The angle of $1^\circ$ (degree) will be equal to:
(Use $360^\circ=2\pi$ rad)
1. $1.034\times10^{-3}$ rad
2. $1.745\times10^{-2}$ rad
3. $1.524\times10^{-2}$ rad
4. $1.745\times10^{3}$ rad

A man wishes to estimate the distance of a nearby tower from him. He stands at point A in front of tower C and spots a very distant object O in line with AC. He then walks perpendicular to AC up to B, a distance of 100 m, and looks at O and C again. Since O is very distant, the direction BO is practically the same as AO; but he finds the line of sight of C shifted from the original line of sight by an angle $\theta=40^\circ$ ($\theta$ is known as ‘parallax’), the distance of the tower C from his original position A is: (Given $\tan40^\circ=0.8391$)
1. 119 m
2. 126 m
3. 320 m
4. 219 m

The Sun’s angular diameter is measured to be 1920′′. The distance D of the Sun from the Earth is $1.496\times {10}^{11} \mathrm{m}.$ The diameter of the Sun:

1.  $2.39\times {10}^9 \mathrm{m}$

2.  $0.39\times {10}^9 \mathrm{m}$

3.  $1.39\times {10}^9 \mathrm{m}$

4.  $1.39\times {10}^{10} \mathrm{m}$

If the size of a nucleus (in the range of $10^{-15}$ to $10^{-14}$ m) is scaled up to the tip of a sharp pin, what roughly is the size of an atom? Assume tip of the pin to be in the range $10^{-5}$ m to $10^{-4}$ m.
1. $1$ m
2. $10$ m
3. $10^{-10}$ m
4. $10^{-5}$ m

Two clocks are being tested against a standard clock located in a national laboratory. At 12:00:00 noon by the standard clock, the readings of the two clocks are:

If you are doing an experiment that requires precision time interval measurements, which of the two clocks will you prefer?

We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be $2.63~\text s, 2.56~\text s, 2.42~\text s, 2.71~\text s,$ and $2.80~\text s.$ The average absolute error and percentage error, respectively, are:
1. $0.22~\text s$ and $4\%$
2. $0.11~\text s$ and $4\%$
3. $4~\text s$ and $0.11\%$
4. $5~\text s$ and $0.22\%$

The temperatures of two bodies measured by a thermometer are $t_1=20^\circ \text{C}\pm0.5^\circ \text{C}$ and $t_2=50^\circ \text{C}\pm0.5^\circ \text{C}.$ The temperature difference with permissible error is:
1. $31^\circ \text{C}\pm0.5^\circ \text{C}$
2. $30^\circ \text{C}\pm1.0^\circ \text{C}$
3. $30^\circ \text{C}\pm0.0^\circ \text{C}$
4. $30^\circ \text{C}\pm1.5^\circ \text{C}$

The resistance $R=\frac{V}{I}$ where $V=(100 \pm 5) ~V$ and $I=(10 \pm 0.2)~ A$. The percentage error in $R$ is:
1. $5\%$
2. $2\%$
3. $7\%$
4. $3\%$

Two resistors of resistances ${\mathrm{R}}_1 = \left(100 \pm 3\right)$ ohm and $R_2 = \left(200 \pm 4\right)$ ohm are connected in series, the equivalent resistance of the series combination is:

1.  (300 ± 7) ohm

2.  (300 ± 1) ohm

3.  (300 ± 0) ohm

4.  (100 ± 1) ohm