CGL MAINS SCORE BOOSTER QUANT QUIZ-7

ABCD is a cyclic quadrilateral whose diagonals intersect at E. If AB = BC, $\angle B A C=35^{\circ}$ and $\angle D B C=65^{\circ}$, then, $\angle DCE$ =?

If $x^{2}-x y+y^{2}=13$ and $x^{2}+x y+y^{2}=13$, then find the value of $\frac{x^{6}-y^{6}}{x^{2}-y^{2}}$ is.

If $8 x^{3}-27 y^{3}=(A x+B y)\left(C x^{2}-D y^{2}+6 x y\right)$, then $(A-B-C-D)$ is equal to?

If $x+y=4, \quad x y=3, \quad y+z=5, \quad y z=4, \quad z+x=7$ and $z x=12$, then find the value of $x^{3}+y^{3}+z^{3}-3 x y$?

The value of $\frac{1}{a^{2}+a x+x^{2}}-\frac{1}{a^{2}-a x+x^{2}}+\frac{2 a x}{a^{4}+a^{2} x^{2}+x^{4}}$:

A train crosses a Pole in 16 seconds running at a speed of $54 \mathrm{~km} / \mathrm{hr}$. Find the time (in seconds) in which it will cross another train moving in opposite direction at a speed which is greater than the speed of the former train by $33 \frac{1}{3} \%$, and the length of the later is $\left(\frac{3}{4}\right)^{\text {th }}$ of the length of the former train.

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 $\mathrm{cm}$ ).

Mr. Mukesh spends $37 \frac{1}{2} \%$ of his salary on item of daily use and $25 \%$ of the remainder on house rent after that he is left with Rs. 750. How much is his salary-

Ruchika's expenditure and savings are in the ratio $5: 3$. If her income increase by $12 \%$ and expenditure by $15 \%$ then by how much percent does his saving increase?

The average age of workers in a factory is $45 \%$ of the total strength of the factory. When strength of the factory is increased by $25 \%$, the average age of workers of the factory is increased by 3 months. If initial strength of factory was 80 then find the average age of newly admitted workers.