Correct4
Incorrect-1
The density of material in CGS system of units is {tex} 4 \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
0.4 unit
40 unit
400 unit
0.04 unit
Correct4
Incorrect-1
The time period of a body under S.H.M. is represented by: {tex} \mathrm { T } = \mathrm { P } ^ { \mathrm { a } } \mathrm { D } ^ { \mathrm { b } } \mathrm { S } ^ { \mathrm { c } } {/tex} where {tex} \mathrm { P } {/tex} is pressure, {tex} \mathrm { D } {/tex} is density and {tex} \mathrm { S } {/tex} is surface tension, then values of {tex} \mathrm { a } , \mathrm { b } {/tex} and {tex} \mathrm { c } {/tex} are
{tex} - \frac { 3 } { 2 } , \frac { 1 } { 2 } , 1 {/tex}
{tex} - 1 , - 2,3 {/tex}
{tex} \frac { 1 } { 2 } , - \frac { 3 } { 2 } , - \frac { 1 } { 2 } {/tex}
{tex} 1,2 , \frac { 1 } { 3 } {/tex}
Correct4
Incorrect-1
The respective number of significant figures for the numbers {tex} 23.023,0.0003 {/tex} and {tex} 2.1 \times 10 ^ { - 3 } {/tex} are
{tex} 5,1,2 {/tex}
{tex} 5,1,5 {/tex}
{tex} 5,5,2 {/tex}
{tex} 4,4,2 {/tex}
Correct4
Incorrect-1
Young's modulus of a material has the same unit as that of
pressure
strain
compressibility
force
Correct4
Incorrect-1
Of the following quantities, which one has dimensions different from the remaining three?
Energy per unit volume
Force per unit area
Product of voltage and charge per unit volume
Angular momentum
Correct4
Incorrect-1
The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula {tex} P = \frac { F } { \ell ^ { 2 } } {/tex} . If the maximum errors in the measurement of force and length are 4{tex} \% {/tex} and 2{tex} \% {/tex} respectively, then the maximum error in the measurement of pressure is
1{tex} \% {/tex}
2{tex} \% {/tex}
8{tex} \% {/tex}
10{tex} \% {/tex}
Correct4
Incorrect-1
The siemen is the SI unit of
resistivity
resistance
conductivity
conductance
Correct4
Incorrect-1
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
{tex} \left[ \mathrm { ML } ^ { - 1 } \mathrm { T } ^ { - 1 } \right] {/tex}
{tex} \left[ \mathrm { MLT } ^ { - 1 } \right] {/tex}
{tex} \left[ \mathrm { M } ^ { 0 } \mathrm { L T} ^ { -1 } \right] {/tex}
{tex} \left[ \mathrm { ML } ^ { 0 } \mathrm { T } ^ { - 1 } \right] {/tex}
Correct4
Incorrect-1
The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 second. The percentage error in the measurement of time will be
8{tex} \% {/tex}
1.8{tex} \% {/tex}
0.8{tex} \% {/tex}
0.1{tex} \% {/tex}
Correct4
Incorrect-1
Weber is the unit of
magnetic susceptibility
intensity of magnetisation
magnetic flux
magnetic permeability
Correct4
Incorrect-1
The physical quantity which has the dimensional formula {tex} \left[ \mathrm { M } ^ { 1 } \mathrm { T } ^ { - 3 } \right] {/tex} is
surface tension
solar constant
density
compressibility
Correct4
Incorrect-1
The dimensions of Wien's constant are
{tex} \left[ \mathrm { ML } ^ { 0 } \mathrm { T } \mathrm { K } \right] {/tex}
{tex} \left[ \mathrm { M } ^ { 0 } \mathrm { LT } ^ { 0 } \mathrm { K } \right] {/tex}
{tex} \left[ \mathrm { M } ^ { 0 } \mathrm { L } ^ { 0 } \mathrm { T } \mathrm { K } \right] {/tex}
{tex} [ \mathrm { MLTK } ] {/tex}
Correct4
Incorrect-1
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
{tex} \mathrm { u } = \frac { \mathrm { e } ^ { 2 } \mathrm { h } } { \mathrm { a } _ { 0 } } {/tex}
{tex} \mathrm { u } = \frac { \mathrm { hc } } { \mathrm { e } ^ { 2 } \mathrm { a } _ { 0 } } {/tex}
{tex} \mathrm { u } = \frac { \mathrm { e } ^ { 2 } \mathrm { c } } { \mathrm { ha } _ { 0 } } {/tex}
{tex} \mathrm { u } = \frac { \mathrm { e } ^ { 2 } \mathrm { a } _ { 0 } } { \mathrm { hc } } {/tex}
Correct4
Incorrect-1
The dimensions of {tex} \frac { 1 } { \epsilon _ { \mathrm { o } } } \frac { \mathrm { e } ^ { 2 } } { \mathrm { hc } } {/tex} are
{tex} \mathrm { M } ^ { - 1 } \mathrm { L } ^ { - 3 } \mathrm { T } ^ { 4 } \mathrm { A } ^ { 2 } {/tex}
{tex} \mathrm { ML } ^ { 3 } \mathrm { T } ^ { - 4 } \mathrm { A } ^ { - 2 } {/tex}
{tex} { M } ^ { 0 } { L } ^ { 0 } { T } ^ { 0 } { A } ^ { 0 } {/tex}
{tex} \mathrm { M } ^ { - 1 } \mathrm { L } ^ { - 3 } \mathrm { T } ^ { 2 } \mathrm { A } {/tex}
Correct4
Incorrect-1
The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4{tex} \% {/tex} and 3{tex} \% {/tex} respectively, the maximum error in the measurement of density will be
7{tex} \% {/tex}
9{tex} \% {/tex}
12{tex} \% {/tex}
13{tex} \% {/tex}
Correct4
Incorrect-1
Which is different from others by units?
Phase difference
Mechanical equivalent
Loudness of sound
Poisson's ratio
Correct4
Incorrect-1
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, DV is a potential difference and Dt is a time interval. The dimensional formula for {tex} X {/tex} is the same as that of
resistance
charge
voltage
current
Correct4
Incorrect-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
2{tex} \% {/tex}
3{tex} \% {/tex}
4{tex} \% {/tex}
7.5{tex} \% {/tex}
Correct4
Incorrect-1
If velocity {tex} ( \mathrm { V } ) , {/tex} force {tex} ( \mathrm { F } ) {/tex} and energy {tex} ( \mathrm { E } ) {/tex} are taken as fundamental units, then dimensional formula for mass will be
{tex} \mathrm { V } ^ { - 2 } \mathrm { F } ^ { 0 } \mathrm { E } {/tex}
{tex} V^0FE^2{/tex}
{tex} \mathrm { VF } ^ { - 2 } \mathrm { E } ^ { 0 } {/tex}
{tex} \mathrm { V } ^ { - 2 } \mathrm { F } ^ { 0 } \mathrm { E } {/tex}
Correct4
Incorrect-1
Multiply 107.88 by 0.610 and express the result with correct number of significant figures.
65.8068
65.807
65.81
65.8
Correct4
Incorrect-1
Which of the following is a dimensional constant?
Refractive index
Poissons ratio
Strain
Gravitational constant
Correct4
Incorrect-1
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
angle
length
mass
time
Correct4
Incorrect-1
The refractive index of water measured by the relation {tex} \mathrm { m } = \frac { \text { real depth } } { \text { apparent depth } } {/tex} is found to have values of {tex} 1.34, 1.38, 1.32 {/tex} and {tex} 1.36 ; {/tex} the mean value of refractive index with percentage error is
{tex} 1.35 \pm 1.48 \% {/tex}
{tex} 1.35 \pm 0 \% {/tex}
{tex} 1.36 \pm 6 \% {/tex}
{tex} 1.36 \pm 0 \% {/tex}
Correct4
Incorrect-1
If e is the charge, {tex} V {/tex} the potential difference, T the temperature, then the units of {tex} \frac { \mathrm { eV } } { \mathrm { T } } {/tex} are the same as that of
Planck's constant
Stefan's constant
Boltzmann's constant
gravitational constant
Correct4
Incorrect-1
The dimensions of mobility are
{tex} \mathrm { M } ^ { - 2 } \mathrm { T } ^ { 2 } \mathrm { A } {/tex}
{tex} \mathrm { M } ^ { - 1 } \mathrm { T } ^ { 2 } \mathrm{ A } {/tex}
{tex} \mathrm { M } ^ { - 2 } \mathrm { T } ^ { 3 } \mathrm { A } {/tex}
{tex} \mathrm { M } ^ { - 1 } \mathrm { T } ^ { 3 } \mathrm { A } {/tex}
