A light-year is a unit of: 
1. Time
2. Mass
3. Distance
4. Energy

In $$\(S= a+bt+ct^2,~S\) is measured in metres and \(t\) in seconds. The unit of \(c\) will be:

If \(u_1\) and \(u_2\) are the units selected in two systems of measurement and \(n_1\) and \(n_2\) are their numerical values, then:

The dimensional formula for impulse is:
1. \([MLT^{-2}]\)
2.  \([MLT^{-1}]\)
3.  \([ML^2T^{-1}]\)
4. \([M^2LT^{-1}]\)

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 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. \(1\%\)

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 \(0.1~\text{cm}\). Its diameter is measured with vernier callipers having the least count of \(0.01~\text{cm}\). Given that the length is \(5.0~\text{cm}\) and the radius is \(2.0~\text{cm}\). The percentage error in the calculated value of the volume will be:
1. \(1\%\)
2. \(2\%\)
3. \(3\%\)
4. \(4\%\)

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:
1. \(A\)
2. \(B\)
3. \(C\)
4. \(D\)