SSC CGL QUANT QUIZ

Question 1:

The angle of election of a tower from a distance $80 \mathrm{~m}$ from its foot is $30^{\circ}$. Find the height of the tower.

$\frac{80}{\sqrt{3}} \mathrm{~m}$

$90 \sqrt{3} \mathrm{~m}$

$\frac{50}{\sqrt{3}} \mathrm{~m}$

$80 \sqrt{3} \mathrm{~m}$

Question 2:

The shadow of a tower is $\sqrt{3}$ times its height. Then the angle of elevation of the top of the tower is.

$45^{\circ}$

$30^{\circ}$

$60^{\circ}$

$90^{\circ}$

Question 3:

The angle of elevation of the top of a building from the foot of the tower is $30^{\circ}$ and the angle of elevation of the top of the tower from the foot of the building is $60^{\circ}$. If the tower is $50 \mathrm{~m}$ high, Find the height of the building.

$18.66 \mathrm{~m}$

$16.66 \mathrm{~m}$

$15.33 \mathrm{~m}$

$14.33$

Question 4:

A ladder $10 \mathrm{~m}$ long reaches a point $10 \mathrm{~m}$ below the top of $\mathrm{a}$ vertical flagstaff. From foot of the ladder, the elevation of top of the flagstaff is $60^{\circ}$. What is the height of flagstaff ?

$12 \mathrm{~m}$

$15 \mathrm{~m}$

$16 \mathrm{~m}$

$20 \mathrm{~m}$

Question 5:

From the top of building $15 \mathrm{~m}$ high the angle of elevation of the top of a tower is found to be $30^{\circ}$. From the bottom of the same building, the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the height of the tower and the distance between the tower and building.

$11.975 \mathrm{~m}$

$15.238 \mathrm{~m}$

$12.975 \mathrm{~m}$

$16.326 \mathrm{~m}$

Question 6:

Two men standing on same side of a 66 meters high pillar, observe the angles of elevation of the top of the pillar to be $30^{\circ}$ to $60^{\circ}$ respectively. The distance between two men is.

$44 \sqrt{3} \mathrm{~m}$

$36 \mathrm{~m}$

$66 \sqrt{3} \mathrm{~m}$

$22 \sqrt{3} \mathrm{~m}$

Question 7:

The angle of elecation of an aeroplane from a point on the ground is $60^{\circ}$. After $15 \mathrm{sec}-$ onds, the elevation changes to $30^{\circ}$. If the aeroplane is flying at a height of $1500 \sqrt{3} \mathrm{~m}$,then find the speed of the plane.

$300 \mathrm{~m} / \mathrm{sec} $

$200 \mathrm{~m} / \mathrm{sec} $

$100 \mathrm{~m} / \mathrm{sec} $

$150 \mathrm{~m} / \mathrm{sec} $

Question 8:

At the foot of mountain the elevation of its summit is $45^{\circ}$, after ascending $1 \mathrm{~km}$ towards the mountain up a slope of $30^{\circ}$ inclination, the elevation is found to be $60^{\circ}$. Find the height of the mountain.

$\frac{(\sqrt{3}-2)}{2} \mathrm{~km}$

$\frac{(\sqrt{3}+2)}{2} \mathrm{~km}$

$\frac{(\sqrt{3}-1)}{2} \mathrm{~km}$

$\frac{(\sqrt{3}+1)}{2} \mathrm{~km}$

Question 9:

From the top of a $7 \mathrm{~m}$ high building, the angle of elevation of th top of a cube tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.

$6(\sqrt{3}+1)$

$14(\sqrt{3}-1)$

$7(\sqrt{3}+1)$

$7(\sqrt{3}-1)$

Question 10:

A vertical building casts a shadow of 20 metre long on the ground. At the same time 60 meter casts a shadow of length 50 metre. Find the height of building?

$16 \mathrm{~m}$

$24 \mathrm{~m}$

$32 \mathrm{~m}$