Mathematics questions
18011 published questions with worked solutions.
- If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 3 2 and the curve y = 1 + 4x – x^2, then 12 m is...
- Let B be the centre of the circle x^2+y^2-2x+4y+1=0. Let the tangents at two points P and Q on the circle intersect at the point...
- Let f(x) be a cubic polynomial with f(1) = –10, f(–1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x =...
- The sum of absolute maximum and minimum values of the function f(x) = |x^2-5x+6|-3x+2 in the interval [–1, 3] is equal to :
- The value of the integral _ - /4 ^ /4 x+ 4 2- 2x dx is :
- Let a, b be two real numbers such that ab < 0. If the complex number 1+ai b+i is of unit modulus and a + ib lies on the circle |z...
- Let the plane P pass through the intersection of the planes 2x + 3y – z = 2 and x + 2y + 3z = 6, and be perpendicular to the...
- Let s = x R:0<x<1 and 2 ^ -1 ( 1-x 1+x )= ^ -1 ( 1-x^2 1+x^2 ) If n(S) denotes the number of elements in S then :
- Let a =2 i -7 j +5 k , b = i + k , c = i +2 j -3 k be three given vectors. If r is a vector such that r a = c a and r b =0, then...
- Let P(x_0, y_0) be the point on the hyperbola 3x^2-4y^2=36, which is nearest to the line 3x + 2y = 1. Then 2(y_0-x_0) is equal to...
- The number of integral values of k, for which one root of the equation 2x^2-8x+k=0 lies in the interval (1, 2) and its other root...
- Let P(S) denote the power set of S = 1, 2, 3,…,10 . Define the relations R_1 and R_2 on P(S) as AR_1B if (A B^c) (B A^c)= and...
- Let x= (x^ y^ ) be the solution of differential equation 2x^2ydy-(1-xy^2)dx=0, x > 0, y(2) = _e2 . Then + - equals :
- For the system of linear equations ax + y + z = 1, x + ay + z = 1, x + y + az = , which one of the following is NOT correct?
- Two dice are thrown independently. Let A be the event that the number appeared on the 1^ st die is less than the number appeared...
- The area of the region given by (x,y):xy 8,1 y x^2 is :
- Let a =5 i - j -3 k and b = i +3 j +5 k be two vectors. Then which one of the following statements is True?
- If A = 1 2 bmatrix 1& 3 - 3&1 bmatrix , then :
- If the term without x in the expansion of (x^ 2/3 + x^3 )^ 22 is 7315, then | | is equal to __________.
- The point of intersection C of the plane 8x + y + 2z = 0 and the line joining the points A(–3, –6, 1) and B(2, 4, –3) divides the...