Question 5 :
If unit of length and force are increased {tex}4{/tex} times. The unit of energy

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

Question 8 :
What is the correct number of significant figures in {tex} 0.0003026 ? {/tex}

Question 9 :
What is the correct number of significant figures in {tex} 0.0003026 ? {/tex}

Question 11 :
If {tex}\mathrm L{/tex} denotes the inductance of an inductor through which a current {tex}i{/tex} is flowing, the dimensions of {tex}\mathrm {Li^2}{/tex} are

Question 12 :
The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of

Question 13 :
A physical quantity of the dimensions of length that can be formed out of {tex} \mathrm { c } , \mathrm { G } {/tex} and {tex} \frac { { e } ^ { 2 } } { 4 \pi \varepsilon _ { 0 } } {/tex} is [{tex} \mathrm { c }{/tex} is velocity of light, {tex} \mathrm { G }{/tex} is universal constant of gravitation and {tex} { e }{/tex} is charge]

Question 14 :
Write the dimensions of a {tex} \times b {/tex} in the relation {tex} E = \frac { b - x ^ { 2 } } { a t } , {/tex} where {tex} E {/tex} is the energy, {tex} x {/tex} is the displacement and {tex} t {/tex} is time

Question 15 :
A wire has a mass {tex} 0.3 \pm 0.003 {/tex} g, radius {tex} 0.5 \pm 0.005 {/tex} mm and length {tex} 6 \pm 0.06 \mathrm { cm } {/tex}. The maximum percentage error in the measurement of its density is

Question 16 :
The speed of light in vacuum, {tex} c , {/tex} depends on two fundamental constants, the permeability of free space, {tex} \mu _ { 0 } {/tex} and the permittivity of free space, {tex} \varepsilon _ { 0 } {/tex} The speed of light is given by {tex} c = \frac { 1 } { \sqrt { \mu _ { 0 } \varepsilon _ { 0 } } } . {/tex} The units of {tex} \varepsilon _ { 0 } {/tex} are {tex} \mathrm { N } ^ { - 1 } \mathrm { C } ^ { 2 } \mathrm { m } ^ { - 2 } {/tex}. The units for {tex} \mu _ { 0 } {/tex} are

Question 17 :
In the eqn. {tex} \left( P + \frac { a } { V ^ { 2 } } \right) ( V - b ) = {/tex} constant, the unit of a is

Question 18 :
If {tex} \mathrm { v } = \frac { \mathrm { a } } { \mathrm { t } } + \mathrm { bt } ^ { 3 } {/tex} where {tex} \mathrm { v } = \mathrm { velocity } {/tex} and {tex} \mathrm { t } {/tex} is time The dimensional formula of {tex}\mathrm{a}{/tex} and {tex}\mathrm{b}{/tex} are

Question 19 :
Resistance {tex} \mathrm { R } = \mathrm { V } / \mathrm { I } , {/tex} here {tex} \mathrm { V } = ( 100 \pm 5 ) \mathrm { V } {/tex} and {tex} \mathrm { I } = ( 10 \pm 0.2 ) \mathrm { A } . {/tex} Find percentage error in {tex} \mathrm { R } . {/tex}

Question 20 :
If {tex} \mathrm { E } , \mathrm { m } , \mathrm { J } {/tex} and {tex} \mathrm { G } {/tex} represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of {tex} \mathrm { E } \mathrm { J } ^ { 2 } / \mathrm { m } ^ { 5 } \mathrm { G } ^ { 2 } {/tex} is same as that of the

Question 21 :
A quantity {tex} X {/tex} is given by {tex} \varepsilon _ { 0 } L \frac { \Delta V } { \Delta t } {/tex} where {tex} \epsilon _ { 0 } {/tex} is the permitttivity of the free space, {tex} L {/tex} is a length, {tex} \Delta V {/tex} is a potential difference and {tex} \Delta t {/tex} is a time interval. The dimensional formula for {tex} X {/tex} is the same as that of

Question 22 :
You measure two quantities as {tex} A = 1.0 \mathrm { m } \pm 0.2 \mathrm { m } {/tex} {tex},B = 2.0 \mathrm { m } \pm 0.2 \mathrm { m } . {/tex} We should report correct value for {tex} \sqrt { A R } {/tex} as

Question 23 :
The density of material in CGS system of units is 4{tex} \mathrm { g } / \mathrm { cm } ^ { 3 } . {/tex} In a system of units in which unit of length is 10{tex} \mathrm { cm } {/tex} and unit of mass is 100{tex} \mathrm { g } {/tex} , the value of density of material will be

Question 24 :
In a simple pendulum experiment, the maximum percentage error in the measurement of length is {tex} 2 \% {/tex} and that in the observation of the time-period is {tex} 3 \% . {/tex} Then the maximum percentage error in determination of the acceleration due to gravity {tex} \mathrm { g } {/tex} is

Question 25 :
The solar constant is defined as the energy incident per unit area per second. The dimensional formula for solar constant is

Question 26 :
The current voltage relation of a diode is given by {tex} \mathrm { I } = \left( \mathrm { e } ^ { \text {1000V } / T } - 1 \right) \mathrm { mA } , {/tex} where the applied voltage {tex} \mathrm { V } {/tex} is in volts and the temperature {tex} \mathrm T {/tex} is in degree kelvin. If a student makes an error measuring {tex} \pm 0.01 \mathrm { V } {/tex} while measuring the current of {tex} 5 \mathrm { mA } {/tex} at {tex} 300 \mathrm { K } , {/tex} what will be the error in the value of current in {tex} \mathrm { mA } ? {/tex}

Question 27 :
Intensity observed in an interference pattern is {tex} I = I _ { 0 } \sin ^ { 2 } \theta \cdot \mathrm { At } \theta = 30 ^ { \circ } {/tex} intensity {tex} I = 5 \pm 0.0020 {/tex} {tex} \mathrm { W } / \mathrm { m } ^ { 2 } . {/tex} Find percentage error in angle if {tex} I _ { 0 } = 20 {/tex} {tex} \mathrm { W } / \mathrm { m } ^ { 2 } . {/tex}

Question 28 :
The resistance of a metal is given by {tex} \mathrm { R } = \frac { \mathrm { V } } { \mathrm { I } } {/tex} where {tex} \mathrm { V } {/tex} is potential difference and I is the current. In a circuit the potential difference across resistance is {tex} \mathrm { V } = ( 8 \pm 0.5 ) \mathrm { V } {/tex} and current in resistance, {tex} \mathrm { I } = ( 2 \pm 0.2 ) \mathrm { A } . {/tex} What is the value of resistance with its percentage error?

Question 29 :
In the equation {tex} P = \frac { R T } { V - b } e ^ { \frac { a V } { R T } } {/tex} {tex} V = {/tex} volume, {tex} P = V - b {/tex} constant, and {tex} T = {/tex} temperature The dimensional formula of a is same as that of

Question 30 :
{tex} \begin{array} { l l } { \text { Column I } } & { \text { Column II } } \\ { \text { (A) Length } } & { \text { (1) burette } } \\ { \text { (B) Volume } } & { \text { (2) Vernier callipers } } \\ { \text { (C) Diameter of a thin wire } } & { \text { (3) screw gauge } } \\ { \text { (D) Mass } } & { \text { (4) common balance } } \end{array} {/tex}