In the context of the accuracy of measurement and significant figures in expressing the results of the experiment, which of the following is/are correct?

(1) Out of the two measurements 50.14 cm and 0.00025 Amperes, the first one has greater accuracy.

(2) If one travels 478 km by rail and 397 m by road, the total distance traveled is 478 km.

1. Only (1) is correct

2. Only (2) is correct

3. Both are correct

4. None of them is correct.

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = $b^{\alpha }{c}^{\beta }/d^{\gamma }{e}^{\delta }$. If the maximum errors in the measurement of b, c, d and e are b₁%, c₁%, d₁% and e₁%, 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) ($\alpha b_1+\beta c_1+\gamma d_1+\delta e_1$)%

The resistance R = $\frac{V}{i}$ where V= 100 ± 5 volts and i = 10 ± 0.2 amperes. What is the total error in R

(1) 5%

(2) 7%

(3) 5.2%

(4) $\frac{5}{2}$%

The periods of oscillation of a simple pendulum in an experiment are recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s respectively. The average absolute error will be:

1. 0.1 s

2. 0.11 s

3. 0.01 s

4. 1.0 s

According to Joule's law of heating, heat produced H = I²Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is

(1) ± 17%

(2) ± 16%

(3) ± 19%

(4) ± 25%

A physical quantity \(P\) is given by \(P=\dfrac{A^3 B^{1/2}}{C^{-4}D^{3/2}}.\) The quantity which contributes the maximum percentage error in \(P\) is:

If L = 2.331 cm, B = 2.1 cm, then L + B =?

1. 4.431 cm

2. 4.43 cm

3. 4.4 cm

4. 4 cm

The number of significant figures in the numbers \(25.12,\) \(2009,\) \(4.156\) and \(1.217\times 10^{-4}\) is:

If the length of rod A is 3.25 ± 0.01 cm and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by 

(1) 0.94 ± 0.00 cm

(2) 0.94 ± 0.01 cm

(3) 0.94 ± 0.02 cm

(4) 0.94 ± 0.005 cm