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Question 1:

If a natural number $N$ is divided by 223 then it leaves 79 as remainder. Again, if $N$ is divided by 179 then the quotient is 315 ; find the remainder.

Question 2:

There are five bells which start ringing together at intervals of 3,6,9,12 and 15 seconds respectively. In 45 minutes, how many times will the bells ring simultaneously?

Question 3:

Given $P=2^{56}$ and $Q=\left(2^{0}+2^{1}+2^{2}+\cdots+2^{55}\right)$

Question 4:

A two-digit number is such that the product of the digits is 8 . If 63 is added to this number, the digits interchange their places. What is the sum of the digits in the number?

Question 5:

If the equation $4 x^{2}-2 k x+3 k=0$ has equal roots, then what are the values of $k$ ?

Question 6:

If 8 - digit number 4432A43B is divisible by 9 and 5 , then the sum of $\mathrm{A}$ and $\mathrm{B}$ is equal to:-

Question 7:

When 732 is divided by a positive integer $x$, the remainder is 12 . How many value of $x$ are there?

Question 8:

Find the total number of even factors of 2400

Question 9:

Find the least number which when divided by 6,7,8,9 and 12 leaves the same remainder 1 in each case?

Question 10:

If 5 times the sixth term of an Arithmetic Progression (AP) is equal to 6 times its eleventh term, then the 36 th term of the AP will be