CDS MATHEMATICS QUIZ

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Question 1:

Sunil has been growing two types of bacteria $\mathrm{A}$ and $\mathrm{B}$ in two different enclosures on a particular day. A bacteria had a starting population of 2 . While B Bacteria had a starts population of 8 . However, A bacteria starts growing five hours before the 13 bacteria starts growing on the same day at 8p.m. Sunil checks the enclosures and finds that the two types of bacteria have the same population. If the population of A doubles every hours, but the population of $B$ is quardruple el every hour, at what time did he start growing B.

Question 2:

In a hostel, food is available for 200 students for 50 days. After 10 days, 50 more students join the hostel. For how many more days will the food last?

Question 3:

The sum of three numbers in A.P. is 27 , and their product is 504 then find fifth terms of an AP.

Question 4:

Find the value of $x$.

$109.07 \sqrt{x}-\frac{61}{21.02} \times x=47.96 \sqrt{x}$

Question 5:

A solid sphere of radius $2 \mathrm{~cm}$ is melted to convert in to a wire of length is $100 \mathrm{~cm}$. The radius of the wire.

Question 6:

In an equilateral $\triangle A B C$, the madians $\mathrm{A} \mathrm{D}$, $\mathrm{BE}$ and $\mathrm{CF}$ intersect each other at point $\mathrm{G}$. if the area of triangle AGE is $12 \sqrt{3} \mathrm{~cm}^{2}$, then find the lentght of AD.

Question 7:

In what ratio does the point $(-4,6)$ divide the line segment joining the points $\mathrm{A}(-6,10)$ and $\mathrm{B}(3,-8)$

Question 8:

If $x^{4}+\frac{1}{x^{4}}=14159$, then the value of $x+\frac{1}{x}$ is:

Question 9:

Atul has Stolen 10 liter of milk from a container and replaced with the same quantity of water. He again repeated this process 2 times. Thus the ratio of the milk become $343: 729$. Find the initial amount of milk in the container.

Question 10:

Find the value.

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

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