Please be patient as the PDF generation may take up to a minute.

1.

The unit of percentage error is
(1) Same as that of physical quantity
(2) Different from that of physical quantity
(3) Percentage error is unit less
(4) Errors have got their own units which are different from that of physical quantity measured

2.

A physical  quantity is given by $X=M^a{L}^b{T}^c$.  The  percentage error in measurement of M, L and T are $\alpha , \beta and \gamma$ respectively.  Then maximum percentage error in the quantity X is
(1) $a\alpha +b\beta +c\gamma$
(2) $a\alpha +b\beta -c\gamma$
(3) $\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }$
(4) None of these

3.

A wire of length $l=6\pm 0.06$ cm and radius $r=0.5\pm 0.005$ cm and mass $m=0.3\pm 0.003$ gm.  The maximum percentage error in density is :
(1) 4
(2) 2
(3) 1
(4) 6.8

4.

The dimensions of the quantity in one of the following pairs is the same. 
(1) Torque and Momentum
(2) Angular momentum and Work
(3) Energy and Young's modulus
(4) Light year and Wavelength

5.

The pairs of physical quantities that have the same dimensions is (are):
(1) Reynolds number and coefficient of friction
(2) Curie and frequency of a light wave
(3) Latent heat and gravitational potential
(4) All of these

6.

Out of the following pair, which one does NOT have identical dimension is
(1) impulse and momentum
(2) angular momentum and planck's constant
(3) work and torque
(4) moment of inertia and moment of a force (towards noth-west)

7.

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading: 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree.
Total divisions on the Vernier scale is 30 and match with 29 division of the main scale.  The angle of the prism from the above data:
(1) 58.59 degree
(2) 58.77 degree
(3) 58.65 degree
(4) 59 degree

8. The period of oscillation of a simple pendulum is \(T = 2\pi \sqrt{\frac{L}{g}}\). Measured value of \(L\) is \(20.0~\text{cm}\) known to \(1~\text{mm}\) accuracy and time for \(100\) oscillations of the pendulum is found to be \(90~\text{s}\) using a wrist watch of \(1~\text{s}\) resolution.  The accuracy in the determination of \(g\) is:
1. \(1\%\)
2. \(5\%\)
3. \(2\%\)
4. \(3\%\)

9.

A physical quantity P is described by the relation $P=a^{1/2}{b}^2{c}^3{d}^{-4}$ 
If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5% then the relative error in p will be:
(1) 8%
(2) 12%
(3) 32%
(4) 25%

10.

The number of significant figures in 0.06900 is
(1) 5
(2) 4
(3) 2
(4) 3

11.

The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give
(1) 2.75 and 2.74
(2) 2.74 and 2.73
(3) 2.75 and 2.73
(4) 2.74 and 2.74

12.

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively.  The area of the sheet in appropriate significant figures and error is
(1) 164 $\pm$ 3 $c{m}^2$
(2) 163.62 $\pm$ 2.6 $c{m}^2$
(3) 163.6 $\pm$ 2.6 $c{m}^2$
(4) 163.62 $\pm$ 3 $c{m}^2$

13.

Which of the following measurements is most precise?
(1) 5.00 mm
(2) 5.00 cm
(3) 5.00 m
(4) 5.0 cm

14.

If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula
(1) $\left(P^1{A}^{-1}{T}^1\right)$
(2) $\left(P^2{A}^1{T}^1\right)$
(3) $\left(P^1{A}^{-1/2}{T}^1\right)$
(4) $\left(P^1{A}^{1/2}{T}^{-1}\right)$