A \(250\) turn rectangular coil of length \(2.1\) cm and width \(1.25\) cm carries a current of \(85~\mu\text{A}\) and subjected to the magnetic field of strength \(0.85~\text{T}\). Work done for rotating the coil by \(180^\circ\) against the torque is:
1. \(4.55~\mu\text{J} \)
2. \(2.3~\mu\text{J} \)
3. \(1.15~\mu\text{J} \)
4. \(9.4~\mu\text{J} \)
1. \(4.55~\mu\text{J} \)
2. \(2.3~\mu\text{J} \)
3. \(1.15~\mu\text{J} \)
4. \(9.4~\mu\text{J} \)
The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is:
1. \(1\)
2. \(4\)
3. \(0.5\)
4. \(2\)
A Carnot engine having an efficiency of \(\frac{1}{10}\) as heat engine, is used as a refrigerator. If the work done on the system is \(10\) J, the amount of energy absorbed from the reservoir at a lower temperature is:
1. \(90\) J
2. \(99\) J
3. \(100\) J
4. \(1\) J
A gas mixture consists of \(2\) moles of \(O_2\) and \(4\) moles of \(Ar\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:
| 1. | \(15RT\) | 2. | \(9RT\) |
| 3. | \(11RT\) | 4. | \(4RT\) |
An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current in the same direction is shown in the figure. The magnitude of force per unit length on the middle wire \(B\) is given by:
| 1. | \(\frac{\mu_0i^2}{2\pi d}\) | 2. | \(\frac{2\mu_0i^2}{\pi d}\) |
| 3. | \(\frac{\sqrt{2}\mu_0i^2}{\pi d}\) | 4. | \(\frac{\mu_0i^2}{\sqrt{2}\pi d}\) |
A U-tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a level of \(10~\text{mm}\) above the water level on the other side. Meanwhile, the water rises by \(65~\text{mm}\) from its original level (see diagram). The density of the oil is:
1. \(425~\text{kg m}^{-3}\)
2. \(800~\text{kg m}^{-3}\)
3. \(928~\text{kg m}^{-3}\)
4. \(650~\text{kg m}^{-3}\)
Which of the following statements are correct?
| (a) | centre of mass of a body always coincides with the centre of gravity of the body . |
| (b) | centre of gravity of a body is the point about which the total gravitational torque on the body is zero. |
| (c) | a couple on a body produce both translational and rotation motion in a body. |
| (d) | mechanical advantage greater than one means that small effort can be used to lift a large load. |
| 1. | (a) and (b) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (b) and (d) |
The mechanism of a hypothetical reaction
X2 + Y2 → 2XY is given below:
(i) X2 → X + X (Fast)
(ii) X + Y2 ⇄ XY + Y (slow)
(iii) X + Y → XY (Fast)
The overall order of the reaction will be:
1. 2
2. 0
3. 1.5
4. 1
The element Z = 114 has been discovered recently. Family/group and electronic configuration from which it will belong are:
1. Carbon family and [Rn] 5f14 6d10 7s2 7p2
2. Oxygen family and [Rn] 5f14 6d10 7s2 7p4
3. Nitrogen family and [Rn] 5f14 6d10 7s2 7p6
4. Halogen family and [Rn] 5f14 6d10 7s2 7p5
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