Practice questions
88551 published questions with worked solutions.
- Matrix A is such that A^2 = 2A - I where I is the identity matrix, then for n 2, A^n is equal to
- If P(n): 2 + 4 + 6 + (2n), n N, then P(k) = k(k+1) + 2 implies P(k+1) = (k+1)(k+2) + 2 is true for all k N. So, statement P(n) =...Not in JEE syllabus
- If A = bmatrix 1 & 0 1 & 1 bmatrix and I = bmatrix 1 & 0 0 & 1 bmatrix , then which one of the following holds for all n 1, by...Not in JEE syllabus
- Using mathematical induction, the numbers a_n's are defined by a_0 = 1, a_ n+1 = 3n^2 + n + a_n, (n 0). Then a_n is equal toNot in JEE syllabus
- The product of three consecutive natural numbers is divisible by
- Let P(n): n^2 + n + 1 is an even integer. If P(k) is assumed true P(k+1) is true. Therefore, P(n) is trueNot in JEE syllabus
- 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