JEE Advanced questions
579 published questions with worked solutions.
- Let a ∈ ℝ and let f : ℝ → ℝ be given by f(x) = x^5 - 5x + a. Then
- Let f : [a, b] → [1, ∞) be a continuous function and let g : ℝ → ℝ be defined as g(x) = cases 0 & if x < a, _a^x f(t) ,dt & if a...
- From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = −x, z = −1. If P is...
- Let x, y and z be three vectors each of magnitude 2 and the angle between each pair of them is 3 . If a is a nonzero vector...
- A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 + y^2 = 16 and x^2 + y^2 = 1. Then
- Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if
- Let f : ℝ → ℝ and g : ℝ → ℝ be respectively given by f(x) = |x| + 1 and g(x) = x^2 + 1. Define h : ℝ → ℝ by h(x) = cases f(x),...
- The value of _0^1 4x^3 d^2 dx^2 (1 - x^2)^5 dx is
- The slope of the tangent to the curve (y - x^5)^2 = x(1 + x^2)^2 at the point (1, 3) is
- The largest value of the nonnegative integer a for which _ x 1 -ax + (x - 1) + a x + (x - 1) - 1 ^ 1-x 1- x = 1 4 is
- Let f : [0, 4π] → [0, π] be defined by f(x) = ^ -1 ( x). The number of points x ∈ [0, 4π] satisfying the equation f(x) = 10 - x...
- Let a, b, and c be three non-coplanar unit vectors such that the angle between every pair of them is 3 . If a b + b c = p a + q b...
- Parallel rays of light of intensity I = 912 W m⁻² are incident on a spherical black body kept in surroundings of temperature 300...
- A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons...
- If _ Cu is the wavelength of K_ X-ray line of copper (atomic number 29) and _ Mo is the wavelength of the K_ X-ray line of...
- A planet of radius R = 1 10 (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth R 5 on it and...
- Hydrogen peroxide in its reaction with KIO_4 and NH_2OH respectively, is acting as a
- For the identification of β-naphthol using dye test, it is necessary to use
- For the elementary reaction M → N, the rate of disappearance of M increases by a factor of 8 upon doubling the concentration of...
- Assuming 2s-2p mixing is NOT operative, the paramagnetic species among the following is