JEE Main questions
34495 published questions with worked solutions.
- The number a^n - b^n (a, b are distinct rational numbers and n N) is always divisible by
- If P(n) is a statement such that P(3) is true. Assuming P(k) is true P(k+1) is true for all k 3, then P(n) is trueNot in JEE syllabus
- For natural number n, 2^n (n-1)! < n^n, if
- The greatest positive integer, which divides (n+2)(n+3)(n+4)(n+5)(n+6) for all n N, is
- For each n N, 10^ 2n-1 + 1 is divisible by
- Let P(n) denotes the statement that n^2 + n is odd. It is seen that P(n) P(n+1), P(n) is true for allNot in JEE syllabus
- For all n N, 2 4^ 2n+1 + 3^ 3n+1 is divisible by
- For all positive integral values of n, 3^ 2n - 2n + 1 is divisible by
- Statement 1: If P(n) is defined as 2^n < n!, then P(n) is true for all n > 3 Statement 2: In P(n), n may be negativeNot in JEE syllabus
- If x^ 2n-1 + y^ 2n-1 is divisible by x + y, if n is
- If P(n) is a statement (n N) such that, if P(k) is true, P(k+1) is true for k N, then p(n) is trueNot in JEE syllabus
- x(x^ n-1 - n ^ n-1 ) + ^n(n-1) is divisible by (x - )^2 for
- If A = bmatrix & - & bmatrix , then for n N, A^n is equal to
- If P(n): 3^n < n!, n N, then P(n) is trueNot in JEE syllabus
- 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