Which of the following comes under the category of random errors?

  • A
    Improper calibration of thermometer
  • B
    Zero error of $1 \mu V$ in voltmeter
  • C
    Student measures $22^{\circ}$,whereas the correct angle is $20^{\circ}$
  • D
    Errors resulting from the fluctuations in electric power supply

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$A$ physical quantity $x$ is calculated from the relation $x = \frac{a^2 b^3}{c \sqrt{d}}$. If the percentage errors in $a, b, c,$ and $d$ are $2\%, 1\%, 3\%,$ and $4\%$ respectively,what is the percentage error in $x$?

The length $l$,breadth $b$,and thickness $t$ of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $l = 15.12 \pm 0.01 \; cm$,$b = 10.15 \pm 0.01 \; cm$,and $t = 5.28 \pm 0.01 \; cm$. The percentage error in volume up to proper significant figures is: (in $\%$)

$A$ body travels uniformly a distance of $(13.8 \pm 0.2) \ m$ in a time $(4.0 \pm 0.3) \ s$. The velocity of the body within error limits is

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Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
Student No. Length of pendulum $(cm)$ No. of oscillations $(n)$ Total time for oscillations $(s)$ Time period $(s)$
$1.$ $64.0$ $8$ $128.0$ $16.0$
$2.$ $64.0$ $4$ $64.0$ $16.0$
$3.$ $20.0$ $4$ $36.0$ $9.0$

(Least count of length $= 0.1 \, cm$,least count for time $= 0.1 \, s$)
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $g$ for students $1, 2$ and $3$ respectively,then the minimum percentage error is obtained by student no. ....... .

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