SSC CHSL MATHS QUIZ

Question 1:

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 $\angle A=78^{\circ}$, then the measure of $\angle P$ is:

$51^{\circ}$

$61^{\circ}$

$55^{\circ}$

$56^{\circ}$

Question 2:

The center of a circle of diameter $20 \mathrm{~cm}$ is $O$. $T$ is a point outside the circle and $T A$ is the tangent to the circle. If OT is $=26 \mathrm{~cm}$, then what is the length of the tangent TA in $(\mathrm{cm}$)?

24

26

18

20

Question 3:

In a circle with centre $\mathrm{O}$, chords $\mathrm{PR}$ and $\mathrm{QS}$ meet at the point $\mathrm{T}$, when produced, and $\mathrm{PQ}$ is a diameter. If $\angle R O S=42^{\circ}$, then the measure of $\angle \mathrm{PTQ}$ is

$59^{\circ}$

$48^{\circ}$

$69^{\circ}$

$58^{\circ}$

Question 4:

In $\triangle \mathrm{ABC}$, the bisector of $\angle \mathrm{B}$ meets $\mathrm{AC}$ at the point $\mathrm{D}$. If $\mathrm{AB}=12 \mathrm{~cm}, \mathrm{BC}=18 \mathrm{~cm}$ and $\mathrm{AC}=$ $15 \mathrm{~cm}$, then Find the length (in $\mathrm{cm}$) of $\mathrm{AD}$.

6

9

5

12

Question 5:

In $\triangle A B C, \angle B=90^{\circ}, A B=8 \mathrm{~cm}$ and $B C=15 \mathrm{~cm}$. $D$ is a point on $B C$ such that $A D$ bisects $\angle A$. The length (in cm) of $B D$ is:

$4.5$

$4.8$

$4.2$

$3.6$

Question 6:

In triangles $\mathrm{ABC}$ and $\mathrm{PQR}, \mathrm{BC}=3 \mathrm{~cm}, \mathrm{AC}=3.5 \mathrm{~cm}, \mathrm{PQ}=3.5 \mathrm{~cm}$, $\angle \mathrm{C}=48^{\circ}, \mathrm{QR}=3 \mathrm{~cm}$ and $\angle \mathrm{Q}=48^{\circ}$. Then, which of the following is true?

$\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}$

$\triangle \mathrm{ABC} \cong \triangle \mathrm{RPQ}$

$\triangle \mathrm{ABC} \cong \triangle \mathrm{PRQ}$

$\triangle \mathrm{ABC} \cong \triangle \mathrm{QPR}$

Question 7:

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:

$318^{\circ}$

$304^{\circ}$

$264^{\circ}$

$128^{\circ}$

Question 8:

$O$ is a point on a line $A B$ and $O C$ and $O D$ are two rays on the same side of $\mathrm{AB}$ such that ray $\mathrm{OC}$ lies between rays $\mathrm{OA}$ and $\mathrm{OD}$. If $\angle \mathrm{AOC}=3 \mathrm{y}, \angle \mathrm{COD}=$ $30^{\circ}$ and $\angle \mathrm{BOD}=5 \mathrm{y}$, then the value of $4 y+10^{\circ}$ is:

$70^{\circ}$

$75^{\circ}$

$85^{\circ}$

$90^{\circ}$

Question 9:

$\mathrm{ABCD}$ is a rhombus in which $\angle \mathrm{BAC}=50^{\circ}$, then $3 \angle \mathrm{D}-2 \angle \mathrm{DAC}$ is equal to:

$120^{\circ}$

$140^{\circ}$

$150^{\circ}$

$160^{\circ}$

Question 10:

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:

$95^{\circ}$

$110^{\circ}$