The measurements of two quantities along with the precision of their respective measuring instruments are $A = 2.5 \, m/s \pm 0.5 \, m/s$ and $B = 0.10 \, s \pm 0.01 \, s$. The value of $AB$ will be:

The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is about $100 \, cm$ and is known to have $1 \, mm$ accuracy. The period is about $2 \, s$. The time of $100$ oscillations is measured by a stopwatch of least count $0.1 \, s$. The percentage error in $g$ is ......... $\%$

$A$ cylindrical wire of mass $(0.4 \pm 0.01) \, g$ has length $(8 \pm 0.04) \, cm$ and radius $(6 \pm 0.03) \, mm$. The maximum error in its density will be $...... \, \%$.

$A$ physical quantity $Q$ is related to four observables $a, b, c, d$ as follows: $Q = \frac{ab^4}{cd}$,where $a = (60 \pm 3) \ Pa$,$b = (20 \pm 0.1) \ m$,$c = (40 \pm 0.2) \ Nsm^{-2}$,and $d = (50 \pm 0.1) \ m$. The percentage error in $Q$ is $\frac{x}{1000}$,where $x = $ . . . . . . .

$A$ student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L^{3}}{4 b d^{3} \delta}$. The value of $g$ is taken to be $9.8 \, m/s^2$, without any significant error. His observations are as follows:

Physical Quantity	Least count and Observed value
Mass $(M)$	$1 \, g$ and $2 \, kg$
Length of bar $(L)$	$1 \, mm$ and $1 \, m$
Breadth of bar $(b)$	$0.1 \, mm$ and $4 \, cm$
Thickness of bar $(d)$	$0.01 \, mm$ and $0.4 \, cm$
Depression $(\delta)$	$0.01 \, mm$ and $5 \, mm$

Then the fractional error in the measurement of $Y$ is:

Write a note on the combination of errors.