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

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

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

A physical quantity \(A\) is related to four observable quantities \(a\), \(b\), \(c\) and \(d\) as follows, \(A= \frac{a^2b^3}{c\sqrt{d}},\) the percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are \(1\%\), \(3\%\), \(2\%\) and \(2\%\) respectively. The percentage error in quantity \(A\) will be: 
1. \(12\%\)
2. \(7\%\)
3. \(5\%\)
4. \(14\%\)

If the acceleration due to gravity is 10 ms^–2 and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is 

(1) 360000

(2) 72,000

(3) 36,000

(4) 129600

If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency? [This question includes concepts from the 12th syllabus]

(1) $\frac{1}{RC}$

(2) $\frac{R}{L}$

(3) $\frac{1}{\sqrt{LC}}$

(4) $\frac{C}{L}$