If the length of rod $A$ is $3.25 \pm 0.01 \,cm$ and that of $B$ is $4.19 \pm 0.01\, cm $ then the rod $B$ is longer than rod $A$ by

If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be

A physical quantity $y$ is represented by the formula $y=m^{2}\, r^{-4}\, g^{x}\,l^{-\frac{3}{2}}$. If the percentage error found in $y, m, r, l$ and $g$ are $18,1,0.5,4$ and $p$ respectively, then find the value of $x$ and $p$.

The period of oscillation of a simple pendulum is $T=2\pi \sqrt {\frac{l}{g}} $. Measured value of $L$ is $20.0\; cm$ known to $1\; mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\ s$ using a wrist watch of $1\; s$ resolution. The accuracy in the determination of $g$ is   ........ $\%$

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is   ........ $\%$

The mean time period of second's pendulum is $2.00s$ and mean absolute error in the time period is $0.05s$. To express maximum estimate of error, the time period should be written as