A physical parameter '\(a\)' can be determined by measuring the parameters \(b\), \(c\), \(d\) and \(e\) using the relation\(,a= \frac{b^{\alpha}c^{\beta}}{d^{\gamma}e^{\delta}}.\) If the maximum errors in the measurement of \(b, ~c, ~d,~\text{and}~e\) are \(b_1\%,~c_1\%,~d_1\%~\text{and}~e_1\%\), then the maximum error in the value of '\(a\)' determined by the experiment is:
1.  \((b_1+c_1+d_1+e_1)\%\)
2.  \((b_1+c_1-d_1-e_1)\%\)
3.  \(\alpha b_1+\beta c_1-\gamma d_1-\delta e_1\%\)
4.  \(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1\%\)

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 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%