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

In an experiment, the following observations were recorded: initial length $L =2.820~\text{m}$, mass $M = 3.00~\text{kg}$, change in length $l = 0.087~\text{cm}$, diameter $D = 0.041~\text{cm}$. Taking $g = 9.81~\text{m/s}^2$ and using the formula, $Y = \dfrac{4MgL}{\pi D^2l},$ the maximum permissible error in $Y$ will be:
1. $7.96\%$
2. $4.56\%$
3. $6.50\%$
4. $8.42\%$

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%

If there is a positive error of $50\%$ in the measurement of the velocity of a body, then the error in the measurement of kinetic energy is:
1. $25\%$
2. $50\%$
3. $100\%$
4. $125\%$

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