Practice questions
88551 published questions with worked solutions.
- Let x = x(y) be the solution of the differential equation 2y^2 dx dy - 2xy + x^2 = 0, y > 1, x(e) = e. Then x(e²) is equal to:
- Let A = 2, 3, 4, 5, 6 . Let R be a relation on the set A × A given by (x, y)R(z, w) if and only if x divides z and y ≤ w. Then...
- Consider the matrices A = bmatrix 2 & -2 4 & -2 bmatrix and B = bmatrix 3 & 9 1 & 3 bmatrix . If matrices P and Q are such that...
- Let A be the point (3, 0) and circles with variable diameter AB touch the circle x² + y² = 36 internally. Let the curve C be the...
- If the area of the region bounded by 16x² − 9y² = 144 and 8x − 3y = 24 is A, then 3(A + 6log_e(3)) is equal to _______.
- The number of points in the interval [2, 4], at which the function f(x) = [x^2 - x - 12 ], where [·] denotes the greatest integer...
- Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are...
- A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The...
- In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are...
- The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is απ ×...
- If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m³ at a rate of 0.5 cm/s, then the...
- A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average...
- An electromagnetic wave travels in free space along the x-direction. At a particular point in space and time, B = 2 10^ -7 j T is...
- Two resistors of 200 Ω and 400 Ω are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected...
- Two metal plates (A, B) are kept horizontally with separation of ( 12 ) cm, with plate A on the top. An atomizer jet sprays oil...
- A circular current loop of radius R is placed inside a square loop of side length L (L >> R) such that they are co-planar and...
- The binding energy per nucleon of ^ 209 _ 83 Bi is _______ MeV. [Take m(^ 209 _ 83 Bi) = 208.980388 u, m_p = 1.007825 u, m_n =...
- The equation of motion of a particle is given by x = a sin (50t + 3 ) cm. The particle will come to rest at time t₁ and it will...
- In a Young's double slit experiment, the intensity at some point on the screen is found to be 34 times of the maximum of the...
- Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2ⁿᵈ and 4ᵗʰ...