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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

Question 2:

What is the height (in $\mathrm{cm}$) of an equilateral triangle whose length of each side is $8 \mathrm{~cm}$?

Question 3:

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 $\mathrm{AD}$.

Question 4:

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 $\mathrm{cm}) ?$

Question 5:

Measures of two supplementary angles are $(2 a+b)^{\circ}$ and $(3 a-b)^{\circ}$ then, value of $3 \mathrm{a}$ is equal to

Question 6:

In a triangle $\mathrm{ABC}, \mathrm{D}$ is the midpoint of side $\mathrm{BC}$ such that $\mathrm{AD}=\mathrm{CD}$. If $\angle B=37^{\circ}$, then $\angle C$ is equal to:

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:

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:

Question 9:

The length of the median PS of a triangle $P Q R$ is half of the length of its side $\mathrm{QR}$. If $\angle \mathrm{R}=24^{\circ}$, then $\angle \mathrm{Q}$ is equal to:

Question 10:

The lengths of two sides of a triangle are 13 cm and 19 cm. The length of the third side of the triangle must lie between: