Identify the incorrect statement among the following.

  • A
    $A$ true length of $5.678 \ km$ has been measured in two experiments as $5.5 \ km$ and $5.51 \ km$, respectively. The second measurement has more precision.
  • B
    Length of $1 \ m$ and $0.5 \ m$ have been both measured with the same absolute error of $0.01 \ m$. Both the measurements are equally accurate.
  • C
    The numbers of significant digits in $1.6$ and $0.60$ are two and two respectively.
  • D
    The number $2.445$ can be rounded to two decimal places as $2.45$.

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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.
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The ratio $\left(\frac{E}{W}\right)$ of relative strength of electromagnetic force $(E)$ to weak nuclear force $(W)$ is,

Match the physical quantities in Column-$I$ with those in Column-$II$ having the same dimensions. The correct matching is:
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$D$. Decay constant$IV$. Planck's constant

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its rotational kinetic energy $(K = \frac{1}{2} I \omega^{2})$. (in $\%$)

Match List $I$ with List $II$ :
List $I$ (Physical Quantity) List $II$ (Dimensional Formula)
$(A)$ Pressure gradient $(I)$ $[M^0 L^2 T^{-2}]$
$(B)$ Energy density $(II)$ $[M^1 L^{-1} T^{-2}]$
$(C)$ Electric Field $(III)$ $[M^1 L^{-2} T^{-2}]$
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Choose the correct answer from the options given below:

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