Practice questions
88551 published questions with worked solutions.
- Let y = y(x) be the solution of the differential equation (x² + 4)² dy + (2x³y + 8xy − 2)dx = 0. If y(0) = 0, then y(2) is equal...
- Let a = i + j + k, b = 2 i + 4 j - 5 k and c = x i + 2 j + 3 k, x ∈ R. If d is the unit vector in the direction of b + c such...
- Let P the point of intersection of the lines x - 2 1 = y - 4 5 = z - 2 1 and x - 3 2 = y - 2 3 = z - 3 2 . Then, the shortest...
- Let S = sin²2θ : (sin⁴θ + cos⁴θ)x² + (sin 2θ)x + (sin⁶θ + cos⁶θ) = 0 has real roots . If α and β be the smallest and largest...
- If ^5x ,dx = x x ( ^2x + 32 ) + _e | x2 | + C where α, β ∈ R and C is constant of integration, then the value of 8(α + β) equals...
- Let f : R → R be a thrice differentiable function such that f(0) = 0, f(1) = 1, f(2) = –1, f(3) = 2 and f(4) = –2. Then, the...
- Consider the function f : R → R defined by f(x) = 2x 1 + 9x^2 . If the composition of f, (f∘f∘f∘…∘f)(x) (10 times) = 2^ 10 x 1 +...
- Let A be a 2 × 2 symmetric matrix such that A bmatrix 1 1 bmatrix = bmatrix 3 7 bmatrix and the determinant of A be 1. If A⁻¹ =...
- There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the...
- In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 13 and 23 respectively. Let x be...
- Consider a line L passing through the points P(1, 2, 1) and Q(2, 1, −1). If the mirror image of the point A(2, 2, 2) in the line...
- Let y = y(x) be the solution of the differential equation (x + y + 2)² dx = dy, y(0) = −2. Let the maximum and minimum values of...
- An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:
- The electric field in an electromagnetic wave is given by E = i ,40 (t - zc ) NC^ -1 . The magnetic field induction of this wave...
- Which of the following nuclear fragments corresponding to nuclear fission between neutron (^1_0n) and uranium isotope (^ 235 _ 92...
- In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object...
- The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8 Ω and 10 Ω...
- A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is...
- On celsius scale the temperature of a body increases by 40°C. The increase in temperature on Fahrenheit scale is:
- An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25 D....