SSC CGL MATHS QUIZ

In the following figure, $\mathrm{AB}$ be the diameter of a circle whose center is $\mathrm{O} .$ If $\angle A O E=150^{\circ}, \angle D A O=51^{\circ}$, then the measure of $\angle C B E$ is:

In any triangle $\mathrm{ABC}$, the base angles at $\mathrm{B}$ and $C$ are bisected by $B O$ and $C O$ respectively.Then $\angle \mathrm{BOC}$ is:

If $\triangle \mathrm{ABC}$ is an isosceles triangle with $\mathrm{AB}=\mathrm{AC}$ and $\angle \mathrm{ABC}=54^{\circ}$, then $\angle  \mathrm{BAC}$ is:

PRT is a tangent to a circle with centre O, at the point $R$ on it. Diameter SQ of the circle is produced to meet the tangent at $\mathbf{P}$ and $\mathbf{Q R}$ is joined. If $\angle \mathbf{Q R P}$ $=28^{\circ}$, then the measure of $\angle S P R$ is:

If G be the centroid of $\Delta \mathrm{ABC}$ and the area of $\Delta \mathrm{GBD}$ is $6 \mathrm{sq}.\mathrm{cm}$, where $\mathrm{D}$ is the mid-point of side BC, then the area of $\Delta \mathrm{ABC}$ is:

PQRS is a cyclic quadrilateral in which $PQ =14.4 \mathrm{~cm}, Q R=12.8 \mathrm{~cm}$ and $S R=9.6 \mathrm{~cm}$. If PR bisects QS, what is the length of PS?

Two circles with centres $\mathrm{O}$ and $\mathrm{P}$ of radii $16 \mathrm{~cm}$ and $9 \mathrm{~cm}$, respectively, touches each other externally at a point A. BC is a direct common tangent to these two circles Where B and C are the points on the circles respectively. The length of $\mathrm{BC}$ (in $\mathrm{cm}$ ) is:

In quadrilateral $A B C D$, the bisectors of $\angle A$ and $\angle B$ meet at $O$ and $\angle A O B=64^{\circ} \cdot \angle C+\angle D$ is equal to: