Practice questions
88551 published questions with worked solutions.
- Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the...
- Let β(m, n) = _0^1x^ m-1 (1 - x)^ n-1 dx, m, n > 0. If _0^1(1 - x^ 10 )^ 20 dx = a (b, c), then 100(a + b + c) equals _______.
- Let αβ ≠ 0 and A = bmatrix & & 3 & & - & & 2 bmatrix . If B = bmatrix 3 & -9 & 3 - & 7 & -2 -2 & 5 & -2 bmatrix is the matrix of...
- If y( ) = 2 + 2 3 + 4 2 + 5 + 2 , then at θ = 2, y″ + y′ + y is equal to:
- For x ≥ 0, the least value of K, for which 4^ 1+x + 4^ 1-x , K2, 16^x + 16^ -x are three consecutive terms of an A.P. is equal to:
- Let the mean and the standard deviation of the probability distribution | X | α | 1 | 0 | −3 | |---|---|---|---|---| | P(X) | 1/3...
- 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...