SSC CGL MATHS QUIZ

$\mathrm{AB}$ is the diameter of a circle with centre $\mathrm{O} . \mathrm{C}$ and $\mathrm{D}$ are two points on the circumference of the circle on either side of $\mathrm{AB}$, such that $\angle C A B=43^{\circ}$ and $\angle A B D=58^{\circ}$. What is difference (in degrees) between the measures of $\angle C A D$ and $\angle C B D$ ?

In $\triangle L M N$, the bisectors of $\angle L$ and $\angle N$ intersect at an angle of $116^{\circ}$. What is the measure (in degrees) of $\angle M$ ?

The bisector of $\angle B$ in $\triangle A B C$ meets $\mathrm{AC}$ at $\mathrm{D}$. If $\mathrm{AB}=15 \mathrm{~cm}, \mathrm{BC}=24 \mathrm{cm}$ and $\mathrm{AC}=26 \mathrm{~cm}$, then the length of $\mathrm{AD}$ (in $\mathrm{cm}$ ) is :

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

In $\triangle A B C, \angle A=92^{\circ}$. If $\mathrm{I}$ is the incentre of the triangle, then the measure of $\angle B I C$ 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?

$ABC$ 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 $ABD$?

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 $\triangle \mathrm{ABC}, \angle \mathrm{BAC}=90^{\circ}$ 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: