Mathematics questions
18011 published questions with worked solutions.
- The length of the minor axis (along y-axis) of an ellipse in the standard form is 4 3 . If this ellipse touches the line, x + 6y...
- If x=2 - 2 and y=2 - 2 , [0,2 ], then d^2y dx^2 at = is -
- If dy dx = xy x^2+y^2 ; y(1) = 1; then a value of x satisfying y(x) = e is -
- Let a – 2b + c = 1. If f(x)= vmatrix x+a & x+2 & x+1 x+b & x+3 & x+2 x+c & x+4 & x+3 vmatrix , then -
- If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain...
- The following system of linear equations 7x+6y-2z=0 3x+4y+2z=0 x-2y-6z=0, has
- If one end of a focal chord AB of the parabola y^2=8x is at A ( 1 2 ,-2 ), then the equation of the tangent to it at B is -
- Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b R, g'(a) = 5 and g(a) = b,...
- If the distance between the plane, 23x – 10y – 2z + 48 = 0 and the plane containing the lines x+1 2 = y-3 4 = z+1 3 and x+3 2 =...
- If C_r= ^ 25 C_r and C_0+5 C_1+9 C_2+ +(101) C_ 25 =2^ 25 k, then k is equal to ___________.
- The number of terms common to the two A.P.'s 3, 7, 11, ….. 407 and 2, 9, 16, …. 709 is ___________.
- If the curves, x^2-6x+y^2+8=0 and x^2-8y+y^2+16-k=0, (k > 0) touch each other at a point, then the largest value of k is...
- Let a , b and c be three vectors such that | a |= 3 , | b |=5, b c =10 and the angle between b and c is 3 . If a is perpendicular...
- In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at...
- A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a...
- If for some and in R, the intersection of the following three planes x + 4y - 2z = 1 x + 7y - 5z = x + 5y + z = 5 is a line in...
- If the matrices A = bmatrix 1 & 1 & 2 1 & 3 & 4 1 & -1 & 3 bmatrix , B = adj A and C = 3A, then | adj B| |C| is equal to :
- If f(x)= cases (a+2)x+ x x & ; x<0 b & ; x=0 (x+3x^2)^ 1/3 -x^ 1/3 x^ 4/3 & ; x>0 cases is continuous at x = 0, then a + 2b is...
- The value of _0^ 2 x ^8 x ^8 x+ ^8 x dx is equal to
- The integral dx (x+4)^ 8/7 (x-3)^ 6/7 is equal to : (where C is a constant of integration)