SSC CGL MATHS QUIZ

In a quadrilateral $\mathrm{ABCD}$, the bisectors of $\angle C$ and $\angle D$ meet at point $\mathrm{E}$. If $\angle C E D=67^{\circ}$ and $\angle A=57^{\circ}$, then the measure of $\angle B$ is

Sides $\mathrm{AB}$ and $\mathrm{AC}$ of $\triangle A B C$ are produced to points $\mathrm{D}$ and $\mathrm{E}$, respectively. The bisectors of $\angle C B D$ and $\angle B C E$ meet at P. If $\angle A=72^{\circ}$, then the measure of $\angle P$ is:

A cyclic quadrilateral $\mathrm{ABCD}$ is drawn in a circle with centre $\mathrm{O} . \mathrm{A}$ and $\mathrm{C}$ are joined to $\mathrm{O}$. If $\angle \mathrm{ABC}=4 \mathrm{p}$ and $\angle \mathrm{ADC}=5 \mathrm{p}$, what is the measure (in degrees) of the $\angle \mathrm{AOC}$ reflex?

In the given figure, find the value of PR.

$ABC$ is a triangle. $A B=5 \mathrm{~cm}, A C=\sqrt{41} \mathrm{~cm}$ and $B C=8 \mathrm{~cm}_{}$, $A D$ is perpendicular to $B C$. What is Area of triangle $ABD$?

A circle inscribed in $\triangle P Q R$ with touches its side $P Q, Q R$ and $R T$ at point $S, T$ and $U$ respectively. If $P Q=12 \mathrm{~cm}, Q R=8 \mathrm{~cm}$, and $R P=16 \mathrm{~cm}$ then find the length of $P S, Q T$ and $R U$.

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 :

In $\triangle A B C$, the sides $\mathrm{AB}$ and $\mathrm{AC}$ are produced to $\mathrm{P}$ and $\mathrm{Q}$, respectively. The bisectors of $\angle \mathrm{PBC}$ and $\angle \mathrm{QCB}$ intersect at a point $\mathrm{O}$. If $\angle \mathrm{A}=56^{\circ}$, then $\angle \mathrm{BOC}$ equals:

The perimeters of two similar triangles $\Delta \mathrm{ABC}$ and $\Delta \mathrm{PQR}$ are $36 \mathrm{~cm}$ and $24 \mathrm{~cm}$ respectively. If $\mathrm{PQ}=10 \mathrm{~cm}$, then $\mathrm{AB}$ is: