Mathematics questions
18011 published questions with worked solutions.
- The centre of the circle passing through the point (0, 1) and touching the parabola y=x^2 at the point (2, 4) is :
- The sum of distinct values of for which the system of equations ( -1)x+(3 +1)y+2 z=0 ( -1)x+(4 -2)y+( +3)z=0 2x+(3 +1)y+3(...
- The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never...
- Consider the data on x taking the values 0, 2, 4, 8, ..., 2^n with frequencies ^nC_0, ^nC_1, ^nC_2, ..., ^nC_n respectively. If...
- If x and y be two non-zero vectors such that | x + y |=| x | and 2 x + y is perpendicular to y , then the value of is __________.
- If n is a positive integer, then n^3 + 2n is divisible by
- 10^n + 3(4^ n+2 ) + 5 is divisible by (n N)Not in JEE syllabus
- Statement 1: For every natural number n 2, 1 1 + 1 2 + + 1 n > n Statement 2: For every natural number n 2, n(n+1) < n+1Not in JEE syllabus
- If a_1 = 1 and a_n = n a_ n-1 for all positive integer n 2, then a_5 is equal to
- 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