JEE Advanced questions
1003 published questions with worked solutions.
- For the function f(x) = x 1 x , x 1,
- 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...
- For 0 < < 2 , the solution(s) of _ m=1 ^ 6 cosec ( + (m - 1) 4 ) cosec ( + m 4 ) = 4 2 is(are)
- The maximum value of the function f(x) = 2x^3 - 15x^2 + 36x - 48 on the set A = x x^2 + 20 9x is
- Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations: 3x - y - z = 0 -3x + z = 0 -3x +...
- Let ABC and ABC′ be two non-congruent triangles with sides AB = 4, AC = AC' = 2 2 and angle B = 30°. The absolute value of the...
- 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^xf(t) ,dt. Then the value of f(ln 5) is
- 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...
- The smallest value of k, for which both the roots of the equation x^2 - 8kx + 16(k^2 - k + 1) = 0 are real, distinct and have...
- If the function f(x) = x^3 + e^ x 2 and g(x) = f^ -1 (x), then the value of g′(1) is
- A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the...
- Under the influence of the Coulomb field of charge +Q, a charge −q is moving around it in an elliptical orbit. Find out the...
- A metal rod AB of length 10x has its one end A in ice at 0 °C and the other end B in water at 100 °C. If a point P on the rod is...
- A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is...
- Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m². The radii of bubbles A and...
- A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the...
- A solid sphere of radius R has a charge Q distributed in its volume with a charge density = r^a, where κ and a are constants and...
- A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set...
- Three students S_1, S_2, and S_3 are given a problem to solve. Consider the following events: U: At least one of S_1, S_2, and...