JEE Advanced questions
3844 published questions with worked solutions.
- Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and _ x 0 (1 + p(x) x^2 ) = 2. Then the value of p(2) is
- Let f : R R be a continuous function which satisfies f(x) = _0^x f(t) ,dt. Then the value of f( _e 5) is
- The number of 3 3 matrices A whose entries are either 0 or 1 and for which the system A bmatrix x y z bmatrix = bmatrix 1 0 0...
- Let P, Q, R and S be points on the plane with position vectors -2 i - j, 4 i, 3 i + 3 j and -3 i + 2 j respectively. The...
- Two adjacent sides of a parallelogram ABCD are given by AB = 2 i + 10 j + 11 k and AD = - i + 2 j + 2 k. The side AD is rotated...
- The equation of the plane containing the straight line x 2 = y 3 = z 4 and perpendicular to the plane containing the straight...
- If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = , where > 0, is 5 then the foot of the perpendicular from P...
- Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^ x^2 + e^ -x^2 , g(x) = xe^ x^2 + e^ -x^2 and...
- The value of _ x 0 1 x^3 _0^x t (1+t) t^4+4 ,dt is
- Let f be a real-valued function defined on the interval (-1, 1) such that e^ -x f(x) = 2 + _0^x t^4+1 ,dt , x (-1, 1). Let f^ -1...
- Let z_1 and z_2 be two distinct complex numbers and let z = (1-t)z_1 + tz_2 for some real number t, where 0 < t < 1. If (w)...
- Let ABC be a triangle such that ACB = 6 and let a, b, c denote the lengths of the sides opposite to A, B, C respectively. The...Not in JEE syllabus
- Let A and B be two distinct points on the parabola y^2 = 4x. If the axis of the parabola touches a circle of radius r having AB...
- Let f be a real-valued function defined on the interval (0, ) by f(x) = _e x + _0^x 1 + t ,dt. Which of the following...
- Match the statements in **Column I** with those in **Column II**. [**Note:** Here z takes values in the complex plane and Im (z)...
- Let = 2 3 + i 2 3 . Then the number of distinct complex numbers z satisfying vmatrix z + 1 & & ^2 & z + ^2 & 1 ^2 & 1 & z +...
- The number of values of in the interval (- 2, 2 ) such that n 5 , where n = 0, 1, 2 and = 5 as well as 2 = 4 isNot in JEE Main syllabus
- The maximum value of the expression 1 ^2 + 3 + 5 ^2 is
- The line 2x + y = 1 is tangent to the hyperbola x^2 a^2 - y^2 b^2 = 1. If this line passes through the point of intersection of...
- If a and b are vectors in space given by a = i - 2 j 5 and b = 2 i + j + 3 k 14 then the value of (2 a + b) [( a b) ( a - 2 b) ]...