# CDS MATHEMATICS QUIZ -12

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## Question 1:

The average of the ages of four persons is 36 years 3 months. If their ages are in the ratio of 5:7:9:8 respectively, then what is the difference between the ages of eldest and youngest person? (in years)

## Question 2:

The centroid of an equilateral triangle $\triangle \mathrm{ABC}$ is $\mathrm{G}$. If $\mathrm{AC}=30 \mathrm{~cm}$, and $\mathrm{AD}$ is a median then what is the length (in $\mathrm{cm}$ ) of AG is?

## Question 3:

If $\sin 5 x=\cos 4 x, 5 x$ is an acute angle then $\tan 3 x$ is equal to:

## Question 4:

A cylindrical vessel of radius $30 \mathrm{~cm}$ and height $42 \mathrm{~cm}$ is full of water. Its contents are emptied into a rectangular tub of length $75 \mathrm{~cm}$ and breadth $44 \mathrm{~cm}$. The height (in $\mathbf{c m}$ ) to which the water rises in the tub is. (Take $\pi=\frac{22}{7}$ )

## Question 5:

The sum of the digits of a two-digit number is $1 / 7$ of the number. The unit digit is 4 less than the tens digit. If the number obtained on reversing its digits is divided by 7 , the remainder will be:

## Question 6:

Two pillars of equal height are standing on either side of a road $60 \mathrm{~m}$ wide. From a point on the road, the angles of elevation of the tops of the two pillars from the middle of the pillars are $60^{\circ}$ and $30^{\circ}$ Respectively, then the height of the pillars will be

## Question 7:

In what ratio should oil costing Rs.200/liter be mixed with oil costing 240/liter so that after selling the mixture at Rs.258/liter there is a gain of $20 \%$ ?

## Question 8:

Ranjit can do a piece of work in 25 days while Anji can do it in 20 days. They work together for 5 days and then Ranjit leaves. In how many days will Anji take to finish the remaining work?

## Question 9:

If the mean and standard deviation coefficients of a set of data are 10 and 5 respectively, then the standard deviation of the set of data will be

## Question 10:

A train $A$ moving with a speed of $60 \mathrm{~km} / \mathrm{h}$, another train $B$ coming from the opposite direction with a speed of $48 \mathrm{~km} / \mathrm{h}$ Completely crosses in 20 seconds. The length of train $B$ is $1.5$ times the length of train $A$. Train $B$ crosses a tunnel in 57 seconds. What is the length of the tunnel (in $\mathrm{m}$)?