Mathematics questions
18011 published questions with worked solutions.
- If a variable line, 3x + 4y − λ = 0 is such that the two circles x^2 + y^2 - 2x - 2y + 1 = 0 and x^2 + y^2 - 18x - 2y + 78 = 0...
- Considering only the principal values of inverse functions, the set A = x 0 : ^ -1 (2x) + ^ -1 (3x) = 4
- The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the...
- For x > 1, if (2x)^ 2y = 4e^ 2x-2y , then (1 + _e2x)^2 dy dx is equal to:
- The perpendicular distance from the origin to the plane containing the two lines, x+2 3 = y-2 5 = z+5 7 and x-1 1 = y-4 4 = z+4 7...
- If the straight line, 2x − 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals:
- The area (in sq. units) of the region bounded by the parabola, y = x^2 + 2 and the lines, y = x + 1, x = 0 and x = 3, is:
- Let C_1 and C_2 be the centres of the circles x^2 + y^2 - 2x - 2y - 2 = 0 and x^2 + y^2 - 6x - 6y + 14 = 0 respectively. If P and...
- _ x /4 ^3x - x (x + 4 ) is:
- A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(−1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is:
- Let S be the set of all points in (−π, π) at which the function, f(x) = min sin x, cos x is not differentiable. Then S is a...
- The integral ( _ex) ,dx is equal to: (where C is a constant of integration)
- The maximum value of 3 + 5 ( - 6 ) for any real value of θ is:
- An ordered pair (α, β) for which the system of linear equations (1 + α)x + βy + z = 2, αx + (1 + β)y + z = 3, αx + βy + 2z = 2...
- Let P = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and Q = [q_ ij ] be two 3 × 3 matrices such that Q - P^5 = I_3. Then q_ 21...
- If λ be the ratio of the roots of the quadratic equation in x, 3m^2x^2 + m(m - 4)x + 2 = 0, then the least value of m for which +...
- Let P(4, −4) and Q(9, 6) be two points on the parabola, y^2 = 4x and let X be any point on the arc POQ of this parabola, where O...
- Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes....
- The solution of the differential equation, dy dx = (x - y)^2, when y(1) = 1, is:
- Let K be the set of all real values of x where the function f(x) = sin|x| − |x| + 2(x − π) cos|x| is not differentiable. Then the...