CDS MATHEMATICS QUIZ

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Question 1:

When a number is divided by 30,20 and 10 successively the remainders are 5,5 $\& 5$ respectively. Find the least number:

Question 2:

When a number divided by $5,4,3$ successively it gives remainder 4,3,1 respectively and last quotient is 2 , if the same number is divided by 15 find the remainder?

Question 3:

When a number is divided by 3 and 5 successively the remainders are 1, 2 respectively. What will be the remainder if the number is divided by $15 ?$

Question 4:

When a number divided by $6,4 \& 3$ successively it gives remainder $3,2 \& 1$ respectively, if the order of divisor be reversed then, find the successive remainder.

Question 5:

In the given expression find the Remainder

$\left(\frac{24 !}{23}\right)$

Question 6:

When $x$ is divided by 6 , remainder obtained is 3 . Find the remainder when $\left(x^{4}+\right.$ $\left.x^{3}+x^{2}+x+1\right)$ is divided by 6 .

Question 7:

Raju had to divide 1080 by $N$, a two-digit number. Instead, he performed the division using $M$, which is obtained by reversing the digits of $N$, and ended up with a quotient that was 25 less than what he should have obtained otherwise. If 1080 is exactly divisible both by $N$ and $M$, find the sum of the digits of $N$.

Question 8:

Two friends Harry and Jayesh were discussing about two numbers. They found the two numbers to be such that one was twice the other. However, both had the same number of prime factors, while the larger one had 4 more factors than the smaller one. What are the numbers?

Question 9:

To celebrate their victory in the World Cup, the Indian Team distributed sweets. If the sweets were distributed among 11 players, 2 sweets were left. When the sweets were distributed to 11 players, 3 extra players, and 1 coach, even then 2 sweets were left. What is the minimum number of sweets in the box?

Question 10:

Simplify and find the value of $x$ in the following questions:

$(7)^{x}=16 \frac{2}{3} \%$ of $9846+19(22+18)$