To an AC power supply of \(220~\text V\) at \(50~\text{Hz},\) a resistor of \(20~\Omega,\) a capacitor of reactance \(25~\Omega\) and an inductor of reactance \(45~\Omega\) are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively:
1. \(15.6~\text {A and} ~30^\circ\)
2. \(15.6~\text {A and} ~45^\circ\)
3. \(7.8~\text {A and} ~30^\circ\)
4. \(7.8~\text {A and} ~45^\circ\)
1. \(15.6~\text {A and} ~30^\circ\)
2. \(15.6~\text {A and} ~45^\circ\)
3. \(7.8~\text {A and} ~30^\circ\)
4. \(7.8~\text {A and} ~45^\circ\)
Subtopic: Different Types of AC Circuits |
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Which of the following options represents the variation of photoelectric current with the property of light shown on the \(x \text{-}\)axis?
| (A) |  |
(B) |  |
| (C) |  |
(D) |  |
| 1. | (A) and (D) | 2. | (B) and (D) |
| 3. | (A) only | 4. | (A) and (C) |
Subtopic: Photoelectric Effect: Experiment |
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A pipe open at both ends has a fundamental frequency \(f \) in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental of the air column is now equal to:
| 1. | \(\dfrac{3f}{2}\) | 2. | \(2f\) |
| 3. | \(\dfrac{f}{2}\) | 4. | \(f\) |
Subtopic: Standing Waves |
Level 3: 35%-60%
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Two identical point masses \(P\) and \(Q,\) suspended from two separate massless springs of spring constant \(k_1\) and \(k_2,\) respectively, oscillate vertically. If their maximum speeds are the same, the ratio \(\left(\dfrac{A_Q}{A_P} \right)\) of the amplitude \(A_Q\) of mass \(Q \) to the amplitude \(A_P\) of mass \(P\) is:
| 1. | \(\sqrt{\dfrac{k_2}{k_1}}\) | 2. | \(\sqrt{\dfrac{k_1}{k_2}}\) |
| 3. | \(\dfrac{k_2}{k_1}\) | 4. | \(\dfrac{k_1}{k_2}\) |
Subtopic: Spring mass system |
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The output \(Y \) of the given logic implementation is similar to the output of which gate?
| 1. | OR | 2. | NOR |
| 3. | AND | 4. | NAND |
Subtopic: Logic gates |
Level 3: 35%-60%
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An oxygen cylinder of volume \(30\) litre has \(18.20\) moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to \(11\) atmospheric pressure at temperature \(27^{\circ} \text{C}.\) The mass of the oxygen withdrawn from the cylinder is nearly equal to:
\([\)Given, \(R=\frac{100}{12}~ \text{J} \mathrm{~mol}^{-1} {~\text K}^{-1},\) and molecular mass of \(O_2=32,\) \(1\) atm pressure \(\left.=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}\right]\)
1. \(0.116\text{ kg}\)
2. \(0.156\text{ kg}\)
3. \(0.125\text{ kg}\)
4. \(0.144\text{ kg}\)
\([\)Given, \(R=\frac{100}{12}~ \text{J} \mathrm{~mol}^{-1} {~\text K}^{-1},\) and molecular mass of \(O_2=32,\) \(1\) atm pressure \(\left.=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}\right]\)
1. \(0.116\text{ kg}\)
2. \(0.156\text{ kg}\)
3. \(0.125\text{ kg}\)
4. \(0.144\text{ kg}\)
Subtopic: Ideal Gas Equation |
Level 4: Below 35%
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In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power \(( p )\) and magnification \(( m )\) for each lens will be, respectively -
| 1. | \(4 p\) and \(m^4\) | 2. | \(p^4\) and \(m^4\) |
| 3. | \(4 p\) and \(4 m\) | 4. | \(p^4\) and \(4 m\) |
Subtopic: Lenses |
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Two gases \(A\) and \(B\) are filled at the same pressure in separate cylinders with movable pistons of radius \(r_A\) and \(r_B,\) respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas \(A\) and \(B\) are displaced by \(16~ \text{cm}\) and \(9~ \text{cm},\) respectively. If the change in their internal energy is the same, then the ratio \(r_A / r_B\) is equal to:
| 1. | \(\dfrac{2}{\sqrt{3}}\) | 2. | \(\dfrac{\sqrt{3}}{2}\) |
| 3. | \(\dfrac{4}{3}\) | 4. | \(\dfrac{3}{4}\) |
Subtopic: Work Done by a Gas |
Level 3: 35%-60%
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A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A.\) It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R.\) When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to \(0\) (zero) in time \(T.\) If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^\alpha A^\beta \rho^\gamma R^\delta\) then:
| 1. | \(a=-\dfrac{1}{2},~ \alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 2. | \(a=\dfrac{1}{2},~\alpha=\dfrac{1}{2},~ \beta=-\dfrac{1}{2}, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 3. | \(a=\dfrac{1}{2}, ~\alpha=\dfrac{1}{2}, ~\beta=-1, ~\gamma=+1, ~\delta=\dfrac{3}{2}\) |
| 4. | \(a=-\dfrac{1}{2}, ~\alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=-\dfrac{1}{2}, ~\delta=\dfrac{5}{2}\) |
Subtopic: Dimensions |
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A bob of heavy mass \(m\) is suspended by a light string of length \(l.\) The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point \(P\) making an angle \(\theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point \(P\) to its initial speed \(v_0\) is:
| 1. | \(\left(\dfrac{\cos \theta}{2+3 \sin \theta}\right)^{-1 / 2}\) | 2. | \(\left(\dfrac{\sin \theta}{2+3 \sin \theta}\right)^{1 / 2}\) |
| 3. | \((\sin \theta)^{1 / 2}\) | 4. | \(\left(\dfrac{1}{2+3 \sin \theta}\right)^{1 / 2}\) |
Subtopic: Conservation of Mechanical Energy |
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