The dimensions of $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2$ where ${\epsilon }_0$ is the permittivity of free space and E is the electric field, are:

1. [ML²T^-2]

2. [ML^-1T^-2]

3.  [ML²T^-1]

4.  [MLT^-1]

In producing chlorine by electrolysis, 100 kW power at 125 V is being consumed.
How much chlorine per minute is liberated:
(Given -ECE of chlorine is 0.367 X 10-6 kgC^-1)

1.$\mathrm{<mspace\; width="1em"></mspace>1}.76\times {10}^{-3}$ $kg$

2. $9.67\times {10}^{-3}$ $kg$

3. $17.61\times {10}^{-3}$ $kg$

4. $3.67\times {10}^{-3}$ $kg$

A man of \(50\) kg mass is standing in a gravity-free space at a height of \(10\) m above the floor. He throws a stone of \(0.5\) kg mass downwards with a speed of \(2\) ms^-1. When the stone reaches the floor, the distance of the man above the floor will be:
1. \(9.9\) m
2. \(10.1\) m
3. \(10\) m
4. \(20\) m

A lens having focal length \(f\) and aperture of diameter \(d\) forms an image of intensity \(I\). An aperture of diameter \(\frac{d}{2}\) in central region of lens is covered by a black paper. The focal length of lens and intensity of the image now will be respectively:
1. \(f\) and \(\frac{I}{4}\)
2.  \(\frac{3f}{4}\) and \(\frac{I}{2}\)
3.  \(f\) and \(\frac{3I}{4}\)
4.  \(\frac{f}{2}\) and \(\frac{I}{2}\)

If \(\Delta U\) and \(\Delta W\) represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

The total radiant energy per unit area, normal to the direction of incidence, received at a distance \(R\) from the centre of a star of radius \(r,\) whose outer surface radiates as a black body at a temperature \(T\) K is given by: (Where \(\sigma\) is Stefan’s constant):

In the given circuit, the reading of voltmeter V₁ and V₂ are 300 V each. The reading of the voltmeter V₃ and ammeter A are respectively:

1. 150 V, 2.2 A

2. 220 V, 2.2 A

3. 220 V, 2.0 A

4. 100 V, 2.0 A

A \(220\) V input is supplied to a transformer. The output circuit draws a current of \(2.0\) A at \(440\) V. If the efficiency of the transformer is \(80\)%, the current drawn by the primary windings of the transformer is:
1. \(3.6\) A
2. \(2.8\) A
3. \(2.5\) A
4. \(5.0\) A

A source S₁ is producing 10¹⁵ photons per sec of wavelength 5000 Å. Another source S₂ is producing 1.02×10¹⁵ photons per second of wavelength 5100 Å. Then, (power of S₂)/(power of S₁) is equal to:

1. 1.00

2. 1.02

3. 1.04

4. 0.98