Mathematics questions
18011 published questions with worked solutions.
- If the sum of the coefficients of all even powers of x in the product (1+x+x^2+ +x^ 2n )(1-x+x^2-x^3+ +x^ 2n ) is 61, then n is...
- If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is...
- Let S be the set of points where the function, f(x) = |2– | x – 3||, x R, is not differentiable. Then _ x S f(f(x)) is equal to ….
- For which of the following ordered pairs ( , ), the system of linear equations x+2y+3z=1 3x+4y+5z= 4x+4y+4z= is inconsistent ?
- If x ,dx ^3x(1+ ^6x)^ 2/3 =f(x)(1+ ^6x)^ 1/ +c where c is a constant of integration, then f ( 3 ) is equal to -
- Let A and B be two independent events such that P(A)= 1 3 and P(B)= 1 6 . Then, which of the following is TRUE ?
- For a > 0, let the curves C_1:y^2=ax and C_2:x^2=ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect...
- The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x^2=4y, internally in...
- If the equation, x^2+bx+45=0 (b R) has conjugate complex roots and they satisfy |z+1|=2 10 , then -
- Let y = y(x) be a solution of the differential equation, 1-x^2 dy dx + 1-y^2 =0, |x| < 1. If y ( 1 2 )= 3 2 , then y ( -1 2 ) is...
- Let two points be A(1, –1) and B(0, 2). If a point P(x', y') be such that the area of = 5 sq. units and it lies on the line,...
- Let the line y = mx and the ellipse 2x^2+y^2=1 intersect at a point P in the first quadrant. If the normal to this ellipse at P...
- The inverse function of f(x)= 8^ 2x -8^ -2x 8^ 2x +8^ -2x , x (-1,1), is ______________ -
- Let f(x)=x ^ -1 (- |x|), x [- 2 , 2 ], then which of the following is true ?
- The shortest distance between the lines x-3 3 = y-8 -1 = z-3 1 and x+3 -3 = y+7 2 = z-6 4 is -
- Let the volume of a parallelopiped whose coterminous edges are given by u = i + j + k , v = i + j +3 k and w =2 i + j + k be 1...
- If c is a point at which Rolle's theorem holds for the function, f(x)= _e ( x^2+ 7x ) in the interval [3, 4], where R, then...
- Let f(x)=( ( ^ -1 x)+ ( ^ -1 x))^2-1, |x| > 1. If dy dx = 1 2 d dx ( ^ -1 (f(x))) and y( 3 )= 6 , then y(- 3 ) is equal to -
- The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is...
- Let f:R R be such that for all x R (2^ 1+x +2^ 1-x ), f(x) and (3^x+3^ -x ) are in A.P., then the minimum value of f(x) is -