JEE Main questions
34495 published questions with worked solutions.
- Let y = y(x) be the solution of the differential equation dy dx + 2x (1 + x^2)^2 y = xe^ 1 (1 + x^2) ; y(0) = 0. Then the area...
- The number of solutions of sin²x + (2 + 2x − x²)sin x − 3(x − 1)² = 0, where −π ≤ x ≤ π, isNot in JEE Main syllabus
- Let the point (−1, α, β) lie on the line of the shortest distance between the lines x + 2 -3 = y - 2 4 = z - 5 2 and x + 2 -1 = y...
- If 1 + 3 - 2 2 3 + 5 - 2 6 18 + 9 3 - 11 2 36 3 + 49 - 20 6 180 + up to ∞ = 2 + ( ba + 1 ) _e ( ab ), where a and b are integers...
- Let a > 0 be a root of the equation 2x² + x − 2 = 0. If _ x 1a 16 (1 - (2 + x - 2x^2) ) (1 - ax)^2 = + 17 , where α, β ∈ Z then α...
- Let the maximum and minimum values of ( 8x - x^2 - 12 - 4 )^2 + (x - 7)^2, x ∈ R be M and m respectively. Then M² − m² is equal...
- Let a line perpendicular to the line 2x − y = 10 touch the parabola y² = 4(x − 9) at the point P. The distance of the point P...
- The number of real solutions of the equation x|x + 5| + 2|x + 7| − 2 = 0 is _____.
- To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1%...
- A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy...
- Electromagnetic waves travel in a medium with speed of 1.5 × 10⁸ ms⁻¹. The relative permeability of the medium is 2.0. The...
- Which of the following phenomena does not explain by wave nature of light (A) reflection (B) diffraction (C) photoelectric effect...
- While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular...
- σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of...
- The specific heat at constant pressure of real gas obeying PV² = RT equation is:
- Match List I with List II List-I: A. Torque B. Magnetic field C. Magnetic moment D. Permeability of free space List-II: I....
- Given below are two statements: Statement I: In an LCR series circuit, current is maximum at resonance. Statement II: Current in...
- A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:
- A light string passing over a smooth light pulley connects two blocks of masses m_1 and m_2 (where m_2 > m_1). If the...
- Four particles A, B, C, D of mass m2, m, 2m, 4m have same momentum, respectively. The particle with maximum kinetic energy is: