A black body is at \(727^\circ\text{C}.\) The rate at which it emits energy is proportional to:

An engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by ${62}^{0}C$, its efficiency is doubled. the temperature of the source is:

1. 124^oC

2. 37^oC

3. 62^oC

4. 99^oC

Monochromatic light of frequency 6.0×10¹⁴ Hz is produced by a laser. The power emitted is 2×10^-3 W. The number of photons emitted, on average, by the source per second is:

1. $5\times {10}^{15}$

2. $5\times {10}^{16}$

3. $5\times {10}^{17}$

4. $5\times {10}^{14}$

For a cubic crystal structure, which one of the following relations indicating the cell characteristic is correct?

1. $a\ne b\ne c$ $and$ $\alpha \ne \beta$ $and$ $\gamma \ne 90°$

2. $a\ne b\ne c$ $and$ $\alpha =\beta$ $=$ $\gamma =90°$

3. $a=b=c$ $and$ $\alpha \ne \beta$ $=$ $\gamma =90°$

4. $a=b=c$ $and$ $\alpha =\beta =$ $\gamma =90°$

A common emitter amplifier has a voltage gain of 50, an input impedance of 100Ω, and an output impedance of 200Ω. The power gain of the amplifier is:

1. 500

2. 1000

3. 1250

4. 100

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
1. 0.5$\mathrm{\pi }$
2. $\mathrm{\pi }$
3. 0.707$\mathrm{\pi }$
4. zero

A vertical spring with a force constant \(k\) is fixed on a table. A ball of mass \(m\) at a height \(h\) above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance \(d\). The net work done in the process is:
1. \(mg(h+d)+\frac{1}{2}kd^2\)
2. \(mg(h+d)-\frac{1}{2}kd^2\)
3. \(mg(h-d)-\frac{1}{2}kd^2\)
4. \(mg(h-d)+\frac{1}{2}kd^2\)

$\stackrel{}{\mathrm{}}$\(\overrightarrow{A}\) and \(\overrightarrow B\) are two vectors and \(\theta\) is the angle between them. If \(\left|\overrightarrow A\times \overrightarrow B\right|= \sqrt{3}\left(\overrightarrow A\cdot \overrightarrow B\right),\) then the value of \(\theta\) will be:

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:

1. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}\right]$

2. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

3. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}{\mathrm{I}}^{-1}\right]$

4. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{I}}^{-2}\right]$

A particle moving along the x-axis has acceleration \(f,\) at time \(t,\) given by, \(f=f_0\left ( 1-\frac{t}{T} \right ),\)  where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0,\) the particle’s velocity \( \left ( v_x \right )\) is:
1. \(f_0T\)
2. \(\frac{1}{2}f_0T^{2}\)
3. \(f_0T^2\)
4. \(\frac{1}{2}f_0T\)