cos ^{2} \theta$ .

$\frac{65}{66}$

$\frac{33}{32}$

$\frac{17}{16}$

$\frac{65}{64}$

Question 2:

If $3\sin 20^{\circ}=4 \sin ^{3} 20^{\circ}+x$, then find the value of $x$.

0

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

1

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:

In a triangle $A B C, A B=20 \mathrm{~cm}, \angle A B C=30^{\circ}$ and $\angle A C B=45^{\circ}$, Find the area of the triangle.

$150(\sqrt{3}+1)$

$200(\sqrt{3}+1)$

$50(3+\sqrt{3})$

$50(\sqrt{3}+1)$

Question 5:

The value of $\frac{\sin 23^{\circ} \cos 67^{\circ}+\sec 52^{\circ} \sin 38^{\circ}+\cos 23^{\circ} \sin 67^{\circ}+\operatorname{cosec} 52^{\circ} \cos 38^{\circ}}{\operatorname{cosec}^2 20^{\circ}-\tan ^2 70^{\circ}}$ is

3

4

2

0

Question 6:

The angle of elevation of the top of an unfinished tower at a point distant $78 \mathrm{~m}$ from its base is $30^{\circ}$. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be $60^{\circ}$ ?

$78 \sqrt{3}$

80

$52 \sqrt{3}$

$26 \sqrt{3}$

Question 7:

A kite is attached to a string. Find the length of the string (in $\mathrm{m}$ ) when the height of the kite is $80 \mathrm{~m}$ and the string makes an angle of $30^{\circ}$ with the ground.

180

160

$90 \sqrt{3}$

90

Question 8:

If $\cot B=\frac{84}{13}$, what is the value of $\sin B$ ?

$\frac{13}{85}$

$\frac{85}{13}$

$\frac{84}{85}$

$\frac{85}{84}$

Question 9:

If $\sec x+\cos x=3$, then $\tan ^{2} x-\sin ^{2} x$ is:

10

4

5

16

Question 10:

The value of $\sec ^{2} 12^{\circ}-\frac{1}{\tan ^{2} 78^{\circ}}$ is:

0

1

2

3