The radius of gyration of a solid sphere of mass \(5~\text{kg}\) about \(XY\) is \(5~\text m\) as shown in the figure. The radius of the sphere is \(\frac{5x}{\sqrt{7}}~\text m,\)then the value of \(x\) is:
                    
1. \(5\)
2. \(\sqrt{2}\)
3. \(\sqrt{3}\)
4. \(\sqrt{5}\)
 

Subtopic:  Moment of Inertia |
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The \(I\text-V\) characteristics shown above are exhibited by a:
1. light-emitting diode 2. zener-diode
3. photodiode 4. solar cell
Subtopic:  Applications of PN junction |
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The correct decreasing order of atomic radii (pm) of Li, Be, B and C is:

1. Be > Li > B > C
2. Li > Be > B > C
3. C > B > Be > Li
4. Li > C > Be > B
Subtopic:  Atomic Size |
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The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, \(1.0\times10^{-2}~\text{A m}^{2}\text{and}~\frac{10^{-6}}{\pi^{2}}~\text{kg m}^{2}.\) If it completes \(10\) oscillations in \(10~\text s,\) the magnitude of the magnetic field is:
 
1. \(0.4~\text T\)
2. \(4~\text T\)
3. \(0.4~\text{mT}\)
4. \(4~\text{mT}\)
Subtopic:  Magnetization & Magnetic Intensity |
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The capacitance of a capacitor with charge \(q\) and a potential difference \(V\) depends on:
1. both \(q\)  and \(V\)
2. the geometry of the capacitor
3. \(q\) only
4. \(V\) only
Subtopic:  Capacitance |
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Given below are two statements:

Statement I: Image formation needs regular reflection and/or refraction.
Statement II: The variety in colour of objects we see around us is due to the constituent colours of the light incident on them.

In the light of the above statements, choose the most appropriate answer from the options given below:
1. Statement I is correct but Statement II is incorrect.
2. Statement I is incorrect but Statement II is correct.
3. Both Statement I and Statement II are correct.
4. Both Statement I and Statement II are incorrect.
Subtopic:  Reflection at Plane Surface |
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A uniform metal wire of length \(l\) has \(10~\Omega \) resistance. Now this wire is stretched to a length \(2l\)  and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is:
1. \(10~\Omega \) 2. \(5~\Omega \)
3. \(40~\Omega \) 4. \(20~\Omega \)
Subtopic:  Current & Current Density |
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The spectral series which corresponds to the electronic transition from the levels \(\mathrm{n}_{2}=5,6,\ldots \) to the level \(\mathrm{n}_{1}=4\mathrm~\) is:
1. Pfund series
2. Brackett series
3. Lyman series
4. Balmer series
Subtopic:  Spectral Series |
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Given below are two statements: One is labeled as Assertion (A) and the other is labeled as Reason (R).
Assertion (A):

Houses made of concrete roofs overlaid with foam keep the room hotter during
summer.

Reason (R):

The layer of foam insulation prohibits heat transfer, as it contains air pockets.


In the light of the above statements, choose the correct answer from the options given below:
1. (A) is True but (R) is False.
2. (A) is False but (R) is True.
3. Both (A) and (R) are True but (R) is not the correct explanation of (A).
4. Both (A) and (R) are True and (R) is the correct explanation of (R).
Subtopic:  Conduction |
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A particle executing simple harmonic motion with amplitude \(A\) has the same potential and kinetic energies at the displacement:
1. \(2\sqrt{A}\) 2. \(\dfrac{A}{2}\)
3. \(\dfrac{\mathrm{A}}{\sqrt{2}}\) 4. \(A\sqrt{2}\)
Subtopic:  Energy of SHM |
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