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 would be, respectively,
1. 164 $\pm$ 3 ${\mathrm{cm}}^2$
2. 163.62 $\pm$ 2.6 ${\mathrm{cm}}^2$ 
3. 163.6 $\pm$ 2.6 ${\mathrm{cm}}^2$ 
4. 163.62 $\pm$ 3 ${\mathrm{cm}}^2$

Which of the following pairs of physical quantities does not have the same dimensional formula?

The measure of two quantities along with the precision of respective measuring instrument is $\mathrm{A}=2.5{\mathrm{ms}}^{-1}\pm 0.5{\mathrm{ms}}^{-1}, \mathrm{B}=0.10\mathrm{s}\pm 0.01\mathrm{s}$. The value of AB will be:

1. (0.25 $\pm$ 0.08) m

2. (0.25 $\pm$ 0.5) m

3. (0.25 $\pm$ 0.05) m

4. (0.25 $\pm$ 0.135) m

You measure two quantities as A = 1.0 m $\pm$ 0.2 m, B = 2.0 m $\pm$ 0.2 m. We should report the correct value for $\sqrt{\mathrm{AB}}$ 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

Which of the following measurement is most precise?
1. \(5.00\) mm
2. \(5.00\) cm
3. \(5.00\) m
4. \(5.00\) km

The mean length of an object is \(5~\text{cm}\). Which of the following measurements is most accurate?
1. \(4.9~\text{cm}\)
2. \(4.805~\text{cm}\)
3. \(5.25~\text{cm}\)
4. \(5.4~\text{cm}\)

Young's modulus of steel is \(1.9 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\). When expressed in CGS units of \(\mathrm{dyne/cm^2}\), it will be equal to: \((1 \mathrm{~N}=10^5 \text { dyne, } 1 \mathrm{~m}^2=10^4 \mathrm{~cm}^2)\)
1. \( 1.9 \times 10^{10} \)
2. \( 1.9 \times 10^{11} \)
3. \( 1.9 \times 10^{12} \)
4. \( 1.9 \times 10^9\)

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
a. \(y = a\sin \left(2\pi t / T\right)\)
b. \(y = a\sin(vt)\)
c. \(y = \left({a \over T}\right) \sin \left({t \over a}\right)\)
d. \(y = a \sqrt 2 \left(\sin \left({2 \pi t \over T}\right) - \cos \left({2 \pi t \over T}\right)\right)\)
(Symbols have their usual meanings.)
Choose the correct option:
1. (a), (c)
2. (a), (b)
3. (b), (c)
4. (a), (d)

IF P, Q and R are physical quantities, having different dimensions, which of the following combination/s can never be a meaningful quantity?

(a) (P - Q)/R
(b) PQ - R
(c) PQ/R
(d) (PR - ${\mathrm{Q}}^2)$/R
(e) (R + Q)/P

Choose the correct option:

1. (a, e)

2. (a, d, e)

3. (a, c, d)

4. (b, d)