Practice questions
88551 published questions with worked solutions.
- Statement 1: (n+2)! (n-1)! is divisible by 6 Statement 2: Product of 3 consecutive integers is divisible by 3!
- The remainder when 5^ 99 is divided by 13, is
- If n N, then 3^ 2n + 7 is divisible by
- For all n N, 2 4 2^ n-1 equals to
- The sum to n terms of the series 1^3 + 3^3 + 5^3 + is
- The nth term of the series 4 + 14 + 30 + 52 + 80 + 114 + is
- (n+2)! (n-1)! is divisible by
- 3 + 13 + 29 + 51 + 79 + to n terms =
- The sum of the cubes of three consecutive natural numbers is divisible by
- The sum of n terms of the series 1 + (1+a) + (1+a+a^2) + (1+a+a^2+a^3) + , is
- If n N, then n(n^2 - 1) is divisible by
- For all n N, n
- If n is an odd positive integer, then a^n + b^n is divisible by
- If x^n - 1 is divisible by x - k, then the least positive integral value of k is
- For all n N, 3n^5 + 5n^3 + 7n is divisible byNot in JEE syllabus
- If 10^n + 3 4^ n+2 + is exactly divisible by 9 for all n N, then the least positive integral value of is
- The nth terms of the series 3 + 7 + 13 + 21 + is
- If f(x) = x^2 + 2bx + 2c^2 and g(x) = -x^2 - 2cx + b^2 such that f(x) > g(x), then the relation between b and c, is
- The set of all solutions of the inequation x^2 - 2x + 5 0 in R is
- If 2x 2x^2+5x+2 > 1 x+1 , then