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The decimal equivalent  of 1/20 upto three significant figure is
(1) 0.0500
(2) 0.05000
(3) 0.0050
(4) $5.0\times {10}^{-2}$

The frequency of vibration of string is given by $v=\frac{p}{2l}{\left[\frac{F}{m}\right]}^{1/2}$.  Here p is number of segments in the string and l is the length.  The dimensional formula for m will be
(1) $\left[M^{0}L{T}^{-1}\right]$
(2) $\left[M{L}^0{T}^{-1}\right]$
(3) $\left[M{L}^{-1}{T}^0\right]$
(4) $\left[M^0{L}^0{T}^0\right]$

Which of the following set have different dimensions?
(1) Pressure, Young's modulus, Stress
(2) EMF, Potential difference, Electric potential
(3) Heat, Work done, Energy
(4) Dipole moment, Electric flux, Electric field

In a screw gauge, the zero of mainscale coincides with fifth division of circular scale in figure \((i).\)  The circular divisions of screw gauge are \(50.\)  It moves \(0.5~\text{mm}\) on main scale in one rotation.  The diameter of the ball in figure \((ii)\) is:

1. \(2.25~\text{mm}\)
2. \(2.20~\text{mm}\)
3. \(1.20~\text{mm}\)
4. \(1.25~\text{mm}\)

Match List I with List II and select the correct answer using the codes given below the lists:
List I                                              List II
P. Boltzmann constant                  1. $\left[M{L}^2{T}^{-1}\right]$
Q. coefficient of viscosity              2. $\left[M{L}^{-1}{T}^{-1}\right]$
R. Planck constant                       3. $\left[ML{T}^{-3}{K}^{-1}\right]$
S. Thermal conductivity                4. $\left[M{L}^2{T}^{-2}{K}^{-1}\right]$
Codes:
                    P          Q        R        S
(1)               3            1        2         4
(2)               3            2        1         4
(3)               4            2         1         3
(4)               4            1         2         3

The dimension of magnetic field in M, L, T and C (coulomb) is given as
(1) $ML{T}^{-1}{C}^{-1}$
(2) $M{T}^2{C}^{-2}$
(3) $M{T}^{-1}{C}^{-1}$
(4) $M{T}^{-2}{C}^{-1}$

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 $m{s}^{-1}$.  The  magnitude of its momentum is recorded as
(1) 17.6 $kg m{s}^{-1}$
(2) 17.565 $kg m{s}^{-1}$
(3) 17.56 $kg m{s}^{-1}$
(4) 17.57 $kg m{s}^{-1}$

Two full turn of the circular scale of a screw gauge cover a distance of 1 mm on main scale.  The total number of division on the circular scale is 50. Further , it is found that the screw gauge has a zero error of -0.03 mm.  While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35.  The diameter of the wire is
(1) 3.32 mm
(2) 3.73 mm
(3) 3.67 mm
(4) 3. 38 mm

A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.  The diameter of wire from the above data is:
(1) 0.052 cm
(2) 0.026 cm
(3) 0.005 cm
(4) 0.52 cm

The current voltage relation of diode is given by $I=(e^{1000V/T}-1) mA$, where the applied voltage is in volts and the temperature T is in degree Kelvin.  If a student makes an error measuring $\pm$ 0.01 V while measuring the current of 5 mA
at 300K, what will be the error in the value of current in mA?
(1) 0.5 mA
(2) 0.05 mA
(3) 0.2 mA
(4) 0.02 mA

$$You measure two quantities as A = 1.0 m 
\(\pm 0.2{ ~m}, {B}=2.0 { ~m} \pm 0.2 {~ m}\). We should report correct value for \(\sqrt{A B}\) as: 
1. \(1.4 {~m} \pm 0.4{~m}\)
2. \(1.41{~m} \pm 0.15{~m}\)
3. \(1.4 {~m} \pm 0.3{~m}\)
4. \(1.4 {~m} \pm 0.2{~m}\)
$$

The mean length of an object is 5 cm. which of the following measurements is most accurate?
(1) 4.9 cm
(2) 4.805 cm
(3) 5.25 cm
(4) 5.4 cm

Young's modulus of steel is $1.9\times {10}^{11} N/m^2$.  When expressed in CGS units of dynes / $c{m}^2$, it will be equal to
(1 N = ${10}^5$ dyne, 1 $m^2={10}^4 c{m}^2$)
(1) $1.9\times {10}^{10}$
(2) $1.9\times {10}^{11}$
(3) $1.9\times {10}^{12}$
(4) $1.9\times {10}^{13}$

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct:
(1) $y=a \sin 2\mathrm{\pi t}/\mathrm{T}$
(2) $y=a \sin \frac{vt}{a}$
(3) $y=\frac{a}{t}\sin \left(\frac{t}{a}\right)$
(4) $y=\sqrt[]{2}\left(\sin \frac{2\mathrm{\pi t}}{T}-\cos \frac{2\mathrm{\pi t}}{T}\right)$

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
(1) (P $-$ Q) / R
(2) PQ $-$R
(3) PQ / R
(4) (PQ $-$$Q^2$) / R