CDS Elementary Mathematics 2020 Question Paper

The number $2\times 3\times 5\times 7\times 11+1$ is

Two unequal pairs of numbers satisfy the following conditions:
(i) The product of the two numbers in each pair is 2160
(ii) The HCF of the two numbers in each pair is 12.
If $x$ is the mean of the numbers in the first pair and $y$ is the mean of the numbers in the second pair, then what is the mean of $x$ and $y$?

How many digits are there in $(54{)}^{10}$? (Given that ${\log }_{10}2=0.301$ and ${\log }_{10}3=0.477$)

Which one of the following is a set of solutions of the equation $x^{\sqrt{x}}=\sqrt[n]{x^x}$, if $n$ is a positive integer?

In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics?

If the sum of the digits of a number $10^n-1$, where $n$ is a natural number, is equal to 3798, then what is the value of $n$?

Which one of the following is the largest number among $2222^2$, $222^{22}$, $22^{222}$, $2^{2222}$?

If $m$ is the number of prime numbers between 0 and 50; and $n$ is the number of prime numbers between 50 and 100, then what is $(m-n)$ equal to?

If $\frac{a}{b}=\frac{1}{3}$, $\frac{b}{c}=2$, $\frac{c}{d}=\frac{1}{2}$, $\frac{d}{e}=3$ and $\frac{e}{f}=\frac{1}{4}$, then what is the value of $\frac{abc}{def}$?

Which one of the following is the largest divisor of $3^x+3^{x+1}+3^{x+2}$, if $x$ is any natural number?