If \(\phi_1\) and \(\phi_2\) are the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip \(\phi\) is given by:
1. \(cos^2{\phi}=cos^2{\phi_1}+cos^2{\phi_2}\)
2. \(sec^2{\phi}=sec^2{\phi_1}+sec^2{\phi_2}\)
3. \(tan^2{\phi}=tan^2{\phi_1}+tan^2{\phi_2}\)
4. \(cot^2{\phi}=cot^2{\phi_1}+cot^2{\phi_2}\)
1. \(cos^2{\phi}=cos^2{\phi_1}+cos^2{\phi_2}\)
2. \(sec^2{\phi}=sec^2{\phi_1}+sec^2{\phi_2}\)
3. \(tan^2{\phi}=tan^2{\phi_1}+tan^2{\phi_2}\)
4. \(cot^2{\phi}=cot^2{\phi_1}+cot^2{\phi_2}\)
Two cars moving in opposite directions approach each other at speeds of 22 m/s and 16.5 m/s, respectively. The driver of the first car blows a horn with a frequency of 400 Hz. The frequency heard by the driver of the second car is [assume velocity of sound to be 340 m/s]:
1. 361 Hz
2. 411 Hz
3. 448 Hz
4. 350 Hz
A massless and inextensible string connects two blocks \(\mathrm{A}\) and \(\mathrm{B}\) of masses \(3m\) and \(m,\) respectively. The whole system is suspended by a massless spring, as shown in the figure. The magnitudes of acceleration of \(\mathrm{A}\) and \(\mathrm{B}\) immediately after the string is cut, are respectively:
| 1. | \(\frac{g}{3},g\) | 2. | \(g,g\) |
| 3. | \(\frac{g}{3},\frac{g}{3}\) | 4. | \(g,\frac{g}{3}\) |
A thin prism having refracting angle \(10^\circ\) is made of glass of a refractive index \(1.42\). This prism is combined with another thin prism of glass with a refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism should be:
1. \(6^{\circ}\)
2. \(8^{\circ}\)
3. \(10^{\circ}\)
4. \(4^{\circ}\)
The acceleration due to gravity at a height \(1~\text{km}\) above the earth's surface is the same as at a depth \(d\) below the surface of the earth. Then:
| 1. | \(d= 1~\text{km}\) | 2. | \(d= \frac{3}{2}~\text{km}\) |
| 3. | \(d= 2~\text{km}\) | 4. | \(d= \frac{1}{2}~\text{km}\) |
A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves:
| 1. | the potential gradients. |
| 2. | a condition of no current flow through the galvanometer. |
| 3. | a condition of cells, galvanometer, and resistances. |
| 4. | the cells. |
A spherical black body with a radius of \(12\) cm radiates \(450\) W power at \(500\) K. If the radius were halved and the temperature is doubled, the power radiated in watts would be:
1. \(450\)
2. \(1000\)
3. \(1800\)
4. \(225\)
The figure shows a circuit that contains three identical resistors with resistance \(R = 9.0~\Omega\) each, two identical inductors with inductance \(L = 2.0~\text{mH}\) each, and an ideal battery with emf \(\varepsilon = 18~\text{V}\). The current \('i'\) through the battery just after the switch is closed will be:
1. \(0.2~\text{A}\)
2. \(2~\text{A}\)
3. \(4~\text{A}\)
4. \(2~\text{mA}\)
Radioactive material 'A' has decay constant '8\(\lambda\)' and material 'B' has a decay constant '\(\lambda\)'. Initially, they have the same number of nuclei. After what time, the ratio of the number of nuclei of material 'A' to that of 'B' will be \(\frac{1}{e}\)?
\(1 . \frac{1}{7 \lambda}\)
\(2 . \frac{1}{8 \lambda}\)
\(3 . \frac{1}{9 \lambda}\)
\(4 . \frac{1}{\lambda}\)
The diagrams below show regions of equipotential.
A positive charge is moved from \(\mathrm{A}\) to \(\mathrm{B}\) in each diagram. Choose the correct statement from the options given below:
| 1. | in all four cases, the work done is the same. |
| 2. | minimum work is required to move \(q\) in figure (a). |
| 3. | maximum work is required to move \(q\) in figure (b). |
| 4. | maximum work is required to move \(q\) in figure (c). |
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