# CDS MATHEMATICS QUIZ-1

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## Question 1:

Find the distance between the points $(7 \mathrm{k}+$ $2,5-3 \mathrm{k})$ and $(-3+7 \mathrm{k},-7-3 \mathrm{k})$

## Question 2:

A circular pavement was to be built around a square park of side is $12 \mathrm{~cm}$. The maximum width of pavement is $4 \mathrm{~m}$. calculate the cost of cementing the pavement at Rs. 16 per $\mathrm{m}^{2}$.

## Question 3:

In an euqilateral $\triangle A B C$, the medians, $\mathrm{AD}$, $\mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$. If the area of quardrilateral AEGF is $86 \sqrt{3} \mathrm{~cm}^{2}$, then find the length of $A D$ in $(\mathrm{cm})$.

## Question 4:

Find the value of $\mathrm{x}$.

$56.08 \%$ of $149.92+\sqrt{28.02 \times 6.98}-11 \frac{1}{9} \%$ of $998.9=x$

## Question 5:

If 5 times the sixth term of an Arithmetic Progression (AP) is equal to 6 times its eleventh term, then the 36 th term of the AP will be

## Question 6:

Simplify: $32-[48 \div\{36-(27-\overline{16-9})\}]=$ ?

## Question 7:

The average salary of a company increases by 200 when the salary of the manager, which is Rs. 19500 , is included. If the number of employees excluding the manager is the smallest cube divisible by 16, what is the final average of the company?

## Question 8:

In what ratio, sugar costing Rs. 60 per kg be mixed with sugar costing 40 per kg such that be selling the mixture at Rs. 56 per kg as there is a gain of $12 \%$ ?

## Question 9:

If $x^{4}+x^{2} y^{2}+y^{4}=28$ and $x^{2}+x y+y^{2}=7$, then the value of $\left(\frac{1}{x^{2}}+\frac{1}{y^{2}}\right)$.

## Question 10:

A mixture contains $80 \%$ acid and rest water part of mixture to be removed and replaced by same amount of water to make the ratio of water to Acid $4: 3$ is.