Mathematics questions
18011 published questions with worked solutions.
- The value of ^ -1 ( 12 13 ) - ^ -1 ( 35 ) is equal to:
- If the volume of parallelopiped formed by the vectors i + j + k, j + k and i + k is minimum, then λ is equal to:
- If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these...
- If the line x-2 3 = y+1 2 = z-1 -1 intersects the plane 2x + 3y − z + 13 = 0 at a point P and the plane 3x + y + 4z = 16 at a...
- _ x 1^- - 2 ^ -1 x 1 - x is equal to:
- The equation of a tangent to the parabola, x^2 = 8y, which makes an angle θ with the positive directions of x-axis, is:
- If the sum of the first 15 terms of the series ( 34 )^3 + (1 12 )^3 + (2 14 )^3 + 3^3 + (3 34 )^3 + is equal to 225k, then k is...
- In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the...
- If a curve passes through the point (1, −2) and has slope of the tangent at any point (x, y) on it as x^2 - 2y x , then the curve...
- The integral _1^e ( xe )^ 2x - ( ex )^x _ex ,dx is equal to:
- If ^4 + 4 ^4 + 2 = 4 2 ; α, β ∈ [0, π], then cos(α + β) − cos(α − β) is equal to:
- If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of...
- The integral 3x^ 13 + 2x^ 11 (2x^4 + 3x^2 + 1)^4 dx is equal to: (where C is a constant of integration)
- Let S and S′ be the foci of an ellipse and B be any one of the extremities of its minor axis. If ΔS′BS is a right angled triangle...
- Let Z be the set of integers. If A = x Z : 2^ (x+2)(x^2-5x+6) = 1 and B = x Z : -3 < 2x - 1 < 9 , then the number of subsets of...
- Let S be the set of all real values of λ such that a plane passing through the points (- ^2, 1, 1), (1, - ^2, 1) and (1, 1, - ^2)...
- If the function f given by f(x) = x^3 - 3(a - 2)x^2 + 3ax + 7, for some a ∈ R is increasing in (0, 1] and decreasing in [1, 5),...
- _ n ( n n^2 + 1^2 + n n^2 + 2^2 + n n^2 + 3^2 + + 1 5n ) is equal to:
- In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is...
- If A = bmatrix 1 & & 1 - & 1 & -1 & - & 1 bmatrix ; then for all ( 3 4 , 5 4 ), det(A) lies in the interval: