JEE Advanced questions
1003 published questions with worked solutions.
- Let ℝ denote the set of all real numbers. Define the function f : ℝ → ℝ by f(x) = cases 2 - 2x^2 - x^2 1 x & if x 0, 2 & if x =...
- Consider the matrix P = pmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 3 pmatrix . Let the transpose of a matrix X be denoted by X^T. Then...
- Let L_1 be the line of intersection of the planes given by the equations 2x + 3y + z = 4 and x + 2y + z = 5. Let L_2 be the line...
- Let ℝ denote the set of all real numbers. Let z_1 = 1 + 2i and z_2 = 3i be two complex numbers, where i = -1 . Let S = (x, y) R R...
- Let the set of all relations R on the set a, b, c, d, e, f , such that R is reflexive and symmetric, and R contains exactly 10...
- For any two points M and N in the XY-plane, let MN denote the vector from M to N, and 0 denote the zero vector. Let P, Q and R be...
- Let S be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in S, but...
- Let α and β be the real numbers such that _ x 0 1 x^3 ( 2 _0^x 1 1 - t^2 ,dt + x x ) = 2. Then the value of α + β is _____.
- Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ be a function such that f(x) > 0 for all x ∈ ℝ, and f(x + y) = f(x)f(y)...
- For all x > 0, let y_1(x), y_2(x), and y_3(x) be the functions satisfying dy_1 dx - ( x)^2y_1 = 0, y_1(1) = 5, dy_2 dx - (...
- Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm, 0.05 mm, and 6.0 µm,...
- A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of...
- A cube of unit volume contains 35 10^7 photons of frequency 10^ 15 Hz. If the energy of all the photons is viewed as the average...
- A single slit diffraction experiment is performed to determine the slit width using the equation, bd D = m , where b is the slit...
- List-I shows various functional dependencies of energy (E) on the atomic number (Z). Energies associated with certain phenomena...
- The heating of NH_4NO_2 at 60–70 °C and NH_4NO_3 at 200–250 °C is associated with the formation of nitrogen containing compounds...
- The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is
- Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the INCORRECT statement(s) is(are)
- The pair(s) of diamagnetic ions is(are)
- In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to Cr³⁺. The current (in amperes) that flows...