CGL MAINS SCORE BOOSTER QUANT QUIZ-8

Attempt now to get your rank among 18 students!

Question 1:

If $27(x+y)^{3}-8(x-y)^{3}=(x+5 y)\left(A x^{2}+B y^{2}+C x y\right)$ then what is the value of $(A-B-C)$?

Question 2:

If $m$ and $n$ are distinct natural numbers, then which of the following is/are integer/integers?
1. $\frac{m}{n}+\frac{n}{m}$
$2. \quad m n\left(\frac{m}{n}+\frac{n}{m}\right)\left(m^{2}+n^{2}\right)$
3. $\frac{m n}{m^{2}+n^{2}}$
Select the correct answer using the code given below:

Question 3:

The rate of interest for the first 3 years is $7 \%$ p.a., for the next 2 years is $8 \%$ p.a., and for the period beyond 5 years is $13 \%$ p.a. If a person gets Rs.30800 as total amount with simple interest after 8 years, then how much money did he invest?

Question 4:

If $a^{2}+b^{2}=10 b-34-6 a$, find $(b-a)$ :

Question 5:

If a side of a square is increased by $25 \%$ find the $\%$ change in its area?

Question 6:

In a circle centre at $\mathrm{O}$, a tangent $\mathrm{AP}$ is drawn from an external point $\mathrm{A}$. If $\mathrm{OA}=61 \mathrm{~cm}$ and $\mathrm{OP}=11 \mathrm{~cm}$, then the lengthof tangent AP is:

Question 7:

In an equilateral $\triangle \mathrm{ABC}$, the medians $\mathrm{AD}, \mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$, if the area of quadrilateral $\mathrm{CDGE}$ is $36 \sqrt{3} \mathrm{~cm}^{2}$, then find the length of $\mathrm{AD}$ (in $\mathrm{cm}$ ).

Question 8:

If $\triangle \mathrm{ABC}$ is an isosceles triangle with $\mathrm{AB}=\mathrm{AC}$ and $\angle \mathrm{ABC}=54^{\circ}$, then $\angle  \mathrm{BAC}$ is:

Question 9:

If $\tan \left(3 x+30^{\circ}\right)=\operatorname{cotx}$ and angle $x$ and $\left(3 x+30^{\circ}\right)$ (in degrees) are acute angles, then the value of $\sin 2 x$ is:

Question 10:

In a group of 12 friends, 11 friends spent Rs. 43 each for their meal and the remaining 1 spent Rs.22 more than the average expenditure of all 12 friends. The total expenditure for their meal was:

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