Twenty seven drops of same size are charged at \(220~\text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop:
1. \(1520~\text{V}\)
2. \(1980~\text{V}\)
3. \(660~\text{V}\)
4. \(1320~\text{V}\)
For the given circuit, the input digital signals are applied at the terminals \(A\), \(B\) and \(C\). What would be the output at terminal \(Y\)?
| 1. |  |
| 2. |  |
| 3. |  |
| 4. |  |
A particle of mass \(m\) is projected with a velocity, \(v=kv_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is:
(Where \(v_e=\) escape velocity, \(R=\) the radius of the earth)
| 1. | \(\dfrac{R^{2}k}{1+k}\) | 2. | \(\dfrac{Rk^{2}}{1-k^{2}}\) |
| 3. | \(R\left ( \dfrac{k}{1-k} \right )^{2}\) | 4. | \(R\left ( \dfrac{k}{1+k} \right )^{2}\) |
A car starts from rest and accelerates at \(5~\text{m/s}^{2}.\) At \(t=4~\text{s}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(t=6~\text{s}?\)
(Take \(g=10~\text{m/s}^2\))
| 1. | \(20\sqrt{2}~\text{m/s}, 0~\text{m/s}^2\) | 2. | \(20\sqrt{2}~\text{m/s}, 10~\text{m/s}^2\) |
| 3. | \(20~\text{m/s}, 5~\text{m/s}^2\) | 4. | \(20~\text{m/s}, 0~\text{m/s}^2\) |
A series \(LCR\) circuit containing \(5.0~\text{H}\) inductor, \(80~\mu \text{F}\) capacitor and \(40~\Omega\) resistor is connected to \(230~\text{V}\) variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:
| 1. | \(46~\text{rad/s}~\text{and}~54~\text{rad/s}\) |
| 2. | \(42~\text{rad/s}~\text{and}~58~\text{rad/s}\) |
| 3. | \(25~\text{rad/s}~\text{and}~75~\text{rad/s}\) |
| 4. | \(50~\text{rad/s}~\text{and}~25~\text{rad/s}\) |
| 1. | \( \theta=\sin ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\) | 2. | \(\theta=\sin ^{-1}\left(\frac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) |
| 3. | \(\theta=\cos ^{-1}\left(\frac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) | 4. | \(\theta=\cos ^{-1}\left(\frac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |
1. \(\dfrac{r_1}{r_1+r_2}\)
2. \(\dfrac{r_2}{r_1+r_3}\)
3. \(\dfrac{r_1}{r_2+r_3}\)
4. \(\dfrac{r_2}{r_2+r_3}\)
A point object is placed at a distance of \(60~\text{cm}\) from a convex lens of focal length \(30~\text{cm}\). If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of \(40~\text{cm}\) from it, the final image would be formed at a distance of:
| 1. | \(30~\text{cm}\) from the plane mirror, it would be a virtual image. |
| 2. | \(20~\text{cm}\) from the plane mirror, it would be a virtual image. |
| 3. | \(20~\text{cm}\) from the lens, it would be a real image. |
| 4. | \(30~\text{cm}\) from the lens, it would be a real image. |
A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium?
(Take \(g=10~( \text {m/s}^2)\)
| 1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
| 3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
In the product
\(\vec{F}=q\left ( \vec{v}\times \vec{B} \right )=q\vec{v}\times \left ( B\hat{i}+B\hat{j}+B_0\hat{k} \right ).\) For \(q=1 \) and \(\vec{v}=2\hat{i}+4\hat{j}+6\hat{k} \) and \(\vec{F}=4\hat{i}-20\hat{j}+12\hat{k},\) what will be the complete expression for \(\vec{B} \)?
1. \(8\hat{i}+8\hat{j}-6\hat{k}\)
2. \(6\hat{i}+6\hat{j}-8\hat{k}\)
3. \(-8\hat{i}-8\hat{j}-6\hat{k}\)
4. \(-6\hat{i}-6\hat{j}-8\hat{k}\)
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