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 \(X=[M^aL^bT^c]\). The percentage error in measurement of \(M, L\) and \(T\) are \(𝛼 , 𝛽\) and \(𝛾\) respectively. Then maximum percentage error in the quantity \(X\) is:

1. \(\alpha\alpha+\beta\beta+c\gamma\)
2. \(\alpha\alpha+\beta\beta-c\gamma\)
3. \(\frac{\alpha}{\alpha}+\frac{\beta}{\beta}+\frac{c}{\gamma}\)
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 \(10\ \text{m/s}^{–2}\) 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. $\frac{C}{L}$