Practice questions
88551 published questions with worked solutions.
- If the system of linear equations 3x + y + βz = 3 2x + αy – z = –3 x + 2y + z = 4 has infinitely many solutions, then the value...
- The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is...
- Let A = bmatrix & -1 6 & bmatrix , α > 0, such that det(A) = 0 and α + β = 1. If I denotes 2 × 2 identity matrix, then the...
- The largest n ∈ N such that 3^n divides 50! is :
- If the function f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, where a > 0, attains its local maximum and local minimum values at p and q,...
- If θ ∈ [–2π, 2π], then the number of solutions of 2 2 ^2 + (2- 6) - 3 = 0, is equal to :Not in JEE Main syllabus
- For α, β, γ ∈ R , if _ x 0 x^2 x + ( -1)e^ x^2 2x - x = 3, then β + γ – α is equal to :
- Let one focus of the hyperbola H : x^2 a^2 - y^2 b^2 = 1 be at ( 10 , 0) and the corresponding directrix be x = 9 10 . If e and l...
- If a is a non-zero vector such that its projections on the vectors 2 i - j + 2 k, i + 2 j - 2 k and k are equal, then a unit...
- If the area of the region (x, y) : |4-x^2| y x^2, y 4, x 0 is ( 80 2 - ), α, β ∈ N, then α + β is equal to ______.
- Three distinct numbers are selected randomly from the set 1, 2, 3, …, 40 . If the probability, that the selected numbers are in...
- Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is 'α'....
- The equation for real gas is given by (P+ a V^2 )(V-b) = RT, where P, V, T and R the pressure, volume, temperature and gas...
- The relationship between the magnetic susceptibility (χ) and the magnetic permeability (μ) is given by : (μ₀ is the permeability...Not in JEE Advanced syllabus
- In an adiabatic process, which of the following statements is true?
- Match List-I with List-II. List-I: (A) Coefficient of viscosity (B) Intensity of wave (C) Pressure gradient (D) Compressibility...
- A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave...
- A particle is subjected to two simple harmonic motions as: x_1 = 7 5t cm and x_2 = 2 7 (5t+ 3 ) cm where x is displacement and t...
- A point charge + q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The...
- A person travelling on a straight line moves with a uniform velocity v₁ for a distance x and with a uniform velocity v₂ for the...