# CDS MATHEMATICS QUIZ-6

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## Question 1:

A cuboid of mercury, measuring 40 cm $\times 20$ cm $\times 16$ cm, is melted to form spheres of diameter $10$ cm. How many balls will be made in this way? (in approximation)

## Question 2:

A, B, C, D are four points on a circle. AC and BD intersect at a point $\mathrm{E}$ such that $\angle \mathrm{BEC}=$ $120^{\circ}$ and $\angle \mathrm{ECD}=40^{\circ} \cdot \angle \mathrm{BAC}$ is:

## Question 3:

The average score (runs/match) of Kohli before the start of World Cup was 35 . In the world cup of 6 matches, his total score was 360 runs. Find the total number of matches played by him till date, if his new average after the series is $40$.

## Question 4:

The area of two similar triangles $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are 25 and 36 sq. unit. what is the ratio of their corresponding perimeter ?

## Question 5:

How many terms of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3?

## Question 6:

A shopkeeper gets Rs. there is a loss of $20\%$ by selling 12 toffees in 1 Rupee. How many toffees should I sell to make a profit of $20$?

## Question 7:

Simplify :- $4+\frac{1}{5}[\{-10 \times(25+{13-3})\} \div(-5)]$

## Question 8:

If $x=2+\sqrt{3}$, then the value, $\sqrt{x}+\frac{1}{\sqrt{x}}$

## Question 9:

Average weight of three friends Amar, Vikas and Damani is $70 \mathrm{~kg}$. Another person Vishal joins the group and now the average is $66 \mathrm{~kg}$. If another person Arpit whose weight is $6 \mathrm{~kg}$ more than Vishal, joins the group replacing Amar, then average weight of Vikas, Damani, Vishal and Arpit becomes $75 \mathrm{~kg}$. What is the weight of Amar (in kg )?

## Question 10:

There is a mixture of milk and water of 100 liter. 1/5th part of this mixture is milk. If 20 liter mixture and taken out and 'a' liter milk is added to this mixture and the ration was reversed, then 'b' liter water was added to this mixture than again the ratio was reversed. Find the value of (b - 3a).