JEE Advanced questions
3844 published questions with worked solutions.
- The equation of the common tangent to the curves y^2 = 8x and xy = -1 is
- Let f(x) = _1^x 2 - t^2 ,dt. Then real roots of the equation x^2 - f'(x) = 0 are
- Let T > 0 be a fixed number. Suppose f is a continuous function such that for all x R, f(x + T) = f(x). If I = _0^T f(x) ,dx then...
- The integral _ -1/2 ^ 1/2 [x] + ( 1+x 1-x ) dx equals
- If a and b are two unit vectors such that a + 2 b and 5 a - 4 b are perpendicular to each other then the angle between a and b is
- Let V = 2 i + j - k and W = i + 3 k. If U is a unit vector then the maximum value of the scalar triple product [ U V W] is
- If (0, 2 ) then the interval of values of for which 2 ^2 - 5 + 2 > 0 isNot in JEE Main syllabus
- The axis of a parabola is along the line y = x and the distance of the origin from its vertex is 2 and that from its focus is 2...
- A tangent to the curve y = f(x) at P(x, y) cuts the x-axis and the y-axis at A and B, respectively, such that BP : AP = 3 : 1. If...
- The internal bisector of the angle A of the ABC meets BC at D. A line drawn through D perpendicular to AD intersects the side AC...Not in JEE syllabus
- f(x) is a polynomial of the third degree which has a local maximum at x = -1. If f(1) = -1, f(2) = 18 and f'(x) has a local...
- More than one may match with the same. Column I: (i) If _ n=1 ^ ^ -1 1 2n^2 = t then t equals (ii) If in the ABC the sides a, b,...
- If f(x) is a twice differentiable function such that f(a) = 0, f(b) = 2, f(c) = -1, f(d) = 2 and f(e) = 0, where a < b < c < d <...
- The number of distinct real values of , for which the vectors - ^2 i + j + k, i - ^2 j + k and i + j - ^2 k are coplanar, is
- One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional...
- Let f(x) = x (1 + x^n)^ 1/n for n 2 and g(x) = (f f f) _ f occurs n times (x). Then x^ n-2 g(x) ,dx equals
- A hyperbola, having the transverse axis of length 2 , is confocal with the ellipse 3x^2 + 4y^2 = 12. Then its equation is
- The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c - 1, e^ c-1 ) and (c + 1,...
- A man walks a distance of 3 units from the origin towards the north-east (N 45° E) direction. From there, he walks a distance of...
- Let f(x) be differentiable on the interval (0, ) such that f(1) = 1, and _ t x t^2f(x) - x^2f(t) t - x = 1 for each x > 0. Then...