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Questions Available: 15
Year: 2022
Topic: Units and Measurements
1.
The area of a rectangular field (in m2 ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is
(1).
138 × 101
(2).
1382
(3).
1382.5
(4).
14 × 102

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Year: 2021
Topic: Units and Measurements
2.
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of
(1).
[M2] [L−1] [T 0]
(2).
[M ] [L−1] [T −1]
(3).
[M ] [L0] [T 0]
(4).
[M2] [L−2] [T −1]

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Year: 2025
Topic: Units and Measurements
3.
A baloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density \(\rho\) and takes a spherical share of radius R. When the gas is allowed to flow freely out of it, its radius r changes from R to 0 (zero) in time T. If the speed v(r) of gas coming out of the balloon depends on r as \(r^a\) and \(\text{T} \propto \text{S}^\alpha \text{A}^\beta \rho^\gamma \text{R}^\delta\) then
(1).
\(\text{a}=\frac{1}{2}\), \(\alpha=\frac{1}{2}\), \(\beta=\frac{1}{2}\), \( \gamma=\frac{1}{2} \text{,}\, \delta=\frac{7}{2}\)
(2).
\( \text{a}=\frac{1}{2}\), \(\alpha=\frac{1}{2}\), \(\beta = -1\), \(\gamma=+1\), \(\delta=\frac{3}{2}\)
(3).
\( \text{a}=\frac{1}{2}\), \(\alpha=-\frac{1}{2}\), \(\beta=-1\), \(\gamma=\frac{1}{2}\), \(\delta=\frac{5}{2}\)
(4).
\(\text{a}=-\frac{1}{2}\), \(\alpha=-\frac{1}{2}\), \(\beta=-1\), \(\gamma=\frac{1}{2}\), \(\delta=\frac{7}{2}\)

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Year: 2025
Topic: Units and Measurements
4.
A physical quantity P is related to four observations a, b, c, and d as follows:
\(\text{P}\,=\,\text{a}^3\text{b}^2 / \text{c} \sqrt{d}\)
The percentage errors of measurement in a, b, c, and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is
(1).
15%
(2).
10%
(3).
2%
(4).
13%

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Year: 2024
Topic: Units and Measurements
5.
The quantities which have the same dimensions as those of solid angle are:
(1).
strain and angle
(2).
stress and angle
(3).
strain and arc
(4).
angular speed and stress

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Year: 2024
Topic: Units and Measurements
6.
A force defined by F = αt2 + βt acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is:
(1).
\(\displaystyle \frac{\beta t}{\alpha}\)
(2).
\(\displaystyle \frac{\alpha t}{\beta}\)
(3).
\(\displaystyle \alpha \beta t\)
(4).
\(\displaystyle \frac{\alpha \beta}{t}\)

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Year: 2023
Topic: Units and Measurements
7.
The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are
(1).
Personal errors
(2).
Least count errors
(3).
Random errors
(4).
Instrumental errors

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Year: 2023
Topic: Units and Measurements
8.
A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be
(1).
1.30%
(2).
1.60%
(3).
1.40%
(4).
1.20%

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Solution
Year: 2022
Topic: Units and Measurements
9.
Plane angle and solid angle have
(1).
Units but no dimensions
(2).
Dimensions but no units
(3).
No units and no dimensions
(4).
Both units and dimensions

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Year: 2021
Topic: Units and Measurements
10.
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
(1).
[F ] [A] [T ]
(2).
[F ] [A] [T 2]
(3).
[F ] [A] [T −1]
(4).
[F ] [A−1] [T ]

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Year: 2020
Topic: Units and Measurements
11.
Dimensions of stress are :
(1).
\([M\, L^2\, T^{ −2}]\)
(2).
\([M\, L^0\, T^{ −2}]\)
(3).
\([M\, L^{−1}\, T^{ −2}]\)
(4).
\([M\, L\, T^{ −2}]\)

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Year: 2020
Topic: Units and Measurements
12.
Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 ?
(1).
9.98 m
(2).
9.980 m
(3).
9.9 m
(4).
9.9801 m

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Solution
Year: 2019
Topic: Units and Measurements
13.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where \(\displaystyle X = \frac{A^2B^{1/2}}{C^{1/3}D^3}\) will be
(1).
\(10 \% \)
(2).
\(\left(\displaystyle \frac{3}{13}\right) \% \)
(3).
\(16 \%\)
(4).
\(-10 \%\)

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Solution
Year: 2019
Topic: Units and Measurements
14.
The unit of thermal conductivity is
(1).
\(Wm^{−1}K^{−1}\)
(2).
\(JmK^{−1}\)
(3).
\(Jm^{−1}K^{ −1}\)
(4).
\(WmK^{−1}\)

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Solution
Year: 2017
Topic: Units and Measurements
15.
A physical quantity of the dimensions of length that can be formed out of c, G and \(\displaystyle \frac{e^2}{4\pi \, \epsilon_0}\) is
[c is velocity of light, G is the universal constant of gravitation and e is charge]
(1).
(2).
(3).
(4).

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