Question 1: Palette 1/135

Allen MCQ

Which of the following system of units is not based on units of mass, length and time alone?

A

SI

B

MKS

C

FPS

D

CGS

Question 2: Palette 2/135

Allen MCQ

Which of the following is not a fundamental physical quantity?

A

Mass

B

Length

C

Temperature

D

Density

Question 3: Palette 3/135

Allen MCQ

Which of the following is not the name of a physical quantity :-

A

kilogram

B

impulse

C

energy

D

density

Question 4: Palette 4/135

Allen MCQ

Which of the following is not a unit of time?

A

microsecond

B

leap year

C

lunar month

D

light year

Question 5: Palette 5/135

Allen MCQ

Unit of energy in SI system is :-

A

erg

B

calorie

C

joule

D

electron volt

Question 6: Palette 6/135

Allen MCQ

In the SI system, the unit of temperature is :-

A

Degree centrigrade

B

Degree Celsius

C

Kelvin

D

Degree Fahrenheit

Question 7: Palette 7/135

Allen MCQ

The SI unit of momentum is :-

A

$\frac{\mathrm{kg}}{\mathrm{m}}$

B

$\frac{\mathrm{kg.m}}{\mathrm{sec}}$

C

$\frac{\mathrm{kg.m}^2}{\mathrm{sec}}$

D

$\mathrm{kg} \times \mathrm{newton}$

Question 8: Palette 8/135

Allen MCQ

SI unit of pressure is :-

A

pascal

B

Dyne/cm²

C

cm of Hg

D

atmosphere

Question 9: Palette 9/135

Allen MCQ

kg m/s² stand for the unit of :-

A

Energy

B

acceleration

C

Force

D

Momentum

Question 10: Palette 10/135

Allen MCQ

N kg $^{-1}$ is the unit of :-

A

velocity

B

energy

C

acceleration

D

force

Question 11: Palette 11/135

Allen MCQ

If the unit of length is micrometre and unit of time is microsecond, the unit of velocity will be :-

A

100 m/s

B

10 m/s

C

micrometre/s

D

m/s

Question 12: Palette 12/135

Allen MCQ

The unit of power is :-

A

kilowatt

B

kilowatt-hour

C

dyne

D

joule

Question 13: Palette 13/135

Allen MCQ

Kilowatt-hour is a unit of :-

A

electrical charge

B

energy

C

power

D

force

Question 14: Palette 14/135

Allen MCQ

One nanometer is equal to :-

A

$10^{9}$ mm

B

$10^{-6}$ cm

C

$10^{-7}$ cm

D

$10^{-9}$ cm

Question 15: Palette 15/135

Allen MCQ

The units nanometre, fermi, angstrom and attometre, arranged in decreasing order will read as :-

A

angstrom, nanometre, fermi, attometre

B

fermi, attometre, angstrom, nanometre

C

nanometre, angstrom, fermi, attometre

D

attometre, angstrom, fermi, nanometer

Question 16: Palette 16/135

Allen MCQ

Which is the correct unit for measuring nuclear radii:-

A

micron

B

millimetre

C

agnstrom

D

fermi

Question 17: Palette 17/135

Allen MCQ

Which of the following is usually a derived quantity?

A

Mass

B

Velocity

C

Length

D

Time

Question 18: Palette 18/135

Allen MCQ

Temperature can be expressed as a derived quantity in terms of which of the following?

A

Length and mass

B

Mass and time

C

Length. mass and time

D

None of these

Question 19: Palette 19/135

Allen MCQ

Which of the following sets can not enter into the list of fundamental quantities in any system of units?

A

length, mass, velocity

B

length, time, velocity

C

length, time, mass

D

mass, time, velocity

Question 20: Palette 20/135

Allen MCQ

The density of a liquid is 1000 kg m $^{-3}$ . Its value in CGS system :-

A

1 gcm $^{-3}$

B

0.1 gcm $^{-3}$

C

10 gcm $^{-3}$

D

100 gcm $^{-3}$

Question 21: Palette 21/135

Allen MCQ

The surface tension of a liquid is 70 dynes/cm. It may be expressed in M.K.S. system as:

A

70 N/m

B

$7 \times 10^{-2}$ N/m

C

$7 \times 10^{2}$ N/m

D

$7 \times 10^{3}$ N/m

Question 22: Palette 22/135

Allen MCQ

Units of length, velocity and force are doubled. Which of the following is correct:

A

Units of time is doubled

B

Unit of mass is doubled

C

Unit of momentum is doubled

D

Unit of energy is doubled

Question 23: Palette 23/135

Allen MCQ

If the units of length, velocity and force are half, then the units of Power will be :-

A

doubled

B

halved

C

one fourth

D

remains unaffected

Question 24: Palette 24/135

Allen MCQ

A dimensionless quantity

A

Never has a unit

B

Always has a unit

C

May have a unit

D

Does not exist

Question 25: Palette 25/135

Allen MCQ

A unitless quantity

A

Does not exist

B

Always has a nonzero dimension

C

Never has a nonzero dimension

D

May have a nonzero dimension

Question 26: Palette 26/135

Allen MCQ

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

A

angle

B

Luminous intensity

C

coefficient of friction

D

Electric current

Question 27: Palette 27/135

Allen MCQ

Dimensions of relative density is

A

kg m $^{-3}$

B

[ML $^{-3}$ ]

C

dimensionless

D

[M $^{2}$ L $^{-6}$ ]

Question 28: Palette 28/135

Allen MCQ

Which of the following does not have dimensions of length?

A

fermi

B

micron

C

angstrom

D

radian

Question 29: Palette 29/135

Allen MCQ

The quantity having dimension -2 in the time is :-

A

force

B

pressure

C

gravitational constant

D

all of these

Question 30: Palette 30/135

Allen MCQ

The dimensional formula $[ML^{2}T^{-2}]$ represents :

A

pressure

B

linear momentum

C

power

D

energy

Question 31: Palette 31/135

Allen MCQ

Which pair has the same dimensions?

A

Work and power

B

Density and relative density

C

Momentum and impulse

D

Latent heat and specific heat

Question 32: Palette 32/135

Allen MCQ

Dimensions of one pair is same. Identify the pair:-

A

Torque and energy

B

Angular momentum and work

C

Energy and pressure

D

Light year and solar day

Question 33: Palette 33/135

Allen MCQ

The method of dimensional analysis can be used to derive which of the following relations?

A

$N_{0}e^{-\lambda t}$

B

A $\sin(\omega t + kx)$

C

$\frac{1}{2}mv^{2} + \frac{1}{2}I\omega^{2}$

D

None of the above

Question 34: Palette 34/135

Allen MCQ

If dimensions of A and B are different, then which of the following operation is valid?

A

$\frac{A}{B}$

B

$e^{-A/B}$

C

A - B

D

A + B

Question 35: Palette 35/135

Allen MCQ

Which of the following is incorrect statement

A

A dimensionally correct equation may be correct

B

A dimensionally correct equation may be incorrect

C

A dimensionally incorrect equation may be correct

D

A dimensionally incorrect equation is incorrect

Question 36: Palette 36/135

Allen MCQ

Which of the following is incorrect?

A

All derived quantities may be represented dimensionally in terms of the base quantities

B

A base quantity cannot be represented dimensionally in terms of other base quantities

C

The dimension of a derived quantity is never zero in any base quantity

D

The dimension of a base quantity in other base quantities is always zero.

Question 37: Palette 37/135

Allen MCQ

If $x = at + bt^{2}$ , where x is in metre and t is in hour(hr), then unit of b will be :-

A

$m^{2}/hr$

B

m

C

m/hr

D

$m/hr^{2}$

Question 38: Palette 38/135

Allen MCQ

A force is given by $\mathrm{F} = \mathrm{at} + \mathrm{bt}^2$ , where $t$ is time. The dimensions of $a$ and $b$ are

A

[M L T-3] and [M L T-4]

B

[M L T-4] and [M L T-3]

C

[M L T-1] and [M L T-2]

D

[M L T-2] and [M L T0]

Question 39: Palette 39/135

Allen MCQ

If $S = \frac{1}{3} ft^3$ , 'f' has the dimensions of - (S = distance, t = time)

A

$[M^0 L^{-1} T^3]$

B

$[M^1 L^1 T^{-3}]$

C

$[M^0 L^1 T^{-3}]$

D

$[M^0 L^{-1} T^{-3}]$

Question 40: Palette 40/135

Allen MCQ

The time dependence of a physical quantity P is given by $P = P_{0} \exp(-\alpha t^{2})$ , where $\alpha$ is a constant and t is time. The constant $\alpha$

A

is dimensionless

B

has dimensions $[T^{-2}]$

C

has dimensions of P

D

has dimensions $[T^{2}]$

Question 41: Palette 41/135

Allen MCQ

Given the force $F = Pt^{-1} + Qt$ . Here t is time. The unit of P is same as that of :-

A

displacement

B

velocity

C

acceleration

D

momentum

Question 42: Palette 42/135

Allen MCQ

The force F, on a sphere of radius 'a' moving in a medium with velocity v is given by $F = 6\pi\eta av$ . The dimensions of $\eta$ are:

A

$[ML^{-1}T^{-1}]$

B

$[MT^{-1}]$

C

$[MLT^{-2}]$

D

$[ML^{-3}]$

Question 43: Palette 43/135

Allen MCQ

The force is given in terms of time (t) and displacement (x) by the equation: $F = A \cos Bx + C \sin Dt$ Then, the dimensions of $\frac{D}{B}$ are :-

A

$M^{o}L^{o}T^{o}$

B

$M^{o}L^{o}T^{-1}$

C

$M^{o}L^{-1}T^{o}$

D

$M^{o}LT^{-1}$

Question 44: Palette 44/135

Allen MCQ

For a body moving along x-axis, the distance travelled by body from a reference point is given as function of time t as $x = at^{2} + b$ , where a and b are constants, then the dimension of $\sqrt{ab}$ is same as :-

A

speed

B

distance travelled

C

acceleration

D

none of these

Question 45: Palette 45/135

Allen MCQ

In the relation $y = r \sin (\omega t - kx)$ the dimensions of $\frac{\omega}{k}$ are:-

A

$[M^0 L^1 T^0]$

B

$[M^0 L^1 T^{-1}]$

C

$[M^0 L^0 T^3]$

D

$[M^0 L^1 T^0]$

Question 46: Palette 46/135

Allen MCQ

A wave is represented by $y = a \sin (At - Bx + C)$ where A, B, C are constants. The dimensions of A, B, C are

A

$T^{-1}$ , L, $M^{0}L^{0}T^{0}$

B

$T^{-1}$ , $L^{-1}$ , $M^{0}L^{0}T^{0}$

C

T, L, M

D

$T^{-1}$ , $L^{-1}$ , $M^{-1}$

Question 47: Palette 47/135

Allen MCQ

For $10^{(at+3)}$ , the dimensions of a is :-

A

$M^{0}L^{0}T^{0}$

B

$M^{0}L^{0}T^{1}$

C

$M^{0}L^{0}T^{-1}$

D

None of these

Question 48: Palette 48/135

Allen MCQ

The equation $\frac{\mathrm{d}v}{\mathrm{d}t} = AT - Bv$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of A and B are :-

A

$\mathrm{LT^{-3}}$ , T

B

$\mathrm{LT^{-3}}$ , $\mathrm{T^{-1}}$

C

LT, T

D

LT, $\mathrm{T^{-1}}$

Question 49: Palette 49/135

Allen MCQ

If y represents distance and x-represents time, dimensions of $\frac{d^{2}y}{dx^{2}}$ are :-

A

LT $^{-1}$

B

L $^{2}$ T $^{2}$

C

L $^{2}$ T $^{-1}$

D

LT $^{-2}$

Question 50: Palette 50/135

Allen MCQ

If energy (E), velocity (v) and force (F), be taken as fundamental quantities, then what are the dimensions of mass :-

A

EV $^{2}$

B

EV $^{-2}$

C

FV $^{-1}$

D

FV $^{-2}$

Question 51: Palette 51/135

Allen MCQ

A system has basic dimensions as density [D], velocity [V] and area [A]. The dimensional representation of force in this system is:

A

$\mathrm{AV}^2\mathrm{D}$

B

$\mathrm{A}^2\mathrm{VD}$

C

$\mathrm{AVD}^2$

D

$\mathrm{A}^0\mathrm{VD}$

Question 52: Palette 52/135

Allen MCQ

The significant digits in 200.40 are :-

A

4

B

5

C

2

D

3

Question 53: Palette 53/135

Allen MCQ

Number of significant digits in 0.01230 is :-

A

3

B

4

C

5

D

6

Question 54: Palette 54/135

Allen MCQ

Which of the following has the highest number of significant figures?

A

$0.007 \, m^{2}$

B

$2.64 \times 10^{24} \, kg$

C

$0.0006032 \, m^{2}$

D

6.3200 J

Question 55: Palette 55/135

Allen MCQ

Given P = 0.0030 m, Q = 2.40 m and R = 3000m, the number of significant figures in P, Q and R are respectively :-

A

1, 2, 1

B

2, 3, 4

C

4, 2, 1

D

4, 2, 4

Question 56: Palette 56/135

Allen MCQ

After rounding off the number 4621 to 2 significant digits the value becomes :-

A

4600

B

4500

C

4700

D

4720

Question 57: Palette 57/135

Allen MCQ

If L = 2.331 cm and B = 2.1 cm, then L + B = (According to significant figures)

A

4.431 cm

B

4.43 cm

C

4.4 cm

D

4 cm

Question 58: Palette 58/135

Allen MCQ

Subtract 0.2 J from 5.27 J and express the result with correct number of significant figures :-

A

5.1 J

B

5.06 J

C

5.0 J

D

5 J

Question 59: Palette 59/135

Allen MCQ

In arithmetic $17.8 \times 3.1143 = 55.4354$ . But as a result of experimental measurements the best way to express the product is:

A

55.3454

B

55.4

C

55.44

D

55.435

Question 60: Palette 60/135

Allen MCQ

The order of magnitude of the number 1013 is:-

A

1

B

2

C

3

D

4

Question 61: Palette 61/135

Allen MCQ

The length of a rod is $(11.05 \pm 0.05)$ cm. What is the sum of lengths of two such rods:

A

$(22.1 \pm 0.05)$ cm

B

$(22.10 \pm 0.05)$ cm

C

$(22.1 \pm 0.15)$ cm

D

$(22.10 \pm 0.10)$ cm

Question 62: Palette 62/135

Allen MCQ

The external and internal radius of a hollow cylinder are measured to be $(5.23 \pm 0.015)$ cm and $(4.89 \pm 0.005)$ cm. The thickness of the wall of the cylinder is :-

A

$(0.34 \pm 0.02)$ cm

B

$(0.17 \pm 0.02)$ cm

C

$(0.17 \pm 0.01)$ cm

D

$(0.34 \pm 0.01)$ cm

Question 63: Palette 63/135

Allen MCQ

The resistance is $R = \frac{V}{I}$ where $V = (100 \pm 5)$ volt and $I = (10 \pm 0.2)$ ampere. What is the total error in R?

A

5 %

B

7 %

C

5.2 %

D

$\left(\frac{5}{2}\right)\%$

Question 64: Palette 64/135

Allen MCQ

When a copper sphere is heated, maximum percentage change will be observed in-

A

radius

B

area

C

volume

D

none of these

Question 65: Palette 65/135

Allen MCQ

If error in measuring diameter of a circle is 2%, the error in circumference of the circle would be :-

A

2%

B

8%

C

4%

D

1%

Question 66: Palette 66/135

Allen MCQ

The error is the measurement of volume of sphere is 1.5%. The error in the measurement of its diameter is :-

A

1%

B

2%

C

0.5%

D

1.5%

Question 67: Palette 67/135

Allen MCQ

There is an error of 2% in the measurement of side of a cube. The percentage error in the calculation of its volume will be :-

A

1%

B

2%

C

3

D

6%

Question 68: Palette 68/135

Allen MCQ

A thin copper wire of length $\ell$ metre increases in length by 2% when heated through 10°C. What is the percentage increase in area when a square copper sheet of length $\ell$ metre is heated through 10°C?

A

4%

B

8%

C

16%

D

None of these

Question 69: Palette 69/135

Allen MCQ

If $f = x^2$ , then the relative error in $f$ is:

A

$\frac{2\Delta x}{x}$

B

$\frac{(\Delta x)^2}{x}$

C

$\frac{\Delta x}{x}$

D

$(\Delta x)^2$

Question 70: Palette 70/135

Allen MCQ

The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed :-

A

11%

B

8%

C

5%

D

4%

Question 71: Palette 71/135

Allen MCQ

The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are as 1%, 2% and 1% the maximum error in measuring heat will be

A

2%

B

3%

C

6%

D

1%

Question 72: Palette 72/135

Allen MCQ

Percentage error in measuring the radius (R) and mass (M) of a solid sphere are 2% & 1% respectively. Then error in measurement of moment of inertia about to its diameter (i.e. I = $\frac{2}{5}$ MR $^2$ ) is :-

A

3 %

B

6 %

C

5 %

D

4 %

Question 73: Palette 73/135

Allen MCQ

The resistance R of a wire is given by the relation $R = \frac{\rho\ell}{\pi r^{2}}$ . Percentage error in the measurement of $\rho$ , $\ell$ and r is 1%, 3% and 2% respectively. Then the percentage error in the measurement of R is

A

6%

B

9%

C

8%

D

10%

Question 74: Palette 74/135

Allen MCQ

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, the maximum error in the measurement of pressure is –

A

1%

B

2%

C

6%

D

8%

Question 75: Palette 75/135

Allen MCQ

What is the fractional error in g calculated from $T=2\pi\sqrt{\ell/g}$ ? Given that fractional errors in T and $\ell$ are $\pm x$ and $\pm y$ respectively.

A

$x + y$

B

x - y

C

$2x + y$

D

2x - y

Question 76: Palette 76/135

Allen MCQ

While measuring acceleration due to gravity by a simple pendulum a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of the time period. His percentage error in the measurement of the value of g will be (Use time period of a simple pendulum, $T = 2\pi \sqrt{\frac{\ell}{g}}$ ) -

A

2 %

B

4 %

C

7 %

D

10 %

Question 77: Palette 77/135

Allen MCQ

An experiment measures quantities a, b and c, and X is calculated from $X = ab^{2}/c^{3}$ . If the percentage error in a, b and c are $\pm1\%$ , $\pm3\%$ and $\pm2\%$ respectively, the percentage error in X will be –

A

$\pm13\%$

B

$\pm7\%$

C

$\pm4\%$

D

$\pm1\%$

Question 78: Palette 78/135

Allen MCQ

A physical quantity X is given by $X = \frac{2k^{3}\ell^{2}}{m\sqrt{n}}$ The percentage error in the measurements of k, $\ell$ , m and n are 1%, 1%, 3% and 4% respectively. The value of X is uncertain by

A

8%

B

10%

C

12%

D

None

Question 79: Palette 79/135

Allen MCQ

A quantity is represented by $\mathrm{X} = \mathrm{M}^{\mathrm{a}}\mathrm{L}^{\mathrm{b}}\mathrm{T}^{\mathrm{c}}$ . The percentage error in measurement of M, L and T are $\alpha \%$ , $\beta \%$ and $\gamma \%$ respectively. The percentage error in X would be

A

$(\alpha a + \beta b + \gamma c) \%$

B

$(\alpha a - \beta b + \gamma c) \%$

C

$(\alpha a - \beta b - \gamma c) \%$

D

None of these

Question 80: Palette 80/135

Allen MCQ

the dimensional formula of a physical quantity x is $[M^{-1}L^{3}T^{-2}]$ . The error in measuring the quantities M, L, and T are 2%, 3% and 4%. The maximum percentage of error that occurs in measuring the quantity x is :-

A

9

B

10

C

14

D

19

Question 81: Palette 81/135

Allen MCQ

The pressure P and volume V of a gas are related as $PV^{3/2} = K$ , where K is a constant. The percentage change in the pressure for a decrease of 0.5% in the volume is:

A

-0.75%

B

0.75%

C

1.50%

D

-1.50%

Question 82: Palette 82/135

Allen MCQ

Zero error of an instrument introduces

A

Systematic errors

B

Random errors

C

Both

D

None of these

Question 83: Palette 83/135

Allen MCQ

A pendulum clock, designed to give correct time in planes, gives incorrect time at hill station. Type of error in measurement of time can be :-

A

Systematic error

B

Random error

C

Gross error

D

None of these

Question 84: Palette 84/135

Allen MCQ

A vernier callipers has 40 divisions on the vernier scale which coincide with 38 divisions on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of

A

0.5 mm

B

1 mm

C

2 mm

D

1/4 mm

Question 85: Palette 85/135

Allen MCQ

One centimetre on the main scale of vernier callipers is divided into ten equal parts. If 20 divisions of vernier scale coincide with 16 small divisions of the main scale, the least count of the callipers is

A

0.01 cm

B

0.02 cm

C

0.05 cm

D

0.005 cm

Question 86: Palette 86/135

Allen MCQ

In main scale of a vernier callipers 1 cm divided into 10 equal divisions. The vernier scale has 10 equal divisions that correspond to 9 main scale divisions. The measured value by this calliper is :-

A

$2.82\mathrm{cm}$

B

$2.83\mathrm{cm}$

C

$2.87\mathrm{cm}$

D

$2.89\mathrm{cm}$

Question 87: Palette 87/135

Allen MCQ

A student measured the thickness of a metal sheet using a screw gauge with least count 0.001 cm and listed the measurements. The correct measurement is –

A

4.2 cm

B

4.22 cm

C

4.220 cm

D

4.2200 cm

Question 88: Palette 88/135

Allen MCQ

One full rotation of the cap of a screw gauge is equivalent to 5 mm. The cap has 100 division. Find the least count.

A

0.5 m

B

0.05 mm

C

0.005 m

D

$5 \times 10^{-4}$ m

Question 89: Palette 89/135

Allen MCQ

Distance moved by a screw in 5 rotation is 5 mm and total number of circular divisions is 100. The least count of the screw gauge is :

A

1 mm

B

0.001 cm

C

0.0001 cm

D

0.001 mm

Question 90: Palette 90/135

Allen MCQ

The number of circular division on screwgauge is 100. It moves 1 mm on main scale for one complete revolution. Find reading of micrometer.

A

$3.25 \mathrm{~mm}$

B

3.24 mm

C

$3.30 \mathrm{~mm}$

D

3.41 mm

Question 91: Palette 91/135

Allen MCQ

The number of circular division on the shown screw gauge is 100. It moves 1 mm on main scale for one complete rotation and main scale has 1 mm marks. The diameter of the ball is :-

A

$2.25\mathrm{mm}$

B

$2.20\mathrm{mm}$

C

$1.20\mathrm{mm}$

D

$1.25\mathrm{mm}$

Question 92: Palette 92/135

Allen MCQ

If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are:

A

$[F V T^{-1}]$

B

$[F V T^{-2}]$

C

$[F V^{-1} T^{-1}]$

D

$[F V^{-1} T]$

Question 93: Palette 93/135

Allen MCQ

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:

A

$[EV^{-1}T^{-2}]$

B

$[EV^{-2}T^{-2}]$

C

$[E^{-2}V^{-1}T^{-3}]$

D

$[EV^{-2}T^{-1}]$

Question 94: Palette 94/135

Allen MCQ

If dimension of critical velocity $v_{C}$ , of liquid flowing through a tube is expressed as $(\eta^{x} \rho^{y} r^{z})$ , where $\eta$ , $\rho$ and r the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by:

A

1, 1, 1

B

1, -1, -1

C

-1, -1, 1

D

-1, -1, -1

Question 95: Palette 95/135

Allen MCQ

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

A

$\sqrt{\frac{hc}{G}}$

B

$\sqrt{\frac{Gc}{h^{3/2}}}$

C

$\frac{\sqrt{hG}}{c^{3/2}}$

D

$\frac{\sqrt{hG}}{c^{5/2}}$

Question 96: Palette 96/135

Allen MCQ

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4\pi\varepsilon_{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge] :-

A

$c^{2}\left[G\frac{e^{2}}{4\pi\varepsilon_{0}}\right]^{1/2}$

B

$\frac{1}{c^{2}}\left[\frac{e^{2}}{G4\pi\varepsilon_{0}}\right]^{1/2}$

C

$\frac{1}{c}G\frac{e^{2}}{4\pi\varepsilon_{0}}$

D

$\frac{1}{c^{2}}\left[G\frac{e^{2}}{4\pi\varepsilon_{0}}\right]^{1/2}$

Question 97: Palette 97/135

Allen MCQ

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is:

A

0.521 cm

B

0.525 cm

C

$0.053 \mathrm{~cm}$

D

0.529 cm

Question 98: Palette 98/135

Allen MCQ

In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where $X=\frac{A^{2}B^{1/2}}{C^{1/3}D^{3}}$ , will be:

A

$\left(\frac{3}{13}\right)\%$

B

16%

C

-10%

D

10%

Question 99: Palette 99/135

Allen MCQ

The unit of thermal conductivity is:

A

J m K $^{-1}$

B

J m $^{-1}$ K $^{-1}$

C

W m K $^{-1}$

D

W m $^{-1}$ K $^{-1}$

Question 100: Palette 100/135

Allen MCQ

The main scale of a vernier calliper has n divisions/cm. n divisions of the vernier scale coincide with $(n - 1)$ divisions of main scale. The least count of the vernier calliper is,

A

$\frac{1}{(n+1)(n-1)}$ cm

B

$\frac{1}{n}$ cm

C

$\frac{1}{n^{2}}$ cm

D

$\frac{1}{n(n+1)}$ cm

Question 101: Palette 101/135

Allen MCQ

Taking into account of the significant figures, what is the value of 9.99 m - 0.0099 m?

A

9.9 m

B

9.9801 m

C

9.98 m

D

9.980 m

Question 102: Palette 102/135

Allen MCQ

Dimensions of stress are:

A

$[M\ L^{-1}\ T^{-2}]$

B

$[M\ L\ T^{-2}]$

C

$[M\ L^{2}\ T^{-2}]$

D

$[M\ L^{0}\ T^{-2}]$ PP

Question 103: Palette 103/135

Allen MCQ

A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is :

A

1.0 mm

B

0.01 mm

C

0.25 mm

D

0.5 mm

Question 104: Palette 104/135

Allen MCQ

The angle of $1'$ (minute of arc) in radian is nearly equal to

A

$2.91 \times 10^{-4}$ rad

B

$4.85 \times 10^{-4}$ rad

C

$4.80 \times 10^{-6}$ rad

D

$1.75 \times 10^{-2}$ rad

Question 105: Palette 105/135

Allen MCQ

Time intervals measured by a clock give the following readings: 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s. What is the percentage relative error of the observations?

A

2 %

B

4 %

C

16 %

D

1.6 %

Question 106: Palette 106/135

Allen MCQ

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

A

[F] [A] [T]

B

[F] [A] [T $^{2}$ ]

C

[F] [A] [T $^{-1}$ ]

D

[F] [A $^{-1}$ ] [T]

Question 107: Palette 107/135

Allen MCQ

A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :

A

0.52 cm

B

0.026 cm

C

0.26 cm

D

0.052 cm

Question 108: Palette 108/135

Allen MCQ

If E and G respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:

A

$[M^{2}]$ $[L^{-1}]$ $[T^{0}]$

B

$[M]$ $[L^{-1}]$ $[T^{-1}]$

C

$[M]$ $[L^{0}]$ $[T^{0}]$

D

$[M^{2}]$ $[L^{-2}]$ $[T^{-1}]$

Question 109: Palette 109/135

Allen MCQ

Plane angle and solid angle have :

A

Dimensions but no units

B

No units and no dimensions

C

Both units and dimensions

D

Units but no dimensions

Question 110: Palette 110/135

Allen MCQ

The dimensions $\left[\mathrm{MLT}^{-2}\mathrm{A}^{-2}\right]$ belong to the :

A

self inductance

B

magnetic permeability

C

electric permittivity

D

magnetic flux

Question 111: Palette 111/135

Allen MCQ

The physical quantity that has the same dimensional formula as pressure is :

A

Force

B

Momentum

C

Young's modulus of elasticity

D

Coefficient of viscosity

Question 112: Palette 112/135

Allen MCQ

The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$ . The ratio of the proportionality constant, $K = \frac{1}{4\pi\varepsilon_{0}}$ to the Gravitational constant G is nearly (Given that the charge of the proton and electron each $= 1.6 \times 10^{-19}$ C, the mass of the electron $= 9.11 \times 10^{-31}$ kg, the mass of the proton $= 1.67 \times 10^{-27}$ kg):

A

$10^{20}$

B

$10^{30}$

C

$10^{40}$

D

10

Question 113: Palette 113/135

Allen MCQ

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

A

Personal errors

B

Least count errors

C

Random errors

D

Instrumental errors

Question 114: Palette 114/135

Allen MCQ

A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be:

A

1.3%

B

1.6%

C

1.4%

D

1.2%

Question 115: Palette 115/135

Allen MCQ

The diameter of a spherical bob, when measured with vernier callipers yielded the following values: 3.33 cm, 3.32 cm, 3.34 cm, 3.33 cm and 3.32 cm. The mean diameter to appropriate significant figures is:

A

3.328 cm

B

3.3 cm

C

3.33 cm

D

3.32 cm

Question 116: Palette 116/135

Allen MCQ

The mechanical quantity, which has dimensions of reciprocal of mass (M $^{-1}$ ) is :

A

angular momentum

B

coefficient of thermal conductivity

C

torque

D

gravitational constant

Question 117: Palette 117/135

Allen MCQ

In a vernier calipers, $(N+1)$ divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

A

$\frac{1}{10N}$

B

$\frac{1}{100(N+1)}$

C

100N

D

10(N+1)

Question 118: Palette 118/135

Allen MCQ

The quantities which have the same dimensions as those of solid angle are:

A

strain and angle

B

stress and angle

C

strain and arc

D

angular speed and stress

Question 119: Palette 119/135

Allen MCQ

A force defined by $\mathrm{F} = \alpha t^2 + \beta t$ acts on a particle at a given time $t$ . The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

A

$\frac{\beta t}{\alpha}$

B

$\frac{\alpha t}{\beta}$

C

$\alpha \beta t$

D

$\frac{\alpha \beta}{t}$

Question 120: Palette 120/135

Allen MCQ

In an electrical circuit, the voltage is measured as $V = (200 \pm 4)$ volt and the current is measured as $I = (20 \pm 0.2)$ A. The value of the resistance is:

A

$(10 \pm 4.2)\Omega$

B

$(10 \pm 0.3)\Omega$

C

$(10 \pm 0.1)\Omega$

D

$(10 \pm 0.8)\Omega$

Question 121: Palette 121/135

Allen MCQ

The pitch of an error free screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads 1 mm and 63 $^{rd}$ division on the circular scale coincides with the reference line. The diameter of the wire is:

A

1.63 cm

B

0.163 cm

C

0.163 m

D

1.63 m

Question 122: Palette 122/135

Allen MCQ

The potential energy of a particle moving along x-direction varies as $V = \frac{Ax^{2}}{\sqrt{x} + B}$ . The dimensions of $\frac{A^{2}}{B}$ are :

A

$[M^{3/2} L^{1/2} T^{-3}]$

B

$[M^{1/2} L T^{-3}]$

C

$[M^{2} L^{1/2} T^{-4}]$

D

$[M L^{2} T^{-4}]$

Question 123: Palette 123/135

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Absolute error in a physical quantity may be +ve, -ve or zero.
Reason (R) : Absolute error is the difference of measured value and true value of a physical quantity.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 124: Palette 124/135

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Maximum possible error in a reading is taken as least count of the measuring instrument.
Reason (R) : Error in a measurement can not be greater than least count of the measuring instrument.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 125: Palette 125/135

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Higher is the accuracy of measurement, if instrument has smaller least count.
Reason (R) : Smaller the percentage error, higher is the accuracy of measurement.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 126: Palette 126/135

Allen MCQ

Given below are two statements : Statement I : Absolute error is unitless and dimensionless. Statement II : All types of errors are unitless and dimensionless. In the light of the above statements, choose the most appropriate answer from the options given below:

A

Both statement I and statement II are correct.

B

Statement I is correct and statement II is incorrect.

C

Statement I is incorrect and statement II is correct.

D

Both statements I and statements II are incorrect.

Question 127: Palette 127/135

Allen MCQ

Given below are two statements : Statement I : Least count of a screw gauge is directly proportional to the number of divisions on circular scale. Statement II : A screw gauge having a smaller value of pitch has greater accuracy. In the light of the above statements, choose the most appropriate answer from the options given below:

A

Both statement I and statement II are correct.

B

Statement I is correct and statement II is incorrect.

C

Statement I is incorrect and statement II is correct.

D

Both statements I and statements II are incorrect.

Question 128: Palette 128/135

Allen MCQ

Match the quantities having same dimensions in Match the Column-I and Column-II :

Column-I	Column-II
(A) Stress (B) Strain (C) Modulus of elasticity (D) Torque	(P) Pressure (Q) Energy density (R) Angle (S) Energy

A

A → R; B → P; C → S; D → Q

B

A → Q; B → R; C → P; D → S

C

A → P; B → S; C → R; D → Q

D

A → Q; B → S; C → R; D → Q

Question 129: Palette 129/135

Allen MCQ

Match the column Match Column-I with Column-II:

Column-I	Column-II
(A) Electrical resistance (B) Capacitance (C) Magnetic field (D) Inductance	(P) $M^{-1}L^{-1}T^4A^2$ (Q) $ML^2T^{-2}A^{-2}$ (R) $ML^2T^{-3}A^{-2}$ (S) $MT^{-2}A^{-1}$

A

A → r; B → p; C → s; D → q

B

A → s; B → p; C → r; D → q

C

A → p; B → s; C → r; D → q

D

A → q; B → s; C → r; D → q

Question 130: Palette 130/135

Allen MCQ

Match the column Match Column-I with Column-II:

Column-I	Column-II
(A) Boltzmann constant (B) Coefficient of viscosity (C) Planck constant (D) Thermal conductivity	(P) $ML^2T^{-1}$ (Q) $ML^{-1}T^{-1}$ (R) $MLT^{-3}K^{-1}$ (S) $ML^2T^{-2}K^{-1}$

A

A → r ; B → s ; C → p ; D → q

B

A → p ; B → s ; C → r ; D → q

C

A → p ; B → r ; C → s ; D → q

D

A → s ; B → q ; C → p ; D → r

Question 131: Palette 131/135

Allen MCQ

Which two of the following five physical quantities have the same dimensions?
(a) Energy density (b) Refractive index
(c) Dielectric constant (d) Young's modulus
(e) Magnetic field

A

(a) and (e)

B

(b) and (d)

C

(c) and (e)

D

(a) and (d)

Question 132: Palette 132/135

Allen MCQ

Photon is quantum of radiation with energy $E = h\nu$ where $v$ is frequency and $h$ is Planck's constant. The dimensions of $h$ are the same as that of (a) Linear impulse (b) Angular impulse (c) Linear momentum (d) Angular momentum

A

(a) and (c)

B

(b) and (d)

C

(b) and (c)

D

(a) and (d)

Question 133: Palette 133/135

Allen MCQ

Which of the following ratios express pressure?
(a) Force / area (b) Energy / volume
(c) Energy / area (d) Force / volume

A

(a) and (c)

B

(b) and (d)

C

(b) and (c)

D

(a) and (b)

Question 134: Palette 134/135

Allen MCQ

Statement-1: The displacement cannot be added with distance travelled. Statement-2: Addition of scalar and vector of same dimensions is not a meaningful algebraic operation.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Question 135: Palette 135/135

Allen MCQ

Match with Column-I with Column-II:

Column-I	Column-II
(A) $1001$ (B) $0100.1$ (C) $100.100$ (D) $0.001001$	(P) $5$ (Q) $4$ (R) $6$ (S) $3$

A

A → Q, B → Q, C → R, D → Q

B

A → Q, B → P, C → R, D → R

C

A → Q, B → S, C → S, D → Q

D

A → Q, B → Q, C → P, D → Q