JEE Main Test 1...

A wooden block performs SHM on a frictionless surface with frequency v₀ .The block carries a charge + Q on its surface. If now a uniform electric field E is switched on as shown, then the SHM of the block will be

The value of tan α + 2 tan (2α) + 4 tan (4α) +...+2^n-1 tan(2^n-1α) + 2ⁿ cot (2ⁿα) is

The masses of the three wires of copper are in the ratio 5 : 3: 1 and their lengths are in the ratio 1 : 3 : 5. The ratio of their electrical resistance is

A simple pendulum has a length l and the mass of the bob is m . The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is

An air filled parallel plate capacitor has a capacity of 2pF. The separation of the plates is doubled and the interspace between the plates is filled with wax. If the capacity is increased to 6 pF, the dielectric constant of wax is

If tan^-1 a + tan^-1 b = sin^-1 1 - tan^-1 c, then

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux ϕ linked with the primary coil is given by ϕ = ϕ₀ + 4t , where ϕ is in weber, t is in second and ϕ₀ is a constant, the output voltage across the secondary coil is

A rectangular loop of sides 10 cm and 5 cm with a cut is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced, so that the field decreased from its initial value of 0.3 T at the rate of 0.02 Ω. If the cut is joined and the loop has a resitance of 2.0 Ω, the power dissipated by the loop as heat is

The inductance of a coil is L =10 H and resistance R = 5 Ω . If applied voltage of battery is 10 V and it switches off in 1 ms, find induced emf of inductor.