JEE Advanced questions
3844 published questions with worked solutions.
- If a, b, c and d are unit vectors such that ( a b) ( c d) = 1 and a c = 12 then
- Let P(3, 2, 6) be a point in space and Q be a point on the line r = ( i - j + 2 k) + (-3 i + j + 5 k). Then the value of for...
- A line with positive direction cosines passes through the point P(2, -1, 2) and makes equal angles with the coordinate axes. The...
- Let f be a non-negative function defined on the interval [0, 1]. If _0^x 1 - f'(t) ^2 ,dt = _0^x f(t) ,dt, 0 x 1 and f(0) = 0 then
- If ^4 x 2 + ^4 x 3 = 15, then
- For 0 < < 2 , the solution(s) of _ m=1 ^ 6 cosec ( + (m-1) 4 ) cosec ( + m 4 ) = 4 2 is/are
- In a triangle ABC with fixed base BC, the vertex A moves such that B + C = 4 ^2 A 2 . If a, b and c denote the lengths of the...Not in JEE syllabus
- The tangent PT and the normal PN to the parabola y^2 = 4ax at a point P on it meet its axis at points T and N respectively. The...
- An ellipse intersects the hyperbola 2x^2 - 2y^2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the...
- For the function f(x) = x 1x, x 1
- If I_n = _ - ^ nx (1 + ^x) x ,dx, n = 0, 1, 2, , then
- The area of the region bounded by the curve y = e^x and lines x = 0 and y = e is
- Let L = _ x 0 a - a^2 - x^2 - x^2 4 x^4 , a > 0. If L is finite, then
- Match the statements/expressions given in Column I with the values given in Column II. Column I: (A) Root(s) of the equation 2 ^2...Not in JEE Main syllabus
- Match the statements/expressions given in Column I with the values given in Column II. Column I: (A) The number of solutions of...
- Match the conic sections in Column I with the statements/expressions in Column II. Column I: (A) Circle (B) Parabola (C) Ellipse...
- The centres of two circles C_1 and C_2 each of unit radius are at a distance of 6 units from each other. Let P be the mid-point...
- Let (x, y, z) be points with integral coordinates satisfying the system of homogeneous equations 3x - y - z = 0, -3x + z = 0, -3x...
- The maximum value of the function f(x) = 2x^3 - 15x^2 + 36x - 48 on the set A = x x^2 + 20 9x is
- If the function f(x) = x^3 + e^ x/2 and g(x) = f^ -1 (x) then the value of g'(1) is