Mathematics questions
18011 published questions with worked solutions.
- _ x 0 ( 3x^2+2 7x^2+2 )^ 1/x^2 is equal to -
- If a , b and c are the greatest values of ^ 19 C_p, ^ 20 C_q and ^ 21 C_r respectively, then -
- The number of all 3 × 3 matrices A, with enteries from the set –1, 0, 1 such that the sum of the diagonal elements of AA^T is 3,...
- An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so...
- The sum _ k=1 ^ 20 (1+2+3+ +k) is ___________________.
- The least positive value of 'a' for which the equation, 2x^2+(a-10)x+ 33 2 =2a has real roots is ______________.
- Let the normal at a point P on the curve y^2-3x^2+y+10=0 intersect the y-axis at (0, 3 2 ). If m is the slope of the tangent at P...
- The mirror image of the point (1,2,3) in a plane is (- 7 3 ,- 4 3 ,- 1 3 ). Which of the following points lies on this plane ?
- If and be the coefficients of x^4 and x^2 respectively in the expansion of (x+ x^2-1 )^6+ (x- x^2-1 )^6, then :
- The area (in sq. units) of the region (x,y) R^2: x^2 y 3-2x , is :
- Let f:(1,3) R be a function defined by f(x)= x[x] 1+x^2 , where [x] denotes the greatest integer x. Then the range of f is :
- Let A and B be two events such that the probability that exactly one of them occurs is 2 5 and the probability that A or B occurs...
- If a hyperbola passes through the point P(10, 16) and it has vertices at (± 6, 0), then the equation of the normal to it at P is :
- The length of the perpendicular from the origin, on the normal to the curve, x^2+2xy-3y^2=0 at the point (2, 2) is :
- Let = -1+i 3 2 . If a=(1+ ) _ k=0 ^ 100 ^ 2k and b= _ k=0 ^ 100 ^ 3k , then a and b are the roots of the quadratic equation :
- The system of linear equations x+2y+2z=5 2 x+3y+5z=8 4x+ y+6z=10 has :
- _ x 0 _0^xt (10t) ,dt x is equal to :
- Let a = i -2 j + k and b = i - j + k be two vectors. If c is a vector such that b c = b a and c a =0, then c b is equal to :
- Let S be the set of all functions f : [0,1] → R, which are continuous on [0,1] and differentiable on (0, 1). Then for every f in...
- If the 10th term of an A.P is 1 20 and its 20th term is 1 10 , then the sum of its first 200 terms is :