Mumbai needs $1.4 \times 10^{12} \, L$ of water annually. Its effective surface area is $600 \, km^2$ and it receives an average rainfall of $2.4 \, m$ annually. If $10 \%$ of this rainwater is conserved,it will meet approximately:

  • A
    $1 \%$ of Mumbai's water needs
  • B
    $10 \%$ of Mumbai's water needs
  • C
    $50 \%$ of Mumbai's water needs
  • D
    $100 \%$ of Mumbai's water needs

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The related effort to derive the properties of a bigger, more complex system from the properties and interactions of its constituent simpler parts is:

Which of the following is not represented in the correct unit?

Identify the incorrect statement.

Match List-$I$ with List-$II$.
List-$I$List-$II$
$(a)$ Capacitance,$C$$(i)$ $M^{1} L^{1} T^{-3} A^{-1}$
$(b)$ Permittivity of free space,$\varepsilon_{0}$$(ii)$ $M^{-1} L^{-3} T^{4} A^{2}$
$(c)$ Permeability of free space,$\mu_{0}$$(iii)$ $M^{-1} L^{-2} T^{4} A^{2}$
$(d)$ Electric field,$E$$(iv)$ $M^{1} L^{1} T^{-2} A^{-2}$

Choose the correct answer from the options given below:

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists:
List $I$ List $II$
$P.$ Boltzmann constant $1.$ $[ML^2T^{-1}]$
$Q.$ Coefficient of viscosity $2.$ $[ML^{-1}T^{-1}]$
$R.$ Planck constant $3.$ $[MLT^{-3}K^{-1}]$
$S.$ Thermal conductivity $4.$ $[ML^2T^{-2}K^{-1}]$

Codes: $P \quad Q \quad R \quad S$

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