A calorie is a unit of heat (energy in transit) and it equals about \(4.2~\text{J}\) where \(1~\text{J}= 1~\text{kg-m}^2\text{s}^{-2}\). Suppose we employ a system of units in which the unit of mass equals \(\alpha~\text{kg}\) the unit of length equals \(\beta~\text{m}\), and the unit of time is \(\gamma~\text{s}\) then the magnitude of calories in terms of new units is:
1. \(4.2\alpha^{-2}\beta^{-2}\gamma^{2}\)
2. \(4.2\alpha^{2}\beta^{-2}\gamma^{2}\)
3. \(4.2\alpha^{-1}\beta^{-2}\gamma^{2}\)
4. \(4.2\alpha^{-1}\beta^{2}\gamma^{-2}\)

The number of significant figures in \(0.0006032\) m² is:

A physical quantity \(P\) is related to four observables \(a,\) \(b,\) \(c,\) and \(d\) as follows;   \(P=\frac{a^{3}b^{2}}{\sqrt{c}d}.\)
The percentage errors of measurement in \(a,\) \(b,\) \(c,\) and \(d\) are 1%, 3%, 4% and 2%, respectively. Then the percentage error in the quantity \(P\) is:
1. 12%
2. 13%
3. 14%
4. 15%

When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72” of arc. Then the diameter of Jupiter is:

$\left(1\right) 1.34\times {10}^9 m$
$\left(2\right) 1.43\times {10}^9 m$
$\left(3\right) 1.34\times {10}^8 m$
$\left(4\right) 1.43 \times {10}^8 m$

A new unit of length is chosen such that the speed of light in the vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes \(8\) min and \(20\) secs to cover this distance?
1. \(500\) new units of length.
2. \(100\) new units of length.
3. \(300\) new units of length.
4. \(200\) new units of length.

A student measures the thickness of a human hair by looking at it through a microscope of magnification \(100.\) He makes \(20\) observations and finds that the average width of the hair in the field of view of the microscope is \(3.5\) mm. The thickness of the hair is:
1. \(0.035\) mm
2. \(0.0035\) mm
3. \(0.35\) mm
4. \(3.5\) mm

The photograph of a house occupies an area of $1.75 c{m}^2$ on a 35 mm slide. The slide is projected onto a screen, and the area of the house on the screen is $1.55 m^2$. What is the linear magnification of the projector-screen arrangement?

(1) 90.0

(2) 94.1

(3) 99.9

(4) 97.7

The length, breadth, and thickness of a rectangular sheet of metal are \(4.234\) m, \(1.005\) m, and \(2.01\) cm respectively. The volume of the sheet to correct significant figures is:
1. \(0.00856\) m³${}^{}$
2. \(0.0856\) m³${}^{}$
3. \(0.00855\) m³${}^{}$
4. \(0.0855\) m³${}^{}$

Which one of the following formulas is dimensionally incorrect?

$\left(1\right) \mathrm{y}=\mathrm{asin}\frac{2\mathrm{\pi t}}{\mathrm{T}}$
$\left(2\right) \mathrm{y}=\frac{\mathrm{a}}{\sqrt{2}}\left(\sin \frac{2\mathrm{\pi t}}{\mathrm{T}}+\cos \frac{2\mathrm{\pi t}}{\mathrm{T}}\right)$
$\left(3\right) \mathrm{y}=\mathrm{asinvt}$
$\left(4\right) \mathrm{y}=\mathrm{asin}\left(\frac{2\mathrm{\pi t}}{\mathrm{T}}+\mathrm{\pi }\right)$