Mathematics questions
18011 published questions with worked solutions.
- If the domain of the function f(x) = _ (10x^2-17x+7) (18x^2-11x+1) is (- ,a) (b,c) (d,e, ) - e , then 90(a+b+c+d+e) equals:
- Let each of the two ellipses E_1: x^2 a^2 + y^2 b^2 =1, (a>b) and E_2: x^2 A^2 + y^2 B^2 =1, (A<B) have eccentricity 4 5 . Let...
- The value of 3 cosec 20^ - 20^ 20^ 40^ 60^ 80^ is equal to
- Let S = z C : | z-6i z-2i | = 1 and | z-8+2i z+2i | = 3 5 . Then _ z S |z|^2 is equal to
- If x = 5 12 for some x ( , 3 2 ), then 7x ( 13x 2 + 13x 2 ) + 7x ( 13x 2 - 13x 2 ) is equal to
- Let f(t) = ( 1- ( _e t) 1- ( _e t) )dt, t>1. If f(e^ /2 ) = -e^ /2 and f(e^ /4 ) = e^ /4 , then equals
- Let R be a relation defined on the set 1,2,3,4 1,2,3,4 by R = ((a,b),(c,d)): 2a+3b = 3c+4d . Then the number of elements in R is
- Let A(1,0), B(2,-1) and C ( 7 3 , 4 3 ) be three points. If the equation of the bisector of the angle ABC is x + y = 5, then the...
- Let S = 1 25! + 1 3!23! + 1 5!21! + up to 13 terms. If 13S = 2^k n! , k N, then n+k is equal to
- Consider an A.P.: a_1, a_2, , a_n; a_1>0. If a_2 - a_1 = -3 4 , a_n = 1 4 a_1, and _ i=1 ^ n a_i = 525 2 , then _ i=1 ^ 17 a_i is...
- Let , R be such that the function f(x) = cases 2 (x^2-2)+2 x, & x<1 ( +3)x+( - ), & x 1 cases be differentiable at all x R . Then...
- The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation in this data is replaced by ,...
- The number of the real solutions of the equation : x|x+3|+|x-1|-2=0 is
- Let a line L passing through the point P(1,1,1) be perpendicular to the lines x-4 4 = y-1 1 = z-1 1 and x-17 1 = y-71 1 = z 0 ....
- The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0,1,2,5,9, if the...
- The number of 3 2 matrices A, which can be formed using the elements of the set -2,-1,0,1,2 such that the sum of all the diagonal...
- Let the length of the latus rectum of an ellipse x^2 a^2 + y^2 b^2 =1, (a>b), be 30 . If its eccentricity is the maximum value of...
- Let _1, _2, _3, _4 be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If _1+ _2+...
- ( 1 3 + 4 7 )+ ( 1 3^2 + 1 3 4 7 + 4^2 7^2 )+ ( 1 3^3 + 1 3^2 4 7 + 1 3 4^2 7^2 + 4^3 7^3 )+ upto infinite terms is equal to -
- Let P=[p_ ij ] and Q=[q_ ij ] be two square matrices of order 3 such that q_ ij = 2^ (i+j-1) p_ ij and (Q) = 2^ 10 . Then the...