JEE Advanced questions
1003 published questions with worked solutions.
- Consider a branch of the hyperbola x^2 - 2y^2 - 2 2 x - 4 2 y - 6 = 0 with vertex at the point A. Let B be one of the end points...
- The area of the region between the curves y = 1 + x x and y = 1 - x x bounded by the lines x = 0 and x = 4 is
- Consider three points P = (- ( - ), - ), Q = ( ( - ), ) and R = ( ( - + ), ( - )), where 0 < , , < 4 . Then,
- Let two non-collinear unit vectors a and b form an acute angle. A point P moves so that at any time t the position vector OP...
- Let I = e^x e^ 4x + e^ 2x + 1 ,dx, J = e^ -x e^ -4x + e^ -2x + 1 ,dx. Then, for an arbitrary constant C, the value of J − I equals
- Let g(x) = log f(x) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, for N =...
- Suppose four distinct positive numbers a_1, a_2, a_3, a_4 are in G.P. Let b_1 = a_1, b_2 = b_1 + a_2, b_3 = b_2 + a_3 and b_4 =...
- Let a, b, c, p, q be real numbers. Suppose α, β are the roots of the equation x^2 + 2px + q = 0 and , 1 are the roots of the...
- Consider L_1 : 2x + 3y + p - 3 = 0 L_2 : 2x + 3y + p + 3 = 0, where p is a real number, and C : x^2 + y^2 + 6x - 10y + 30 = 0....
- Let a solution y = y(x) of the differential equation x x^2 - 1 ,dy - y y^2 - 1 ,dx = 0 satisfy y(2) = 2 3 . STATEMENT-1 : y(x) =...
- A radioactive sample S1 having an activity of 5 µCi has twice the number of nuclei as another sample S2 which has an activity of...
- A vibrating string of certain length ℓ under a tension T resonates with a mode corresponding to the first overtone (third...
- STATEMENT-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the...
- STATEMENT-1 : It is easier to pull a heavy object than to push it on a level ground. and STATEMENT-2 : The magnitude of...
- STATEMENT-1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits. and STATEMENT-2...
- STATEMENT-1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside...
- Both [Ni(CO)_4] and [Ni(CN)_4]^ 2- are diamagnetic. The hybridisations of nickel in these complexes, respectively, are
- The IUPAC name of [Ni(NH_3)_4][NiCl_4] is
- Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate...
- Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient...