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 |
56%
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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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A block having 12 g of an element is placed in a room. This element is a radioactive element with a half-life of 15 yr. After how many years will there be just 1.5 g of the element in the box?
1. 40 yr
2. 45 yr
3. 20 yr
4. 15 yr
Subtopic: Radioactivity (OLD NCERT) |
65%
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In the given figure what will be the coefficient of mutual inductance?
1. \(\frac{\mu_0a}{2\pi}in\Big(1+\frac{a}{2b}\Big)\)
2. \(\frac{\mu_0a}{\pi}in\Big(1+\frac{b}{2a}\Big)\)
3. \(\frac{\mu_0a}{2\pi}in\Big(1+\frac{a}{b}\Big)\)
4. \(\frac{\mu_0a}{2\pi}in\Big(1+\frac{b}{a}\Big)\)
Subtopic: Mutual Inductance |
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