11.

Two closed organ pipes of length 100 cm and 101 cm produces 16 beats in 20 sec. When each pipe is sounded in its fundamental mode. Calculate the velocity of sound.

• 303 ms^-1

• 332 ms^-1

• 323.2 ms^-1

• 300 ms^-1yes

A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. Order of the most portable speed ν_p of the molecules at these five states is

• ν_{p at 3}  > ν_{p at 1} = ν_{p at 2} > ν_{p at 4} = ν_{p at 5}

• ν_{p at 1} > ν_{p at 2} =  ν_{p at 3} > ν_{p at 4} > ν_{p at 5}

• ν_{p at 3} > ν_{p at 2} = ν_{p at 4} > ν_{p at 1} = ν_{p at 5}

• insufficient information to predict the result

If a wire is extended to a new length l, the work done is

• $\frac{\mathrm{Y} \mathrm{A}}{\mathrm{l}} \left(\mathrm{l} - \mathrm{l}\text{'}\right)$

• $\frac{\mathrm{YA}}{\mathrm{l}} {\left( \mathrm{l} - \mathrm{l}\text{'} \right)}^2$

• $\frac{1}{2} \frac{\mathrm{YA}}{\mathrm{l}} {\left( \mathrm{l} - \mathrm{l}\text{'} \right)}^2$

• $2. \frac{\mathrm{YA}}{\mathrm{l}} {\left( \mathrm{l} - \mathrm{l}\text{'} \right)}^2$

The equivalent resistance between the points X  and  Y in the following circuit diagram will be

• 10 Ω

• 5 Ω

• 7 Ω

• 3 Ω

Two heater wires, made of the same material and having the same length and the same radius, are first connected in series and then in parallel to a constant potential difference. If the rates of I heat produced in the two cases are H_s  and  H_P respectively, then  H_s/H_P  will be

• 1/2

• 2

• 1/4

• 4

Assertion:  In the relation f = $\frac{1}{2\mathrm{l}} \sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$, where symbols have standard meaning, μ represents linear mass density.

Reason: The frequency has the dimensions of inverse of time.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion: A needle placed carefully on the surface of water may float, whereas a ball of the same material will always sink.

Result: The buoyancy of an object depends both on the material and shape of the object.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion: In an SHM, kinetic and potential energies equal when the displacement is 1/$\sqrt{2}$ times the amplitude.

Reason:  In SHM, kinetic energy is zero when potential energy is maximum.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

In an electrical containing L, C and R which of the following does not denote the dimensions and frequency?

• LC

• $\frac{1}{\sqrt{\mathrm{L} \mathrm{C}}}$

• $\frac{1}{\mathrm{RC}}$

• $\frac{\mathrm{R}}{\mathrm{L}}$

The velocity of electromagnetic radiation in a medium of permittivity ε₀ and permeability μ₀ is given by 

• $\frac{1}{\sqrt{{\mathrm{\mu }}_0 {\mathrm{\epsilon }}_0}}$

• $\sqrt{\frac{{\mathrm{\mu }}_0}{{\mathrm{\epsilon }}_0}}$

• $\sqrt{\frac{{\mathrm{\epsilon }}_0}{{\mathrm{\mu }}_0}}$