Mathematics questions
18011 published questions with worked solutions.
- If f: R R is a twice differentiable function such that f''(x)>0 for all x R , and f ( 1 2 )= 1 2 , f(1)=1, then
- How many 3 3 matrices M with entries from 0,1,2 are there, for which the sum of the diagonal entries of M^TM is 5?
- Let S= 1,2,3, ,9 . For k=1,2, ,5, let N_k be the number of subsets of S, each containing five elements out of which exactly k are...
- Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x+y+z=10. Then the probability that z is...
- Let and be nonzero real numbers such that 2( - )+ =1. Then which of the following is/are true?
- If f: R R is a differentiable function such that f'(x)>2f(x) for all x R , and f(0)=1, then
- Let f(x)= 1-x(1+|1-x|) |1-x| ( 1 1-x ) for x 1. Then
- If f(x)= vmatrix (2x) & (2x) & (2x) - x & x & - x x & x & x vmatrix , then
- If the line x= divides the area of region R= (x,y) R ^2:x^3 y x,0 x 1 into two equal parts, then
- If I= _ k=1 ^ 98 _k^ k+1 k+1 x(x+1) ,dx, then
- For a non-zero complex number z, let (z) denote the principal argument with - < (z) . Then, which of the following statement(s)...
- In a triangle PQR, let PQR=30^ and the sides PQ and QR have lengths 10 3 and 10, respectively. Then, which of the following...Not in JEE syllabus
- Let P_1: 2x+y-z=3 and P_2: x+2y+z=2 be two planes. Then, which of the following statement(s) is (are) TRUE?
- For every twice differentiable function f: R [-2,2] with (f(0))^2+(f'(0))^2=85, which of the following statement(s) is (are) TRUE?
- The value of (( _29)^2 )^ 1 _2( _29) ( 7 )^ 1 _47 is _____.
- The number of 5 digit numbers which are divisible by 4, with digits from the set 1,2,3,4,5 and the repetition of digits is...
- Let X be the set consisting of the first 2018 terms of the arithmetic progression 1,6,11, , and Y be the set consisting of the...
- The number of real solutions of the equation ^ -1 ( _ i=1 ^ x^ i+1 -x _ i=1 ^ ( x 2 )^i )= 2 - ^ -1 ( _ i=1 ^ (- x 2 )^i- _ i=1 ^...
- For each positive integer n, let y_n= 1 n ((n+1)(n+2) (n+n) )^ 1 n . For x R , let [x] be the greatest integer less than or equal...
- Let a and b be two unit vectors such that a b =0. For some x,y R , let c =x a +y b +( a b ). If | c |=2 and the vector c is...