Mathematics questions
18011 published questions with worked solutions.
- ( ^ -1 3 5 + ^ -1 5 13 + ^ -1 33 65 ) is equal to :
- Let T_r be the r^ th term of an A.P. If for some m, T_m = 1 25 , T_ 25 = 1 20 and 20 _ r=1 ^ 25 T_r = 13, then 5m _ r=m ^ 2m T_r...
- If the image of the point (4, 4, 3) in the line x-1 2 = y-2 1 = z-1 3 is ( , , ), then + + is equal to
- If _ - /2 ^ /2 96x^2 ^2 x (1+e^x) dx = ( ^2 + ), , Z, then ( + )^2 equals :
- The sum of all local minimum values of the function f(x) = cases 11 18 (x-4)(x-5), & x > 2 1 3 (7+2|x|), & -1 x 2 1-2x, & x < -1...
- The sum, of the squares of all the roots of the equation x^2 + |2x-3| - 4 = 0, is
- Let for some function y = f(x), _0^x t f(t) ,dt = x^2 f(x), x > 0 and f(2) = 3. Then f(6) is equal to
- Let ^nC_ r-1 = 28, ^nC_r = 56 and ^nC_ r+1 = 70. Let A(4cost, 4sint), B(2sint, –2cost) and C(3r – n, r^2 – n – 1) be the vertices...
- Let O be the origin, the point A be z_1 = 3 + 2 2 i, the point B(z_2) be such that 3 |z_2| = |z_1| and arg (z_2) = (z_1) + 6 ....
- Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate...
- Let M denote the set of all real matrices of order 3 × 3 and let S = –3, –2, –1, 1, 2 . Let S_1 = A = [a_ ij ] M : A = A^T and a_...
- If = 1 + _ r=1 ^ 6 (-3)^ r-1 ^ 12 C_ 2r-1 , then the distance of the point (12, 3 ) from the line x - 3 y + 1 = 0 is
- Let a = i + j + k , b = 2 i +2 j + k and d = a b . If c is a vector such that a . c = | c |, | c -2 a |^2 = 8 and the angle...
- Let f(x) = cases 5, & x > 2 1+x+[x], x+2[x] , & 0 x 2 3x, & x < 0 cases where [.] denotes greatest integer function. If and are...
- Let E_1 : x^2 9 + y^2 4 = 1 be an ellipse. Ellipses E_i's are constructed such that their centres and eccentricities are same as...
- Let A, B, C be three points in xy-plane, whose position vectors are given by 3 i + j , i + 3 j and a i +(1-a) j respectively with...
- If the components of a = i + j + k along and perpendicular to b =3 i + j - k respectively, are 16 11 (3 i + j - k ) and 1 11 (-4...
- If α + iβ and γ + iδ are the roots of x^2 - (3-2i)x - (2i-2) = 0, i= -1 , then αγ + βδ is equal to :
- Let S be the set of all the words that can be formed by arranging all the letters of the word 'GARDEN'. From the set S, one word...
- Let f be a real valued continuous function defined on the positive real axis such that g(x)= _0^x tf(t)dt. If g(x^3)=x^6+x^7,...