Question 1 :
If the error in the measurement of the volume of sphere is {tex} 6 \% , {/tex} then the error in the measurement of its surface area will be

Question 2 :
The respective number of significant figures for the number {tex} 23.023,0.0003 {/tex} and {tex} 2.1 \times 10 ^ { - 3 } {/tex} are respectively.

Question 3 :
Which of the following physical quantities has neither dimensions nor unit?

Question 4 :
The number of significant figures in a number "{tex} 1700.00200 ^ { \circ } {/tex}" is

Question 5 :
In equation, {tex} \mathrm { r } = \mathrm { m } ^ { 2 } \sin \pi \mathrm { t } , {/tex} where t represents time. If the unit of {tex} \mathrm { m } {/tex} is {tex} \mathrm { N } {/tex}, then the unit of {tex} \mathrm { r } {/tex} is

Question 6 :
Suppose the kinetic energy of a body oscillating with amplitude {tex}A{/tex} and at a distance {tex}\mathrm x {/tex} is given by {tex} K = \frac { B x } { x ^ { 2 } + A ^ { 2 } } {/tex} The dimensions of {tex} B {/tex} are the same as that of

Question 9 :
The magnitude of the difference between the individual measurement and true value of the quantity is called

Question 11 :
{tex} \left[ \mathrm { MLT } ^ { - 1 } \right] + \left[ \mathrm { MLT } ^ { - 1 } \right] = \ldots \ldots \ldots \ldots {/tex}

Question 13 :
In equation, {tex} r = m ^ { 2 } \sin \pi t , {/tex} where 't' represents time. If the unit of {tex} m {/tex} is {tex} N , {/tex} then the unit of {tex} r {/tex} is

Question 14 :
The physical quantity which has the dimensional formula {tex} \left[ \mathrm { M } ^ { 1 } \mathrm { T } ^ { - 3 } \right] {/tex} is

Question 15 :
Which of the following statements is/are correct?<br>I. Change of units does not change the number of significant digits. <br>II. All the non-zero digits are significant. <br>III. All the zero between two non-zero digits are significant.<br>

Question 16 :
In the eqn. {tex} \left( P + \frac { a } { V ^ { 2 } } \right) ( V - b ) = {/tex} constant, the unit of a is

Question 18 :
Number of significant figures in expression {tex} \frac { 4.327 \mathrm { g } } { 2.51 \mathrm { cm } ^ { 3 } } {/tex} is

Question 19 :
The division of energy by time is {tex} \mathrm { X } . {/tex} The dimensional formula of {tex} \mathrm { X } {/tex} is same as that of

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 permittivity 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 :
{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 24 :
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 25 :
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 26 :
{tex}\mathrm{Assertion} :{/tex} When we change the unit of measurement of a quantity, its numerical value changes.<br>{tex}\mathrm{Reason} :{/tex} Smaller the unit of measurement smaller is its numerical value.

Question 27 :
The unit of the coefficient of viscosity in S.I. system is

Question 28 :
Area of a square is {tex} ( 100 \pm 2 ) \mathrm { m } ^ { 2 } . {/tex} Its side is

Question 29 :
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 30 :
If force (F), length (L) and time (T) assumed to be fundamental units, then the dimensional formula of the mass will be

Question 31 :
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 32 :
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 34 :
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 36 :
The density of a material in CGS system of units is {tex}4\mathrm{g/cm}^3{/tex} In a system of units in which unit of length is {tex} 10 \mathrm { cm } {/tex} and unit of mass is {tex} 100 \mathrm { g } {/tex}, the value of density of material will be

Question 37 :
Write the dimensions of {tex}\mathrm{a \times b }{/tex} in the relation {tex} \mathrm{E = \frac { b - x ^ { 2 } } { a t }} {/tex}, where {tex} \mathrm { E } {/tex} is the energy, {tex} x {/tex} is the displacement and t is time

Question 38 :
Surface tension of a liquid is 70 dyne/cm. Its value in SI is

Question 39 :
Relative density of a metal may be found with the help of spring balance. In air the spring balancereads {tex} ( 5.00 \pm 0.05 ) \mathrm { N } {/tex} and in water it reads {tex} ( 4,00 \pm 0.05 ) \mathrm { N } {/tex}. Then, the relative density along with the maximum permissible percentage error would be

Question 40 :
The heat generated in a circuit is given by {tex} Q = I ^ { 2 } {/tex} Rt, where I is current, {tex} R {/tex} is resistance and {tex} t {/tex} is time. If the percentage errors in measuring {tex} I {/tex}, {tex} R {/tex} and {tex} t {/tex} are {tex} 2 \% , 1 \% {/tex} and {tex} 1 \% {/tex} respectively, then the maximum error in measuring heat will be

Question 41 :
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 43 :
{tex} \mathrm { E } , \mathrm { m } , \mathrm { J } {/tex} and {tex}\mathrm G{/tex} denote energy, mass, angular momentum and gravitational constant respectively, then the unit of {tex} \frac { \mathrm { EJ } ^ { 2 } } { \mathrm { m } ^ { 5 } \mathrm { G } ^ { 2 } } {/tex} is

Question 45 :
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 46 :
Which of the following is the correct decreasing order of the strengths of four fundamental forces of nature?

Question 47 :
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 48 :
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 49 :
Match the Column I and Column II.<br> {tex} \begin{array} {| l| l| }\hline{ \text { Column I } } & { \text { Column II } } \\ \hline{ \text { (A) J C Maxwell } } & { \text { (1) Verified experimentally the prediction of electromagnetic force } } \\ \hline { \text { (B) Cario Rubia } } & { \text { (2) Unified electricity, magnetism and optics, showed that light is an EM waves} } \\ \hline { \text { (C) Isaac Newton } }& { \text { (3) Unified celestial and terrestrial mechanics} } \\ \hline{ \text { (D) Michael Faraday } } & { \text { (4) Showed that electric and magnetic phenomenon i.e., electromagnetism } }\\ \hline \end{array} {/tex}