SSC CGL QUANT QUIZ(GEOMETRY+ALGEBRA)

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Question 1:

If $8 a^{3}+b^{3}=16$ and $2 a+b=4$, then find the value of $16 a^{4}+b^{4}$

Question 2:

What to add to $\frac{2}{x-1}$ to get $\frac{x^{2}+2 x+1}{x^{2}-1}$?

Question 3:

If $a+\frac{1}{a}=-\sqrt{3}$, find the value of $a^{3}+\frac{1}{a^{3}}$.

Question 4:

Simplify the following expression:
$ \frac{\left(a^2-4 b^2\right)^3+64\left(b^2-4 c^2\right)^3+\left(16 c^2-a^2\right)^3}{(a-2 b)^3+(2 b-4 c)^3+(4 c-a)^3}$

Question 5:

In $\mathrm{ △ ABC}, \mathrm{AB}=6 \mathrm{~cm}$ and $\mathrm{AD}$ is the angle bisector of $\mathrm{A}$. If $\mathrm{BD}: \mathrm{DC}=3: 2$, them what will be the value of $\mathrm{AC}$ ?

Question 6:

In the following figure, $\triangle A B O \sim \triangle D C O$ if $A B=3$ cm, $C D=2$ cm, $O C=3.8$ cm and $O D=3.2$ cm, then $(O A+O B )$ is equal to?

Question 7:

In a triangle $\mathrm{ABC}$, points $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are taken on $\mathrm{AB}, \mathrm{BC}$ and $\mathrm{CA}$, respectively, such that $\mathrm{BQ}=\mathrm{PQ}$ and $\mathrm{QC}=\mathrm{QR}$. If $\angle B A C=75^{\circ}$, What is the measure of $\angle P Q R$ (in degrees)?

Question 8:

An equilateral triangle $\mathrm{ABC}$ is inscribed in a circle with centre $\mathrm{O} . \mathrm{D}$ is a point on the minor arc $\mathrm{BC}$ and $\angle C B D=40^{\circ}$. Find the measure of $\angle B C D$.

Question 9:

In a circle with centre $\mathrm{O}, \mathrm{PR}$ 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 $\angle P T Q$ is :

Question 10:

O is the centre of a circle with diameter 20 cm . T is a point outside the circle and TA is a tangent to a circle. If OT = 26 cm, what is the length (in cm) of the tangent TA?

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