A length-scale (I) depends on the permittivity (e) of a dielectric material,  Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for I is dimensionally correct?

(a)

\(l=\sqrt{{{nq^2}\over{\epsilon {k}_{B}T}}}\)

(b)

\(l=\sqrt{{{\epsilon {k}_{B}T}\over{nq^2}}}\)

(c)

\(l=\sqrt{{{q^2}\over{e{n}^{{{2}\over{3}}}{k}_{B}}T}}\)

(d)

\(l=\sqrt{{{q^2}\over{\epsilon n{k}_{B}T}}}\)

The dimensions of K.E. is _______________.

(a)

M²L²T^-1

(b)

M¹L¹T¹

(c)

M¹L²T^-2

(d)

M²L²T^-2

The fraction of \(1\over 273.16\) temperature of the triple point of water represents __________.

(a)

celsius

(b)

fahrenheit

(c)

centigrade

(d)

kelvin

1 CSL is the largest practical unit of _____________.

(a)

time

(b)

mass

(c)

temperature

(d)

intensity of radiation

The diameter of the steel ball is measured using a vernier calipers which has divisions of 0.5 cm on its main scale and 10 division of its vernier scale match 9 division on the main scale. Three such measurements for a ball are as follows.

S.No	MS (cm)	VS (divisions)
1	0.5	8
2	0.5	4
3	0.5	6

 If the zero error is - 0.03 em, then mean corrected diameter is__________________ cm.

(a)

0.56

(b)

0.53

(c)

0.59

(d)

0.52

Which one of the following is used to determine very large distance?

(a)

Radar method

(b)

Parallax method

(c)

Triangulation method

(d)

all the above

The number of significant figures in 2.64\(\times\)10⁴ kg is ________________.

(a)

2

(b)

4

(c)

3

(d)

5

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula p =\(F\over l^2\) .If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is _________________

(a)

1%

(b)

2%

(c)

8%

(d)

10%

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

(a)

R_30° = R_60°

(b)

R_30° = 4R_60°

(c)

R_30° =\(\frac{R_{60°}}{2}\)

(d)

R_30° = 2R_60°

The unit vector along the negative z-axis is ____________.

(a)

\(-\hat k\)

(b)

\(-\hat j\)

(c)

\(-\hat i\)

(d)

\(+\hat k\)

If two vectors are having equal magnitude and same direction is known as _______________.

(a)

equal vectors

(b)

collinear vectors

(c)

parallel vectors

(d)

on it vector

Which of the following graph represents the equation y = mx?

(a)

(b)

(c)

(d)

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F₁ is applied from the left. Later only a force F₂ is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F₁ :F₂ is

(a)

1:1

(b)

1:2

(c)

2:1

(d)

1:3

Which of the following force tends to stopthe moving object?

(a)

Frictional force

(b)

Magnetic force

(c)

Gravitational force

(d)

Electric force

A jet engine works on the principle of ______________.

(a)

conservation of linear momentum

(b)

conservation of mass

(c)

conservation of energy

(d)

conservation of angular momentum

A body of imparted motion from rest to move in a straight line. If it is then obstructed by an opposite force, then ______________.

(a)

the body will necessarily change direction

(b)

the body is sure to slow down

(c)

the body will necessarily continue to move in the same direction at the same speed

(d)

none of these

A body of mass m slides down a rough plane of inclination α If μ is the coefficient of friction, then acceleration of the body will be _____________.

(a)

g sinα

(b)

μcosα

(c)

g(sinα - μcosα)

(d)

g(cosα - μsinα)

A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. Which of the following is conserved?

(a)

Momentum and kinetic energy

(b)

kinetic energy alone

(c)

Momentum alone

(d)

potential energy alone

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(a)

v

(b)

v²

(c)

v³

(d)

v⁴

If the force and the displacement are at an angle of 180°, then work done is ___________.

(a)

F.S

(b)

-F.S

(c)

0

(d)

F-S

Which of the following statements is Wrong?

(a)

K.E of a body is dependent on the direction of motion

(b)

In an elastic collision of two bodies, the momentum and energy of each body is conserved

(c)

If two protons are brought towards each other, the P.E of the system increases

(d)

A body can have energy without momentum

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

(a)

5: 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

The gravitational potential energy of the Moon with respect to Earth is

(a)

always positive

(b)

always negative

(c)

can be positive or negative

(d)

always zero

A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

(a)

energy = 4 V T \(\left( \frac { 1 }{ r } -\frac { 1 }{ R } \right) \)is released

(b)

energy = 3 V T \(\left( \frac { 1 }{ r } +\frac { 1 }{ R } \right) \)is absorbed

(c)

energy = 3 V T \(\left( \frac { 1 }{ r } -\frac { 1 }{ R } \right) \)is released

(d)

energy is neither released nor absorbed

The V-T diagram of an ideal gas which goes through a reversible cycle A→B→C→D is shown below. (Processes D→A and B→C are adiabatic)

The corresponding PV diagram for the process is (all figures are schematic)

(a)

(b)

(c)

(d)