Practice questions
88551 published questions with worked solutions.
- If and are the roots of the equation 2x(2x+1)=1, then is equal to :
- Let z = x + iy be a non-zero complex number such that z^2=i|z|^2, where i= -1 , then z lies on the :
- The common difference of the A.P. b_1, b_2, ..., b_m is 2 more than the common difference of A.P. a_1, a_2, ..., a_n. If a_ 40 =...
- The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit...Not in JEE syllabus
- Let = 5 and A= pmatrix & - & pmatrix . If B=A+A^4, then det(B) :
- Let f : R → R be a function defined by f(x) = max x, x^2 . Let S denote the set of all points in R, where f is not...
- The area (in sq. units) of the region enclosed by the curves y=x^2-1 and y=1-x^2 is equal to :
- The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If P(A ∪ B) = 0.8, P(A ∩ C) =...
- if the constant term in the binomial expansion of ( x - k x^2 )^ 10 is 405, then |k| equals :
- Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in...
- If y= ( 2x -1 ) cosec x is the solution of the differential equation, dy dx +p(x)y= 2 cosec x, 0 < x < 2 , then the function p(x)...
- 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