GK Expert Team Solutions for Exercise 1: OBJECTIVE TYPE QUESTIONS

Find the largest positive integer $n$ such that $n^3+100$ is divisible by $n+10$.

If $n^2+3n+2$ is divisible by $6$ and $n$ is a positive integer and less than $1991$, find how many values of $n$ are possible. 

How many pairs of positive integers $\left(x, y\right)$ exist, such that $\frac{1}{x}+\frac{1}{y}=\frac{1}{6}$?

Find the number of pairs $\left(x, y\right)$ of integers for which $2xy-5x+y=55$.

Let $P$ be a prime number greater than $3$, then $P^2-1$ is always divisible by:

If $n$ is a positive integer, then for how many values of $n$, $2^4+2^7+2^n$ is a square?

If $n$ is an integer, then for how many values of $n$, the expression $n^2+19n+92$ is a square?

For all integers $a$, $a^{13}-a$ is divisible by: