SSC CGL MATHS QUIZ

Question 1:

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 2:

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 3:

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 4:

Points $\mathrm{A}$ and $\mathrm{B}$ are on a circle with centre $\mathrm{O}$. $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle from an external point $\mathrm{P}$. If $\mathrm{PA}$ and $\mathrm{PB}$ are inclined to each other at $42^{\circ}$, then find the measure of $\angle O A B$.

$42^{\circ}$

$21^{\circ}$

$69^{\circ}$

$25^{\circ}$

Question 5:

In a circle with centre $\mathrm{O}, \mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle at point $\mathrm{A}$ and point $\mathrm{B}$, respectively. $\mathrm{C}$ is a point on the major arc $\mathrm{AB}$. If $\angle \mathrm{ACB}=50^{\circ}$, then find the measure of $\angle \mathrm{APB}$.

$100^{\circ}$

$90^{\circ}$

$80^{\circ}$

$50^{\circ}$

Question 6:

In a right triangle $\mathrm{ABC}$, right angled at $\mathrm{B}$, altitude $\mathrm{BD}$ is drawn to the hypotenuse $\mathrm{AC}$ of the triangle. If $\mathrm{AD}=6 \mathrm{~cm}, \mathrm{CD}=5 \mathrm{~cm}$, then find the value of $A B^2+B D^2($ in $\mathrm{cm}) ?$

30

96

36

66

Question 7:

Side $\mathrm{BC}$ of a triangle $\mathrm{ABC}$ is produced to a point $\mathrm{D}$. If $\angle \mathrm{A}=40^{\circ}$ and $\mathrm{AC}$ $=\mathrm{BC}$, then $2 \angle \mathrm{ACD}+3 \angle \mathrm{B}$ is equal to:

$280^{\circ}$

$260^{\circ}$

$240^{\circ}$

$220^{\circ}$

Question 8:

O is the centre of a circle with diameter 16 cm . T is a point outside the circle and TA is a tangent to a circle. If OT = 17 cm, what is the length (in cm) of the tangent TA?

15

20

24

26

Question 9:

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 $\angle M$ ?

72

64

52

44

Question 10:

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 :

12

9

10

16