SSC CHSL MATHS QUIZ

In a triangle $P Q R$, side $Q P$ is produced to a point $S$. If $\angle R P S=108^{\circ}$ and $\angle Q=20^{\circ}$, then $3 \angle R+2 \angle Q$ is equal to:

$\mathrm{AB}$ is a line and a point $\mathrm{P}$ lies on it. $\mathrm{PC}$ and $\mathrm{PD}$ are two rays on the same side of $\mathrm{AB}$ such that ray $\mathrm{PC}$ lies between rays $\mathrm{PB}$ and $\mathrm{PD}$. If $\angle \mathrm{APD}=80^{\circ}$ and angles $\mathrm{CPD}$ and $\mathrm{BPC}$ are in the ratio of $2: 3$, then $3 \angle \mathrm{CPD}+2 \angle \mathrm{BPC}$ is equal to:

The length of the median PS of a triangle $P Q R$ is half of the length of its side $\mathrm{QR}$. If $\angle \mathrm{R}=24^{\circ}$, then $\angle \mathrm{Q}$ is equal to:

In a circle with centre $\mathrm{O}, \mathrm{PR}$ and $\mathrm{QS}$ meet at the point $\mathrm{T}$, when produced, and $\mathrm{PQ}$ is a diameter. If $\angle R O S=36^{\circ}$, then the measure of $\angle P T Q$ is :

Sides $A B$ and $C D$ of a cyclic quadrilateral $A B C D$ are produced to met at $E$, and sides $A D$ and $B C$ are produced to meet at $F$. If $\angle A D C=75^{\circ}$, and $\angle B E C=50^{\circ}$ then the difference between $\angle B A D$ and $\angle A F B$ is.

In a circle with centre O, chords AB and CD are parallel chords on opposite side of O. If AB = 20 cm, CD = 48 cm and the distance between the chords is 34 cm, then the diameter (in cm) of the circle is :

The measure of an angle for which the measure of the supplement is four times the measure of the complement is :

In $\triangle \mathrm{ABC}, \angle \mathrm{BAC}=90^{\circ}$ and $\mathrm{AD} \perp \mathrm{BC} .$ If $\mathrm{BD}=$ $4 \mathrm{~cm}$ and $\mathrm{CD}=9 \mathrm{~cm}$, then the length of the $\mathrm{AD}(\mathrm{in} \mathrm{cm})$ is?

A, B, C, D are four points on a circle. AC and BD intersect at a point $\mathrm{E}$ such that $\angle \mathrm{BEC}=$ $120^{\circ}$ and $\angle \mathrm{ECD}=40^{\circ} \cdot \angle \mathrm{BAC}$ is: