SSC CHSL MATHS QUIZ

In the given figure, if $\mathrm{AB}=\mathrm{AC}=8 \mathrm{~cm}, \mathrm{BC}=$ $11 \mathrm{~cm}$ and $\mathrm{BD}=7 \mathrm{~cm}$, then find $\mathrm{AD}=$ ?

If $0<\alpha<\frac{\pi}{2}$ then $\tan \alpha+\tan 2 \alpha+\tan 3 \alpha=0$ if 

A person standing on one bank of a River finds the angle of elevation of the top of a tree standing on the other bank of the river $60^{\circ}$.$40 \mathrm{~m}$ behind the same place which is further away from the tree, the angle of elevation of the top of the tree becomes $30^{\circ}$, then the width of the river will be

If $\sin \theta=\cos ^{2} \theta$, find the value of $\cos ^{2} \theta(1+$ $\left.\cos ^{2} \theta\right)$ :

$\sin ^{2} \theta_{1}+\cos ^{2} \theta_{2}=1$ then what is the value of $\theta_{1} , \theta_{2} ?$

If $\cos (A-B)=\frac{\sqrt{3}}{2}$ and $\sec A=2,0^{\circ} \leq A \leq 90^{\circ}, 0^{\circ} \leq B \leq 90^{\circ}$ then what is the measure of $\mathrm{B}$ ?

The value of $\left(\frac{1-\cot \theta}{1-\tan \theta}\right)^2-1$ when $0^{\circ} <\theta<90^{\circ}$, is equal to:

In a right $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \mathrm{AC}-\mathrm{BC}=2, \mathrm{AB}=8$, Then $\sec \mathrm{A}+\cot \mathrm{C}$ ?

The value of $\frac{\sin 37^{\circ} \cos 53^{\circ} \cot 45^{\circ}+\cos 37^{\circ} \sin 53^{\circ} \tan 45^{\circ}}{4 \sin 45^{\circ} \cos 45^{\circ}}$ is: