A wave traveling in the +ve \(x\text-\)direction having maximum displacement along \(y\text-\)direction as \(1~\text{m}\), wavelength \(2\pi~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
| 1. | \(y=\sin (2 \pi x-2 \pi t)\) | 2. | \(y=\sin (10 \pi x-20 \pi t)\) |
| 3. | \(y=\sin (2 \pi x+2 \pi t)\) | 4. | \( y=\sin (x-2 t)\) |
The output \((X)\) of the logic circuit shown in the figure will be:
1. \(X= \overline{A\cdot B}\)
2. \(X = A\cdot B\)
3. \(X= \overline{A+ B}\)
4. None of the above
A body of mass \(m\) is taken from the Earth’s surface to the height equal to twice the radius \((R)\) of the Earth. The change in potential energy of the body will be:
| 1. | \(\frac{2}{3}mgR\) | 2. | \(3mgR\) |
| 3. | \(\frac{1}{3}mgR\) | 4. | \(2mgR\) |
| 1. | \(\dfrac{3}{23}\) | 2. | \(\dfrac{7}{29}\) |
| 3. | \(\dfrac{9}{31}\) | 4. | \(\dfrac{5}{27}\) |
| 1. | \(-\dfrac{8}{3}{G}\) | 2. | \(-\dfrac{4}{3} {G}\) |
| 3. | \(-4 {G}\) | 4. | \(-{G}\) |
| 1. | \(\dfrac{M a_0}{e} ~\text{west,}~ \dfrac{M a_0}{e v_0}~\text{up}\) |
| 2. | \(\dfrac{M a_0}{e} ~\text {west,} ~\dfrac{2 M a_0}{e v_0}~\text{down}\) |
| 3. | \(\dfrac{M a_0}{e} ~\text{east,} \dfrac{2 M a_0}{e v_0}~\text{up}\) |
| 4. | \(\dfrac{M a_0}{e} ~\text {east,} \dfrac{3 M a_0}{e v_0} ~\text {down}\) |
For a normal eye, the cornea of the eye provides a converging power of \(40~\text{D}\) and the least converging power of the eye lens behind the cornea is \(20~\text{D}\). Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
1. \(2.5~\text{cm}\)
2. \(1.67~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(5~\text{cm}\)
| 1. | The angular width of the central maximum of the diffraction pattern will increase. |
| 2. | The angular width of the central maximum will decrease. |
| 3. | The angular width of the central maximum will be unaffected. |
| 4. | A diffraction pattern is not observed on the screen in the case of electrons. |
| 1. | \(\dfrac{r}{\sqrt[3]{2}}\) | 2. | \(\dfrac{r}{\sqrt[2]{2}}\) |
| 3. | \(\dfrac{2r}{3}\) | 4. | none of the above |
A stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:
| 1. | \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
| 2. | \(h_2=3h_1\) and \(h_3=3h_2\) |
| 3. | \(h_1=h_2=h_3\) |
| 4. | \(h_1=2h_2=3h_3\) |
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