The displacement $$x$$ of a particle varies with time $$t$$ as $$x=ae^{-\alpha t}+be^{\beta t}$$ where $$a,b,\alpha$$ and $$\beta$$ are positive constants. The velocity of the particle will:
1. decrease with time
2. be independent of $$\alpha$$ and $$\beta$$
3. drop to zero when $$\alpha=\beta$$
4. increase with time

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
Hints

A transformer having an efficiency of $$75\%$$ is working on $$220~\mathrm{V}$$ and $$4.4~\mathrm{kW}$$ power supply. If the current in the secondary coil is $$5~\mathrm{A}$$. What will be the voltage across the secondary coil and the current in the primary coil?
1. $$V_s=220 \mathrm{~V}, I_p=20 \mathrm{~A}$$
2. $$V_s=660 \mathrm{~V}, I_p=15 \mathrm{~A}$$
3. $$V_s=660 \mathrm{~V}, I_p=20 \mathrm{~A}$$
4. $$V_s=220 \mathrm{~V}, I_p=15 \mathrm{~A}$$

Subtopic:  Transformer |
50%
Hints

A fish rising vertically to the surface of the water in a lake uniformly at the rate of $$2~\mathrm{m/s}$$ observes a kingfisher diving vertically towards the water at a rate of $$10~\mathrm{m/s}$$. If the refractive index of water $$n=\frac43$$ what will be the actual velocity of the kingfisher?
1. $$10 \mathrm{~m} / \mathrm{s}$$
2. $$8 \mathrm{~m} / \mathrm{s}$$
3. $$6 \mathrm{~m} / \mathrm{s}$$
4. $$9 \mathrm{~m} / \mathrm{s}$$
Subtopic:  Refraction at Plane Surface |
Hints

One mole of a monoatomic ideal gas undergoes the process $$A\rightarrow B$$ in the given $$P-V$$ diagram. The molar heat capacity for this process is:

1. $$\frac{3R}{2}$$
2. $$\frac{13R}{6}$$
3. $$\frac{5R}{2}$$
4. $$2R$$

Subtopic:  Molar Specific Heat |
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Hints

A pan with a set of weights is attached to a light spring. The period of vertical oscillation is $$0.5~\mathrm{s}$$. When some additional weights are put in the pan, then the period of oscillations increases by $$0.1\mathrm{~s}$$. The extension caused by the additional weight is:
1. $$5.5 \mathrm{~cm}$$
2. $$3.8 \mathrm{~cm}$$
3. $$2.7 \mathrm{~cm}$$
4. $$1.3 \mathrm{~cm}$$

Subtopic:  Simple Harmonic Motion |
Hints

A cylinder of radius $$R$$ and length $$L$$ is placed in a uniform electric field $$E$$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by:
1. $$2\pi R^2E$$
2. $$\frac{\pi R^2}{E}$$
3. $$\frac RE$$
4. zero

Subtopic:  Gauss's Law |
56%
Hints

If A + B = C and that C is perpendicular to A. What is the angle between A and B, if |A| = |C|?
1. $$\frac{\pi}{4}~\text{rad}$$
2. $$\frac{\pi}{2}~\text{rad}$$
3. $$\frac{3\pi}{4}~\text{rad}$$
4. $$\pi~\text{rad}$$

Subtopic:  Scalar Product |
Hints

A beam of light travelling along X-axis is described by the electric field Ey = 600 V/m. $$\sin~\omega \Big(t-\frac xc\Big),$$ the maximum magnetic force on a charge q = 2e, moving along Y-axis with the speed of 3 × 108 m/s is:
1.  19.2 × 10-17 N
2.  1.92 × 10-17 N
3.  0.192 N
4.  None of these
Subtopic:  Properties of EM Waves |
Hints

A body is whirled in a horizontal circle of radius $$25~\mathrm{cm}$$. It has an angular velocity of $$13~\mathrm{rad/s}$$. What is its linear velocity at any point on a circular path?
1. $$2 \mathrm{~m} / \mathrm{s}$$
2. $$3 \mathrm{~m} / \mathrm{s}$$
3. $$3.25 \mathrm{~m} / \mathrm{s}$$
4. $$4.25 \mathrm{~m} / \mathrm{s}$$
Subtopic:  Circular Motion |
67%
Hints

In the given figure, potential difference between $$A$$ and $$B$$ is:

1. 0
2. $$5~\mathrm{V}$$
3. $$10~\mathrm{V}$$
4. $$15~\mathrm{V}$$

Subtopic:  PN junction |
51%