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

1.	none	2.	\(\text{m}\)
3.	\(\text{ms}^{-1}\)	4.	\(\text{ms}^{-2}\)

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:

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:

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

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:

How many significant figures are present in the following numbers?

Select the correct answer set from the following: