JEE Advanced questions
3844 published questions with worked solutions.
- The differential equation for the family of curves x^2 + y^2 - 2ay = 0, where a is an arbitrary constant, is
- The intercept on the line y = x by the circle x^2 + y^2 - 2x = 0 is AB. The equation of the circle on AB as a diameter is
- The eccentricity of an ellipse with its centre at the origin is 12. If one of the directrices is x = 4 then the equation of the...
- A line with direction ratios 2, 1, 2 meets the lines x = y + a = z and x + a = 2y = 2z at P and Q, respectively. Then the length...
- The distance between the planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
- If a b = 1 and a b = j - k, where a = i + j + k, then b is
- The unit vector which is orthogonal to the vector a = 3 i + 2 j + 6 k and is coplanar with the vectors b = 2 i + j + k and c = i...
- For all x R, x^2 + 2ax + 10 - 3a > 0. The interval in which a lies is
- If a_1, a_2, a_3, are in GP then the value of the determinant vmatrix a_1 & a_ n+1 & a_ 2n+1 a_2 & a_ n+2 & a_ 2n+2 a_3 & a_ n+3...
- A question paper contains 10 questions divided in two equal groups. A candidate has to attempt 6 questions selecting not more...
- If f(x) = cases x e^ -(1/|x| + 1/x) & for x 0 0 & for x = 0 cases then f(x) is
- If _ x a x _a^x f(x) ,dx x - a = a^3 + a^2 (a 0) then f(2a) is
- The number of positive integral solutions of (x, y) when x^2 - 4xy + 6y^2 - 2x - 20y = 29 is
- The equation of a line which is parallel to x - y = 0 and touches the hyperbola x^2 - 2y^2 = 18 is
- Let f(x) = 1 + | x|. Then
- If |z_1| = |z_2| = 1 and amp z_1 + amp z_2 = 0 then
- A perpendicular PQ is dropped from the point P(1, 2, 3) to the plane x + y + z = 3, Q being the foot. Then
- The area bounded by the curve y = x(3 - x)^2, the x-axis and the lines of ordinates of the maximum and minimum values of the...
- Let f(x) be a continuous function such that f(x + 4) = f(x + 2) - f(x) and (x) = _x^ x+12 f(x) ,dx. If (3) = 5 then _4^ 16 f(x)...
- Let 0 < < < 2. STATEMENT-1: > STATEMENT-2: If f''(x) > 0, x_1 > x_2 then f(x_1) > f(x_2).