# CDS MATHEMATICS QUIZ-2

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## Question 1:

A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with maximum height of $13.5$ metres above the ground. If the radius of the base is 14 metres, the cost of painting the inner side of the tent at the rate of Rs. 2 per square metre is:

## Question 2:

Rahul does half as much work as Rakesh does and Krishan does half as much work as Rahula and Rakesh do together, in the same time. If krishan alone can do the work in 40 days, then working together, the tree of them will finish the work in?

## Question 3:

Find the polar co-ordinate of a point $(\sqrt{3}, 1)$.

## Question 4:

In a village, each of the $60 \%$ of families has a goat; each of the $30 \%$ of families has a hen and each of the $15 \%$ of families has both a goat and a hen. In all there are 96 families in the village. How many families do not have a goat or a hen?

## Question 5:

Find $\frac{a^{4}+b^{4}}{a^{2}-a b \sqrt{2}+b^{2}}$, if $x=a^{2}+b^{2}$ and $\mathrm{y}=\mathrm{ab} \sqrt{2}$

## Question 6:

If $(x-2)$ is a factor of polynomial $x^{2}+k x+4$. Find the value of $k$.

## Question 7:

Simplify: $7 \frac{1}{2}-\left[2 \frac{1}{4} \div\left\{1 \frac{1}{4}-\frac{1}{2}\left(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\right)\right\}\right]$

## Question 8:

A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by $25^{\circ}$ a distance of 40 meters.

## Question 9:

The equation of circle with centre $(3,1)$ and radius is $4 \mathrm{~cm}$ is:

## Question 10:

50 liters of a mixture contain $30 \%$ of sprit and rest water. If 5 litres of water be mixed in it, the percentage of sprit in the new mixture is.