A piece of length 3.532 m is cut from a rod of length 43.4 m . The length of the remaining rod in metre is (up to correct significant figures)

If the length of a rod is measured as 830600 mm , then the number of significant figures in the measurement is

If $A, B$ and $C$ are three different physical quantities with different dimensional formulae, then the combination which can never give a proper physical quantity is

A physical quantity $X$ is given by $X=\frac{2 k^3 l^2}{m \sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The value of $X$ is uncertain by

The number of significant figures in the measurement of a length 0.079000 m is

The efficiency of an engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \cdot \log _e \frac{\beta x}{k T}$, where $\alpha$ and $\beta$ are constants. If $T$ is the absolute temperature, $k$ is Boltzmann constant, $\theta$ is angular displacement and $x$ is distance, then the incorrect statement is

Velocities $(v)$ and accelerations (a) in two systems of units 1 and 2 are related as $v_2=\frac{n}{m^2} v_1$ and $a_2=\frac{a_1}{m n}$ respectively. Here $m$ and $n$ are constants. Dimensionally relations between distances ( $s_1$ and $s_2$ ) and times ( $t_1$ and $t_2$ ) in the two systems are respectively

The number of significant figures in $3.78 \times 10^{22} \mathrm{~kg}$ is

If the velocity of light $c$, the gravitational constant $G$ and Planck's constant $h$ are chosen as the fundamental units, the dimension of density in the new system is

Select the physical quantities in Column I and Column II having same dimensions

A physical quantity $S$ is related to four observables $a, b, c$ and $d$ as $S=\frac{\sqrt{a b}}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$ and $d$ are $2 \%, 1 \%, 1 \%$ and $1 \%$ respectively, then percentage error in the quantity $S$ is

In a $R$ - $C$ circuit, where $R$ is resistance and $C$ is capacitance, which of the following has the dimension of time?

The dimension of angular momentum in mass $(M)$, length $(L)$ and time $(T)$ is

In an experiment the angles are required to be measured using an instrument in which 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half a degree $\left(=0.5^{\circ}\right)$, then the least count of the instrument is

In five successive measurements, the mass of a ball is measured to be $2.61 \mathrm{~g}, 2.58 \mathrm{~g}, 2.40 \mathrm{~g}, 2.73 \mathrm{~g}$ and 2.80 g . The absolute error in the measurement is

Due to an explosion underneath water, a bubble started oscillating. If this oscillation has time period $T$,which is proportional to $p^\alpha S^\beta E^\gamma$, where $p$ is static pressure, $S$ is density of water and $E$ is total energy of explosion. Determine $\alpha, \beta$ and $\gamma$.