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1.

The dimensions of (${\mu }_0{\epsilon }_0$)${}^{-1/2}$ are
1.  [L${}^{1/2}$T${}^{-1/2}$]
2.  [L${}^{-1}$T]
3.  [LT${}^{-1}$]
4.  [L${}^{1/2}$T${}^{1/2}$]

2.

If the dimensions of a physical quantity are given by ${\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}}$, then the physical quantity will be
1. pressure if a = 1, b =-1, c=-2
2. velocity if a=1, b=0, c=-1
3. acceleration if a = 1, b=1, c=-2
4. force if a=0, b=-1, c=-2

3.

Power dissipated in an L-C-R series circuit connected to an AC source of emf $\mathrm{\epsilon }$ is
1.  $\frac{{\mathrm{\epsilon }}^2\mathrm{R}}{\left[{\mathrm{R}}^2+{\left(\mathrm{L\omega }{\displaystyle - \frac{1}{\mathrm{C\omega }}}\right)}^2\right]}$
2.  $\frac{{\mathrm{\epsilon }}^2\sqrt{{\mathrm{R}}^2+{\left(\mathrm{L\omega }-{\displaystyle \frac{1}{\mathrm{C\omega }}}\right)}^2}}{\mathrm{R}}$
3.  $\frac{{\mathrm{\epsilon }}^2\left[{\mathrm{R}}^2+{\left(\mathrm{L\omega }-{\displaystyle \frac{1}{\mathrm{C\omega }}}\right)}^2\right]}{\mathrm{R}}$
4.  $\frac{{\mathrm{\epsilon }}^2\mathrm{R}}{\sqrt{{\mathrm{R}}^2+{\left(\mathrm{L\omega }-{\displaystyle \frac{1}{\mathrm{C\omega }}}\right)}^2}}$

4.

The dimension of $\frac{1}{2}{\epsilon }_0{{\rm E}}^2$, where ${\epsilon }_0$​ is permittivity of free space and E is electric field, is
1. $$[ML${}^2$T${}^{-2}$]
2. $$[ML${}^{-1}$T${}^{-2}$]
3. [ML${}^2$T${}^{-1}$]
4. $$[MLT${}^{-1}$]

5.

Two positive ions, each carrying a charge q, are seperated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)
1. $\frac{4{\mathrm{\pi \epsilon }}_0{\mathrm{Fd}}^2}{{\mathrm{e}}^2}$
2. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_0{\mathrm{Fe}}^2}{{\mathrm{d}}^2}}$
3. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_0{\mathrm{Fd}}^2}{{\mathrm{e}}^2}}$
4. $\frac{4{\mathrm{\pi \epsilon }}_0{\mathrm{Fe}}^2}{{\mathrm{q}}^2}$

6.

If force (F), velocity (v) and time (T) are taken aas fundamental units, then the dimensions of mass are
1. $\left[{\mathrm{FvT}}^{-1}\right]$
2. $\left[{\mathrm{FvT}}^{-2}\right]$
3. $\left[{\mathrm{Fv}}^{-1}{\mathrm{T}}^{-1}\right]$
4. $\left[{\mathrm{Fv}}^{-1}\mathrm{T}\right]$

7.

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimaensional formula of surface tension will be
1. $\left[{\mathrm{Ev}}^{-2}{\mathrm{T}}^{-1}\right]$
2. $\left[{\mathrm{Ev}}^{-1}{\mathrm{T}}^{-2}\right]$
3. $\left[{\mathrm{Ev}}^{-2}{\mathrm{T}}^{-2}\right]$
4. $\left[{\mathrm{E}}^{-2}{\mathrm{v}}^{-1}{\mathrm{T}}^{-3}\right]$

8.

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, the speed of the ejection of the liquid through the holes is
1. $\frac{{\mathrm{vR}}^2}{{\mathrm{n}}^2{\mathrm{r}}^2}$
2. $\frac{{\mathrm{vR}}^2}{{\mathrm{nr}}^2}$
3. $\frac{{\mathrm{vr}}^2}{{\mathrm{n}}^2{\mathrm{R}}^2}$
4. $\frac{{\mathrm{v}}^2\mathrm{R}}{\mathrm{nr}}$

9.

The velocity of electromagnetic radiation in a medium of permittivity ${\mathrm{\epsilon }}_0$ and permeability ${\mathrm{\mu }}_0$ is given by
1. $\sqrt{\frac{{\mathrm{\epsilon }}_0}{{\mathrm{\mu }}_0}}$
2. $\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}$
3. $\frac{1}{\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}}$
4. $\sqrt{\frac{{\mathrm{\mu }}_0}{{\mathrm{\epsilon }}_0}}$

10.

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimensions of length?
1. $\frac{\sqrt{\mathrm{hG}}}{{\mathrm{c}}^{3/2}}$
2. $\frac{\sqrt{\mathrm{hG}}}{{\mathrm{c}}^{5/2}}$
3. $\sqrt{\frac{\mathrm{hc}}{\mathrm{G}}}$
4. $\sqrt{\frac{\mathrm{Gc}}{{\mathrm{h}}^{3/2}}}$

11.

An electron of mass m and a photon have same energy E. The ratio of de-Brogile wavelengths associated with them is
1. ${\left(\frac{\mathrm{E}}{2\mathrm{m}}\right)}^{\frac{1}{2}}$
2. $\mathrm{c}{\left(2\mathrm{mE}\right)}^{\frac{1}{2}}$
3. $\frac{1}{\mathrm{c}}{\left(\frac{2m}{E}\right)}^{\frac{1}{2}}$
4. $\frac{1}{\mathrm{c}}{\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$

12.

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4{\mathrm{\pi \epsilon }}_0}$ is [c is the velocity of light, G is the universal constant of gravitation, and e is charge]
1. $\frac{1}{{\mathrm{c}}^2}{\left[G\frac{e^2}{4\pi {\epsilon }_0}\right]}^{1/2}$
2. ${\mathrm{c}}^2{\left[\mathrm{G}\frac{{\mathrm{e}}^2}{4{\mathrm{\pi \epsilon }}_0}\right]}^{1/2}$
3. $\frac{1}{{\mathrm{c}}^2}{\left[\frac{e^2}{G 4\pi {\epsilon }_0}\right]}^{1/2}$
4. $\frac{1}{\mathrm{c}}G\frac{e^2}{4\pi {\epsilon }_0}$

13.

Given that y = Asin$\left[\left(\frac{2\mathrm{\pi }}{\lambda }(ct-x)\right)\right]$ where y and x are measured in metre. Which of the following statements is true?
1. The unit of λ is the same as that of x and A
2. The unit of λ is the same as that of x but not of A
3. The unit of $c$ is the same as that of $\frac{2\mathrm{\pi }}{\lambda }$​
4. The unit of $$(ct−x) is the same as that of $\frac{2\mathrm{\pi }}{\lambda }$

14.

Match the following       
A.  Capacitance             i.  Volt ${\left(\mathrm{ampere}\right)}^{-1}$
B.  Magnetic induction   ii.  Volt-sec ${\left(\mathrm{ampere}\right)}^{-1}$
C.  Inductance              iii.  Newton ${\left(\mathrm{ampere}\right)}^{-1}$ ${\left(met\mathrm{re}\right)}^{-1}$
D.  Resistance              iv.  ${\mathrm{Coulomb}}^2{\left(\mathrm{joule}\right)}^{-1}$
1.  A-ii, B-iii, C-iv, D-i
2.  A-iv, B-iii, C-ii, D-i
3.  A-iii, B-iv, C-i, D-ii
4.  A-iv, B-i, C-ii, D-i

15. A student measures the distance traveled in free fall of a body, initially at rest in a given time. He uses this data to estimate \(g,\) the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are \(e_1\) and \(e_2\) respectively, the error in the estimation of \(g\) is:
1. \(e_2-e_1\)
2. \(e_1+2e_2\)
3. \(e_1+e_2\)
4. \(e_1-2e_2\)

$$

16.

The length, breadth and thickness of a block are given by $$l=12cm,b=6cm and $$t=2.45cm. The volume of the block according to the idea of significant figures should be$$

1. \(1\times10^2 \text{cm}^{3}\)
2. \(2\times10^2 \text{cm}^{3}\)
3. \(1.763\times10^2 \text{cm}^{3}\)
4. None of these

17.

The measurements are made as \(18.425\) cm, \(7.21\) cm, and \(5.0\) cm. The addition of these measurements should be written as:
1. \(30.635\) cm
2. \(30.64\) cm
3. \(30.63\) cm
4. \(30.6\) cm

18.

With usual notation, the following equation, said to give the distance covered  in the $$nth second.  i.e., $S_n=u+a\frac{(2n-1)}{2}$ is
1. numerically correct only
2. dimensionally correct only
3. both dimensionally and numerically only
4. neither numerically nor dimensionally correct

19.

A physical parameter '\(a\)' can be determined by measuring the parameters \(b\), \(c\), \(d\) and \(e\) using the relation, \(a= \dfrac{b^{\alpha}c^{\beta}}{d^{\gamma}e^{\delta}}.\) If the maximum errors in the measurement of \(b, ~c, ~d,~\text{and}~e\) are \(b_1\%,~c_1\%,~d_1\%~\text{and}~e_1\%\), then the maximum error in the value of '\(a\)' determined by the experiment is:
1. \((b_1+c_1+d_1+e_1)\%\)
2. \((b_1+c_1-d_1-e_1)\%\)
3. \((\alpha b_1+\beta c_1-\gamma d_1-\delta e_1)\%\)
4. \((\alpha b_1+\beta c_1+\gamma d_1+\delta e_1)\%\)