Mathematics questions
18011 published questions with worked solutions.
- Let (0, 2 ) be fixed. If the integral x + x - dx = A(x) 2 + B(x) 2 + C, where C is a constant of integration, then the functions...
- The general solution of the differential equation (y^2 - x^3)dx - xy ,dy = 0 (x ≠ 0) is: (where c is a constant of integration)
- The equation of common tangent to the curves y^2 = 16x and xy = −4, is:
- A plane which bisects the angle between the two given planes 2x − y + 2z − 4 = 0 and x + 2y + 2z − 2 = 0, passes through the...
- A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (−1, 1) and (2, 3). Then the centroid of...
- If the area (in sq. units) bounded by the parabola y^2 = 4 x and the line y = λx, λ > 0, is 19, then λ is equal to:
- If α, β and γ are three consecutive terms of a non-constant G.P. such that the equations x^2 + 2 x + = 0 and x^2 + x - 1 = 0 have...
- If ^ 20 C_1 + (2^2) , ^ 20 C_2 + (3^2) , ^ 20 C_3 + + (20^2) , ^ 20 C_ 20 = A(2^ ), then the ordered pair (A, β) is equal to:
- The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines r = ( i + j) + ( i + 2 j - k)...
- A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point:
- Let α ∈ R and the three vectors a = i + j + 3 k, b = 2 i + j - k and c = i - 2 j + 3 k. Then the set S = α : a, b and c are...
- The tangents to the curve y = (x - 2)^2 - 1 at its points of intersection with the line x − y = 3, intersect at the point:
- If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [−cos θ]y = 0, [cot θ]x + y = 0
- A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be...
- An ellipse, with foci at (0, 2) and (0, −2) and minor axis of length 4, passes through which of the following points?
- For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the...
- A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular...
- A value of α such that _ ^ +1 dx (x + )(x + + 1) = _e ( 98 ) is:
- _ x 0 x + 2 x x^2 + 2 x + 1 - ^2x - x + 1 is:
- The derivative of ^ -1 ( x - x x + x ), with respect to x2, where x (0, 2 ) is: