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 |
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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 |
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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 |
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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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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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