A network of resistors is connected across a \(10~\text{V}\) battery with an internal resistance of \(1~\Omega\) as shown in the circuit diagram. The equivalent resistance of the circuit is:
1.
\(\dfrac{17}{3}~\Omega\)
2.
\(\dfrac{14}{3}~\Omega\)
3.
\(\dfrac{12}{7}~\Omega\)
4.
\(\dfrac{14}{7}~\Omega\)
When a body of mass \(m\) just begins to slide as shown, match List-I with List-II:
| List-I | List-II | ||
| (a) | Normal reaction | (i) | \(P\) |
| (b) | Frictional force \((f_s)\) | (ii) | \(Q\) |
| (c) | Weight \((mg)\) | (iii) | \(R\) |
| (d) | \(mg \mathrm{sin}\theta ~\) | (iv) | \(S\) |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (ii) | (i) | (iii) | (iv) |
| 2. | (iv) | (ii) | (iii) | (i) |
| 3. | (iv) | (iii) | (ii) | (i) |
| 4. | (ii) | (iii) | (iv) | (i) |
| 1. | \(10~\text{J}\) | 2. | \(2.5~\text{J}\) |
| 3. | \(20~\text{J}\) | 4. | \(5~\text{J}\) |
The value of resistance for the colour code of the given resistor is:
1. \((36\pm36)~k\Omega~\)
2. \((470\pm47)~k\Omega~\)
3. \((360\pm36)~k\Omega~\)
4. \((360\pm18)~k\Omega~\)
A concave lens of focal length \(-25\) cm is sandwiched between two convex lenses, each of focal length, \(40\) cm. The power in dioptre of the combined lens would be:
| 1. | \(55\) | 2. | \(9\) |
| 3. | \(1\) | 4. | \(0.01\) |
A beam of light is incident vertically on a glass slab of thickness \(1\) cm, and refractive index \(1.5.\) A fraction \(A\) is reflected from the front surface while another fraction \(B\) enters the slab and emerges after reflection from the back surface. The time delay between them is:
| 1. | \(10^{-10}\) s | 2. | \(5\times 10^{-10}\) s |
| 3. | \(10^{-11}\) s | 4. | \(5\times 10^{-11}\) s |
At some instant, the number of radioactive atoms in a sample is \(N_0\) and after time \(t\), the number decreases to \(N\). It is found that the graphical representation \(\mathrm{ln} N\) versus \(t\) along the \(y\) and \(x\) axis respectively is a straight line. Then the slope of this line is:
1. \(\lambda\)
2. \(-\lambda\)
3. \(\lambda^{-1}\)
4. \(-\lambda^{-1}\)
When the circular scale of a screw gauge completes \(2\) rotations, it covers \(1\) mm over the pitch scale. The total number of circular scale divisions is \(50\). The least count of the screw gauge in metres is:
1. \(10^{-4}\)
2. \(10^{-5}\)
3. \(10^{-2}\)
4. \(10^{-3}\)
A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
| 1. | \(u\sqrt{\dfrac{m}{k}}\) | 2. | \(4u\sqrt{\dfrac{m}{k}}\) |
| 3. | \(2u\sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac12u\sqrt{\dfrac{k}{m}}\) |
| 1. | \(\lambda_\gamma<\lambda_X<\lambda_I<\lambda_M\) |
| 2. | \(\lambda_M<\lambda_I<\lambda_X<\lambda_\gamma\) |
| 3. | \(\lambda_X<\lambda_\gamma<\lambda_M<\lambda_I\) |
| 4. | \(\lambda_X<\lambda_I<\lambda_\gamma<\lambda_M\) |
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