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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$Assertion$: In the measurement of physical quantities,direct and indirect methods are used.
$Reason$: The accuracy and precision of measuring instruments,along with errors in measurements,should be taken into account while expressing the result.

Match List $I$ with List $II$:
List $I$ List $II$
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$(B)$ Co-efficient of Viscosity $(\eta)$ $(II)$ $[M L^2 T^{-1}]$
$(C)$ Planck's Constant $(h)$ $(III)$ $[M L^{-1} T^{-2}]$
$(D)$ Work Function $(\phi)$ $(IV)$ $[M L^2 T^{-2}]$

Choose the correct answer from the options given below:

Which of the following pairs of physical quantities does not have the same dimensional formula?

State whether the following statements are true or false:
$(a)$ Weight is a fundamental physical quantity.
$(b)$ $A$ micrometer is used to measure the size of an oleic acid molecule at the molecular level.
$(c)$ The dimensions of a derived quantity obtained from any fundamental quantity can never be zero.

Match the following. (Take the relative strength of the strongest fundamental forces in nature as $1$)

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