CDS MATHEMATICS QUIZ

Two $\mathrm{cm}$ of rain has fallen on a square $\mathrm{km}$ of land. Assuming that $50 \%$ of the raindrops could have been collected and contained in a pool having a $100 \mathrm{~m} \times 10 \mathrm{~m}$ base, by what level would the water level in the pool have increased?

The minimum value of $2 \sin ^{2} \theta+3 \cos ^{2} \theta$ is.

In a right angled triangle $A B C, \angle B$ is the right angle and $A C=2 \sqrt{5} \mathrm{~cm}$. If $A B-B C=$ $2 \mathrm{~cm}$ then the value of $\left(\cos ^{2} A-\cos ^{2} C\right)$ is:

Simplify: $4 \frac{4}{5} \div\left\{2 \frac{1}{5}-\frac{1}{2}\left(1 \frac{1}{4}-\overline{\frac{1}{4}-\frac{1}{5}}\right)\right\}$

If $\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+7 \sqrt{5} b$ then find the value of a.

The sum of fourth and sixth term of an A.P is10 . Find the sum of the first 5 terms of the progression.

The graphs of the equation $3 x-10 y-2=0$ and $2 x-3 y+4=0$. Intersect at $\mathrm{P}(\mathrm{a}, \mathrm{b})$. What is the value of $(a-b)$.

Find centroid of the triangle then the vertex of triangle is $(3,8)(5,6)$ and $(7,4)$.

8 men can complete a work in 32 days while 64 women can complete the same work in 12 days. 16 men and 16 women started working and worked for 12 days. How many additional men are required after that to complete the remaining work in 2 days.

Find the value.

$\frac{\tan 5 \theta+\tan 3 \theta}{4 \cos 4 \theta(\tan 5 \theta-\tan 3 \theta)}$