A wire carrying a current \(I\) along the positive \(x\)-axis has length \(L\). It is kept in a magnetic field \(\overrightarrow{B}=(2 \hat{i}+3 \hat{j}-4 \hat{k})~\text{T}\). The magnitude of the magnetic force acting on the wire is:
1. \(\sqrt{3}IL\)
2. \(3IL\)
3. \(\sqrt{5}IL\)
4. \(5IL\)

Subtopic:  Lorentz Force |
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A very long conducting wire is bent in a semi-circular shape from \(A\) to \(B\) as shown in the figure. The magnetic field at point \(P\) for steady current configuration is given by:
      
1. \(\frac{\mu_0 i}{4 R}\left[1-\frac{2}{\pi}\right]\) pointed into the page
2. \(\frac{\mu_0 i}{4 R}\) pointed into the page
3. \(\frac{\mu_0 i}{4 R}\) pointed away from the page
4. \(\frac{\mu_0 i}{4 R}\left[1-\frac{2}{\pi}\right]\) pointed away from the page
Subtopic:  Magnetic Field due to various cases |
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A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels \(24\) cm through the block along its length horizontally, velocity of bullet becomes \(u/3\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
1. \(30\) cm
2. \(27\) cm
3. \(24\) cm
4. \(28\) cm
Subtopic:  Work Energy Theorem |
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An electric dipole is placed as shown in the figure.
        
The electric potential (in \(10^2~\text{V}\)) at the point \(P\) due to the dipole is:
(\(\epsilon_0\)= permittivity of free space and \(\frac{1}{4 \pi \epsilon_0}=k\))
1. \(\left(\frac{8}{3}\right)qk\)
2. \(\left(\frac{3}{8}\right)qk\)
3. \(\left(\frac{5}{8}\right)qk\)
4. \(\left(\frac{8}{5}\right)qk\)
Subtopic:  Energy of Dipole in an External Field |
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NEET - 2023
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In the figure shown here, what is the equivalent focal length of the combination of lenses? (Assume that all layers are thin)
          
1. \(-50~\text{cm}\)
2. \(40~\text{cm}\)
3. \(-40~\text{cm}\)
4. \(-100~\text{cm}\)
Subtopic:  Lens Makers' Formula |
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NEET - 2023
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A satellite is orbiting just above the surface of the earth with period \(T.\) If \(d\) is the density of the earth and \(G\) is the universal constant of gravitation, the quantity \(\frac{3 \pi}{G d}\) represents:
1. \(\sqrt{T}\)
2. \(T\)
3. \(T^2\)
4. \(T^3\)
Subtopic:  Satellite |
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\(10\) resistors, each of resistance \(R\) are connected in series to a battery of \(E\) and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased \(n\) times. The value of \(n\) is: 
1. \(1000\) 2. \(10\)
3. \(100\) 4. \(1\)
Subtopic:  Combination of Resistors |
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A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\) ms–1. The ball strikes the water surface after \(4\) s. The height of bridge above water surface is: (Take \(g=10~ \text {ms}^{-2}\) )
1. \(68\) m 2. \(56\) m
3. \(60\) m 4. \(64\) m
Subtopic:  Uniformly Accelerated Motion |
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Two thin lenses are of the same focal lengths (\(f\)), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:
1. infinite
2. zero
3. \(f/4\)
4. \(f/2\)
Subtopic:  Lenses |
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The radius of inner most orbit of a hydrogen atom is \(5.3 \times 10^{-11}\) m. What is the radius of the third allowed orbit of a hydrogen atom?
1. \(4.77~ \mathring{A}\) 2. \(0.53~ \mathring{A}\)
3. \(1.06~ \mathring{A}\) 4. \(1.59~ \mathring{A}\)
Subtopic:  Bohr's Model of Atom |
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