The dimensions of resistivity in terms of \(M\), \(L\), \(T\), and \(Q\) where \(Q\) stands for the dimensions of charge, will be:
1. \(\left[M L^3 T^{-1} Q^{-2}\right]\)
2. \(\left[M L^3 T^{-2} Q^{-1}\right]\)
3. \(\left[M L^2 T^{-1} Q^{-1}\right]\)
4. \(\left[M L T^{-1} Q^{-1}\right]\)

Dimensions of electric current are:
1. \(\left[M^0L^0T^{-1}Q\right]\)
2. \(\left[M^1L^2T^{-1}Q\right]\)
3. \(\left[M^2L^1T^{-1}Q\right]\)
4. \(\left[M^2L^2T^{-1}Q\right]\)

In the relation, \(y=a \cos (\omega t-k x)\), the dimensional formula for \(k\) will be:
1. \( {\left[M^0 L^{-1} T^{-1}\right]} \)
2. \({\left[M^0 L T^{-1}\right]} \)
3. \( {\left[M^0 L^{-1} T^0\right]} \)
4. \({\left[M^0 L T\right]}\)

The position of a body with acceleration \(a\) is given by \(x= Ka^{m}t^{n}\) (assume \(t\) to be time). The values of \(m\) and \(n\) will be:
1. \(m=1,~n=1\)
2. \(m=1,~n=2\)
3. \(m=2,~n=1\)
4. \(m=2,~n=2\)

The period of oscillation of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$ where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stopwatch of least count 0.1 s. The percentage error in g is:

1. 0.1%

2. 1%

3. 0.2%

4. 0.8%

The percentage errors in the measurement of mass and speed are \(2\%\) and \(3\%\) respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:
1. \(11\%\)
2. \(8\%\)
3. \(5\%\)
4. \(1\%\)

What is the number of significant figures in \(0.310\times 10^{3}\)?
1. \(2\)
2. \(3\)
3. \(4\)
4. \(6\)

The decimal equivalent of \(\frac{1}{20} \) up to three significant figures is:

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

The length of a cylinder is measured with a meter rod having the least count of 0.1 cm. Its diameter is measured with vernier callipers having the least count of 0.01 cm. Given that the length is 5.0 cm and the radius is 2.0 cm. The percentage error in the calculated value of the volume will be

1. 1%

2. 2%

3. 3%

4. 4%