The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
1. \(\dfrac{1}{(n+1)(n-1)}\) cm
2. \(\dfrac{1}{n}\) cm
3. \(\dfrac{1}{n^{2}}\) cm
4. \(\dfrac{1}{(n)(n+1)}\) cm

Two resistors ${\mathrm{R}}_1 = (3.0 \pm 0.3) \mathrm{\Omega } \mathrm{and} {\mathrm{R}}_{2 }= (5.0 \pm 0.1) \mathrm{\Omega }$ are connected in parallel. The equivalent resistance is :

$\begin{array}{}\end{array}\begin{array}{rl}1. & 1.9\pm 0.07 \mathrm{\Omega }\\ 2. & 1.9\pm 0.1 \mathrm{\Omega }\\ 3. & 1.9\pm 0.2 \mathrm{\Omega }\\ 4. & 1.9\pm 0.3 \mathrm{\Omega }\end{array}$

If z=$\frac{A\times B}{A+B}$, and errors in the determination of A and B are respectively $△\mathrm{A} \mathrm{and} △\mathrm{B}$, then the fractional error in the calculation of z is :

$1. \frac{\mathrm{\Delta }A}{A}+\frac{\mathrm{\Delta }B}{B}+\frac{\mathrm{\Delta }A+\mathrm{\Delta }B}{A+B}$
$$
$2. \frac{\mathrm{\Delta }A}{A}+\frac{\mathrm{\Delta }B}{B}-\frac{(\mathrm{\Delta }A+\mathrm{\Delta }B)}{A+B}$
$$
$3. \frac{\mathrm{\Delta }A}{A}+\frac{\mathrm{\Delta }B}{B}$
$$
$4. Zero$

The least count of a stop watch is 0.2 s. The time of 20 Oscillations of a pendulum is measured to be 25 s. The percentage error in the measurement of time will be

(1) 8%

(2) 1.8%

(3) 0.8%

(4) 0.1%

The pitch of a screw gauge is 1 mm and there are 100 divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 divisions on the circular scale are observed. The diameter of the wire is:

1. 2.71 mm 

2. 2.67 mm 

3. 2.63 mm 

4. 2.65 mm

If a copper wire is stretched to make its radius decrease by \(0.1\%\), then the percentage increase in resistance is approximately:
1. \(0.1\%\) 
2. \(0.2\%\) 
3. \(0.4\%\)
4. \(0.8\%\)

The force F is given by expression F = Acos(Bx) + Csin(Dt), where x is the displacement and t is the time. Then dimensions of $\frac{D}{B}$ are the same as that of:

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula $\mathrm{P}=\frac{\mathrm{F}}{{\mathrm{l}}^2}$ . If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is