Question 1 :
The magnitude of the difference between the individual measurement and true value of the quantity is called

Question 3 :
A thin copper wire of length {tex} l {/tex} metre increases in length by {tex} 2 \% {/tex} when heated through {tex} 10 ^ { \circ } \mathrm { C } {/tex}. What is the percentage increase in area when a square copper sheet of length {tex} l {/tex} metre is heated through {tex} 10 ^ { \circ } \mathrm { C } ? {/tex}

Question 4 :
The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of

Question 6 :
When two quantities are divided, the relative error in the result is given by

Question 7 :
{tex} \left[ \mathrm { MLT } ^ { - 1 } \right] + \left[ \mathrm { MLT } ^ { - 1 } \right] = {/tex}

Question 8 :
An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensions of constant of proportionality are

Question 9 :
The displacement of a body at a particular second n is given by the expression {tex} \mathrm { S } _ { \mathrm { nth } } = \mathrm { u } + \frac { \mathrm { a } } { 2 } ( 2 \mathrm { n } - 1 ) . {/tex} The dimensional formula of {tex} \mathrm { S } _ { \mathrm { nth } } {/tex} in this equation is

Question 11 :
{tex}\mathrm {Assertion :}{/tex} The time period of a pendulum is given by the formula, {tex}\mathrm{ T = 2 \pi \sqrt { \mathrm { g } / \ell } }{/tex}<br>{tex}\mathrm{ Reason :}{/tex} According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of {tex}\mathrm{L.H.S.}{/tex} is equal to dimensions of {tex}\mathrm{R.H.S.}{/tex}

Question 12 :
If the dimensions of a physical quantity are given by {tex} \mathrm { M } ^ { \mathrm { a } } \mathrm { L } ^ { \mathrm { b } } \mathrm { T } ^ { \mathrm { c } } , {/tex} then the physical quantity will be

Question 13 :
Let {tex}\mathrm Q {/tex} denote the charge on the plate of a capacitor of capacitance {tex}\mathrm C . {/tex} The dimensional formula for {tex} \frac {\mathrm Q ^ { 2 } } { \mathrm C } {/tex} is

Question 14 :
If the capacitance of a nanocapacitor is measured in terms of a unit {tex}'u'{/tex} made by combining the electric charge {tex}'e'{/tex}, Bohr radius {tex}'a_o'{/tex} , Planck's constant 'h' and speed Of light {tex}'c'{/tex} then

Question 15 :
Which one of the following is not a unit of Young’s modulus?

Question 16 :
The refractive index of water measured by the relation {tex} \mu = \frac { \text { real depth } } { \text { apparent } } {/tex} is found to have values of 1.34, 1.38, 1.32 and 1.36, the mean value of refractive index with perfentage error is

Question 17 :
The unit of the coefficient of viscosity in S.I. system is

Question 18 :
Consider the following statements and select the correct statement(s).<br>{tex} \begin{array} { l l } { \text { I. } } & { 1 \text { calorie } = 4.18 \text { joule } } \\ { \text { II. } } & { 1 \mathrm { A } = 10 ^ { - 10 } \mathrm { m } } \\ { \text { III. } } & { 1 \mathrm { MeV } = 1.6 \times 10 ^ { - 13 } \mathrm { joule } } \\ { \mathrm { IV } . } & { 1 \text { newton } = 10 ^ { - 5 } \mathrm { dyne } } \end{array} {/tex}<br>

Question 19 :
The dimessions of the quantity {tex} \overrightarrow { \mathrm { E } } \times \overrightarrow { \mathrm { B } } {/tex} where {tex} \overrightarrow { \mathrm { E } } {/tex} represents the electric field and {tex} \overrightarrow { \mathrm { B } } {/tex} the magnetic field may be given as:

Question 21 :
Surface tension of a liquid is {tex} 70 \mathrm {\ dyne } / \mathrm { cm } {/tex}. Its value in SI is

Question 24 :
The frequency (f) of a wire oscillating with a length {tex} \ell , {/tex} in {tex} \mathrm { p } {/tex} loops, under a tension {tex} \mathrm T {/tex} is given by {tex} \mathrm { f } = \frac { \mathrm { p } } { 2 \ell } \sqrt { \frac { \mathrm { T } } { \mu } } {/tex} where {tex} \mu = {/tex} linear density of the wire. If the error made in determing length, tension and linear density be {tex} 1 \% , - 2 \% {/tex} and {tex} 4 \% , {/tex}, then find the percentage error in the calculated frequency.

Question 25 :
Diameter of a steel ball is measured using a Vernier callipers which has divisions of {tex} 0.1 \mathrm { cm } {/tex} on its main scale (MS) and {tex} 10 {/tex} divisions of its vernier scale (VS) match {tex} 9 {/tex} divisions on the main scale. Three such measurements for a ball are given below:<br>{tex} \begin{array} { | c | c | c | } \hline \text { S.No. } & { \mathrm { MS } ( \mathrm { cm } ) } & { \text { VS divisions } } \\ \hline 1 & { 0.5 } & { 8 } \\ \hline 2 . & { 0.5 } & { 4 } \\ \hline 3 . & { 0.5 } & { 6 } \\ \hline \end{array} {/tex}<br>If the zero error is {tex} - 0.03 \mathrm { cm } , {/tex} then mean corrected diameter is

Question 29 :
Match the Column I and Column II.<br> {tex} \begin{array} { l l }{ \text { Column I } } & { \text { Column II } } \\ { \text { (A) Johannes Kepler } } & { \text { (1) Nuclear model of the atom } } \\ { \text { (B) Tycho Brahe } } & { \text { (2) Planetary motion } } \\ { \text { (C) Nicolas Copernicus } }& { \text { (3 ) Elliptical orbit theory } } \\ { \text { (D) Ernest Rutherford } } & { \text { (4) Circular orbit theory } } \end{array} {/tex}

Question 30 :
Which of the following is the correct decreasing order of the strengths of four fundamental forces of nature?