Practice questions
90156 published questions with worked solutions.
- Let a line L₁ pass through the origin and be perpendicular to the lines L₂ : r⃗ = (3 + t)î + (2t − 1)ĵ + (2t + 4)k̂ and L₃ : r⃗ =...
- Consider the circle C : x² + y² − 6x − 8y − 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin....
- A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and...
- Consider the equation H= x^p ^qE^r t^s , where H = magnetic field; E = electric field, ε = permittivity, x = distance, t = time....
- A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car....
- A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from...
- A thin biconvex lens is prepared from the glass (μ = 1.5) both curved surfaces of which have equal radii of 20 cm each. Left side...
- Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of...
- A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t = 0 the cylinder has a...
- A liquid of density 600 kg/m³ flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 cm² and...
- A spherical liquid drop of radius R acquires the terminal velocity v₁ when falls through a gas of viscosity η. Now the drop is...
- One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the...
- The frequency of oscillation of a mass m suspended by a spring is ν₁. If the length of the spring is cut to half, the same mass...
- A monochromatic source of light operating at 15 kW emits 2.5×10²² photons/s. The region of an electromagnetic spectrum to which...
- A current carrying circular loop of radius 2 cm with unit normal n= k+ i 2 is placed in a magnetic field, B=B_0(3 i+2 k). If B₀ =...
- A 30 cm long solenoid has 10 turns per cm and area of 5 cm². The current through the solenoid coil varies from 2 A to 4 A in 3.14...
- Two point charges q₁ = 3 μC and q₂ = −4 μC are placed at points (2î+3ĵ+3k̂) and (î+ĵ+k̂) respectively. Force on charge q₂ is...
- Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous α-decay with same Q value of 1...
- A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the...
- Some distant star is to be observed by some telescope of diameter of objective lens a, at an angular resolution of 3.0×10⁻⁷...