n₁ = 72 kmh^-1 n₂ =? ms^-1
L₁ = 1 km       L₂ = 1m
T₁=1h             T₂=1s
\(n_2=n_1[\frac{L_1}{L_2}]^a[\frac{T_1}{T_2}]^b\)
The dimensional formula for velocity is [LT^-1]
a = 1 b =-1
\(n_2=72[\frac{1\ km}{1\ m}][\frac{1\ h}{1\ s}]^{-1}\)
\(=72[\frac{1000\ m}{1\ m}]^1[\frac{3600\ s}{1\ s}]^{-1}=72\times1000\times\frac{1}{3600}=20ms^{-1}\)
72km h^-1 = 20ms^-1

Life of the man = 100 years
100 years includes 76 normal years and 24 leap years
Total no of days = 76\(\times\)365 + 24\(\times\)366 = 36524 days
Number of seconds = 36524\(\times\)24\(\times\)3600 = 3.155\(\times\)10° second
\(\text{Number of hearts beats}=\frac{Total\ no\ of\ seconds}{Time\ period\ of\ heart\ beat}=\frac{3.155\times10^9}{0.8s}=3.94\times10^9\)

\(Mass\ m = 4\pm0.03\) kg ( m + \(\triangle\) m )
Volume \(V=5\pm.01 m^3(V+\triangle V)\)
Density =?
Error in mass \(={{\triangle m}\over{m}}={{0.03}\over{4}}\times 100\)
= 0.75%
Error in volume \(={{\triangle V}\over{V}}={{0.01}\over{5}}\times 100\)
= 0.2%
\(Density={{mass}\over{volume}}.\)
Error in density = error in mass + error in volume
= 0.75% +0.2% = 0.95%

Let, \(Q={{x^2y^3}\over{z^1}}.\)
It is given, \({{Δx}\over{x}}=2\%{{Δy}\over{y}}=3\%{{Δz}\over{z}}=1\%\)
\({{ΔQ}\over{Q}}=2\left( {{Δx}\over{x}} \right)+3\left( {{Δy}\over{y}} \right)+1\left( {{Δz}\over{z}} \right)\)
= 2(2%) + 3(3%) + 1(1%)
\({{ΔQ}\over{Q}}=4\%+9\%+1\%=14\%\)

Systematic error is reproducible inaccuracies that are consistently in the same direction. They can be classified as
(i) Instrumental errors 
(ii) Imperfection in experimental technique or procedure
(iii) personal errors 
(iv) errors due to external causes
(v) Least count error

(i) By choosing the instrument carefully.
(ii) Necessary correction is to be made.
(iii) High precision instrument is to be used.
(iv) Proper setting up of experiments is to be done.
(v) Taking proper precautions is a must, while making observations

(i) Theoretical predictions aided with recent simulation and computation procedures are widely used to identify the most suited materials for robust applications.
(ii) The pharmaceutical industry uses this technique very effectively to design new drugs. Bio compatible materials for organ replacement are predicted using quantum prescriptions of physics before fabrication.
(iii) Thus, experiments and theory work, hand in hand, complementing one another.

(i) An attempt to explain a macroscopic system in terms of its microscopic constituents is reductionism.
(ii) For example, thermodynamics was developed to explain macroscopic properties like temperature, entropy, etc., of bulk systems.
(iii) The above properties have been interpreted in terms of the molecular constituents (microscopic) of the bulk system by kinetic theory and statistical mechanics.

(i) This system makes use of only one unit for one physical quantity, which means a rational system of units.
(ii) In this system, all the derived units can be easily obtained from basic and supplementary units, which means it is a coherent system of units.
(iii) It is a metric system which means that multiples and submultiples can be expressed as powers of 10.