The volume occupied by 1.8 g of water vapour at 374°C and 1 bar pressure will be [Use R = 0.083 bar L K−1 mol−1]
a.
5.37 L
Correct Answer
b.
96.66 L
c.
55.87 L
d.
3.10 L
Step-by-Step AI Explanation
Verified Method
Using PV = nRT, n = 1.8/18 = 0.1 mol and T = 374 + 273 = 647 K. Thus V = nRT/P = 0.1 × 0.083 × 647 = 5.37 L.
Q18mcq
An ideal gas expands isothermally from 10−3 m3 to 10−2 m3 at 300 K against a constant pressure of 105 N m−2. The work done on the gas is
a.
−900 kJ
b.
+270 kJ
c.
−900 J
Correct Answer
d.
+900 kJ
Step-by-Step AI Explanation
Verified Method
Work done on the gas against constant external pressure is W = −Pext(Vf − Vi) = −105(10−2 − 10−3) = −900 J.
Q19mcq
Reversible expansion of an ideal gas under isothermal and adiabatic conditions are as shown in the figure. AB → Isothermal expansion AC → Adiabatic expansion. Which of the following options is not correct?
a.
TC > TA
Correct Answer
b.
ΔS isothermal > ΔS adiabatic
c.
TA = TB
d.
wisothermal > wadia batic
Step-by-Step AI Explanation
Verified Method
In reversible adiabatic expansion, temperature decreases, so TC < TA. For isothermal reversible expansion, ΔS is nonzero, while for adiabatic reversible process ΔS = 0. Hence the statement TC > TA is incorrect.
Q136mcq
The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals 0.51 Å and its ground state energy equals -13.6 eV. If the electron in the hydrogen atom is replaced by a muon (μ−) having charge same as electron and mass 207 me, the first Bohr radius and ground state energy will be:
a.
2.56 × 10^-13 m, -13.6 eV
b.
0.53 × 10^-13 m, -3.6 eV
c.
25.6 × 10^-13 m, -2.8 eV
d.
2.56 × 10^-13 m, -2.8 keV
Correct Answer
Step-by-Step AI Explanation
Verified Method
For a hydrogen-like system, Bohr radius is inversely proportional to particle mass and energy is directly proportional to mass. Thus r1 = 0.51 Å/207 ≈ 2.56 × 10^-13 m and E1 = -13.6 × 207 eV ≈ -2.8 keV.
Q137mcq
The reading of an ideal voltmeter in the circuit shown is:
a.
0.4 V
Correct Answer
b.
0.6 V
c.
0 V
d.
0.5 V
Step-by-Step AI Explanation
Verified Method
Using current division in the two parallel branches, the potential drops from A to P and A to Q differ by 0.4 V, which is the voltmeter reading across P and Q.
Q138mcq
The metre bridge shown is in balance position with l1/l2 = P/Q. If we now interchange the positions of galvanometer and cell, will the bridge work? If yes, what will be the balance condition?
a.
yes, l1/l2 = P/Q
Correct Answer
b.
yes, (l1 - l2)/(l2 + l1)
c.
no, no null point
d.
yes, l1/l2 = Q/P
Step-by-Step AI Explanation
Verified Method
Interchanging the galvanometer and battery in a balanced metre bridge does not change the balance condition; it remains l1/l2 = P/Q.
Q139mcq
The relations amongst the three elements of earth’s magnetic field, namely horizontal component H, vertical component V and dip angle δ, are (BE = total magnetic field):
a.
V = BE, H = BE tanδ
b.
V = BE tanδ, H = BE
c.
V = BE sinδ, H = BE cosδ
Correct Answer
d.
V = BE cosδ, H = BE sinδ
Step-by-Step AI Explanation
Verified Method
The total magnetic field BE makes dip angle δ with the horizontal, so H = BE cosδ and V = BE sinδ.
Q139mcq
The relations amongst the three elements of earth’s magnetic field, namely horizontal component H, vertical component V and dip δ (BE = total magnetic field), are:
a.
V = BE, H = BE tan δ
b.
V = BE tan δ, H = BE
c.
V = BE sin δ, H = BE cos δ
Correct Answer
d.
V = BE cos δ, H = BE sin δ
Step-by-Step AI Explanation
Verified Method
If δ is the angle of dip, then the horizontal component is H = BE cos δ and the vertical component is V = BE sin δ.
Q140mcq
In a U-tube as shown in the figure, water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is (take ρwater = 1000 kg/m^3):
a.
1333 kg/m^3
b.
1200 kg/m^3
c.
750 kg/m^3
Correct Answer
d.
1000 kg/m^3
Step-by-Step AI Explanation
Verified Method
At equilibrium, pressures at the same horizontal level are equal: ρwater g × 15 = ρoil g × 20, giving ρoil = 1000 × 15/20 = 750 kg/m^3.
Q140mcq
In a U-tube as shown in the figure, water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is [take ρwater = 1000 kg/m3].
a.
1333 kg/m3
b.
1200 kg/m3
c.
750 kg/m3
Correct Answer
d.
1000 kg/m3
Step-by-Step AI Explanation
Verified Method
At equilibrium, pressures at the same horizontal level are equal: ρwghw = ρo g ho. So 1000 × 15 = ρo × 20, giving ρo = 750 kg/m3.
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A deep rectangular pond of surface area A, containing water (density = ρ, specific heat capacity = s), is located in a region where the outside air temperature is at a steady value of –26°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant, would be given by
a.
26K / ρx(L + 4s)
b.
26K / ρx(L – 4s)
c.
26K / (ρx2L)
d.
26K / (ρxL)
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The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n – 1) divisions of main scale. The least count of the vernier callipers is,
a.
1/[n(n + 1)] cm
b.
1/[(n − 1)(n + 1)] cm
c.
1/n cm
d.
1/n2 cm
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A person travelling in a straight line moves with a constant velocity v1 for a certain distance x and with a constant velocity v2 for next equal distance. The average velocity v is given by the relation
a.
v = v1 + v2
b.
v = 1/(1/v1 + 1/v2)
c.
v = 2/(1/v1 + 1/v2)
d.
v = (v1 + v2)/2
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Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final – initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by,
a.
+GMm/(Rh)
b.
−GMm/(Rh)
c.
GMmh/[R(R + h)]
d.
mgh
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Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by
a.
+GMm/(Rh)
b.
-GMm/(R+h)
c.
GMmh/(R(R+h))
d.
mgh
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1 g of water, of volume 1 cm3 at 100°C, is converted into steam at same temperature under normal atmospheric pressure (1 × 10^5 Pa). The volume of steam formed equals 1671 cm3. If the specific latent heat of vaporisation of water is 2256 J/g, the change in internal energy is,
a.
2256 J
b.
2423 J
c.
2089 J
d.
167 J
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1 g of water, of volume 1 cm^3 at 100°C, is converted into steam at same temperature under normal atmospheric pressure (1 × 10^5 Pa). The volume of steam formed equals 1671 cm^3. If the specific latent heat of vaporisation of water is 2256 J/g, the change in internal energy is
a.
2256 J
b.
2423 J
c.
2089 J
d.
167 J
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Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000 Å is θ0. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is
a.
420 Å
b.
1800 Å
c.
4200 Å
d.
6000 Å
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The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photoemission from the substance is approximately
a.
310 nm
b.
3100 nm
c.
966 nm
d.
31 nm
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An object kept in a large room having air temperature of 25°C takes 12 minutes to cool from 80°C to 70°C. The time taken to cool for the same object from 70°C to 60°C would be nearly
a.
15 min
b.
10 min
c.
12 min
d.
20 min
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Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2 (ρ1 = 8ρ2) and have radii of 1 mm and 2 mm, respectively. They are made to fall vertically from rest in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ2. The ratio of their terminal velocities would be
a.
79/36
b.
79/72
c.
19/36
d.
3/72
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A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time t1 if the elevator is at rest and in time t2 if the elevator is moving uniformly. Then
a.
t1 = t2
b.
t1 < t2 or t1 > t2 depending upon whether the lift is going up or down
c.
t1 < t2
d.
t1 > t2
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A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. The pendulum will tilt
a.
to the left and angle of inclination of the pendulum with the vertical is tan^-1(g/a)
b.
to the left and angle of inclination of the pendulum with the vertical is sin^-1(g/a)
c.
to the left and angle of inclination of the pendulum with the vertical is tan^-1(a/g)
d.
to the left and angle of inclination of the pendulum with the vertical is sin^-1(a/g)
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A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. The pendulum will tilt
a.
to the left and angle of inclination of the pendulum with the vertical is tan^-1(g/a)
b.
to the left and angle of inclination of the pendulum with the vertical is sin^-1(g/a)
c.
to the left and angle of inclination of the pendulum with the vertical is tan^-1(a/g)
d.
to the left and angle of inclination of the pendulum with the vertical is sin^-1(a/g)
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Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry the same current i, the ratio of the magnetic fields along the two loops is
a.
1 : 2
b.
1 : 1
c.
4 : 1
d.
2 : 1
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A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is
a.
μ0 i/(2R), inward
b.
Zero
c.
3μ0 i/(32R), outward
d.
3μ0 i/(32R), inward
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Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?
a.
σ1 = 5σ/36, σ2 = 5σ/6
b.
σ1 = 5σ/6, σ2 = 5σ/2
c.
σ1 = 5σ/2, σ2 = 5σ/6
d.
σ1 = 5σ/6, σ2 = 5σ/3
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A mass falls from a height h and its time of fall t is recorded in terms of time period T of a simple pendulum. On the surface of earth it is found that t = 2T. The entire set up is taken on the surface of another planet whose mass is half that of earth and radius the same. Same experiment is repeated and corresponding times noted as t' and T'. Then we can say
a.
t' = 2T'
b.
t' = T'/2
c.
t' > 2T'
d.
t' < 2T'
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A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is
a.
172 m/s
b.
500 m/s
c.
156 m/s
d.
344 m/s
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A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is:
a.
172 m/s
b.
500 m/s
c.
156 m/s
d.
344 m/s
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An object flying in air with velocity (20i + 25j − 12k) m/s suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity (100i + 35j + 8k) m/s. The velocity of the larger piece will be:
a.
(−20i − 15j − 80k) m/s
b.
(4i − 23j − 16k) m/s
c.
(−100i − 35j − 8k) m/s
d.
(20i − 15j − 80k) m/s
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An object flying in air with velocity (20î - 25ĵ + 12k̂) suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity (100î + 35ĵ + 8k̂). The velocity of the larger piece will be
a.
(-20î - 15ĵ - 80k̂)
b.
(4î - 23ĵ - 16k̂)
c.
(-100î - 35ĵ - 8k̂)
d.
(20î - 15ĵ - 80k̂)
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The time period of a geostationary satellite is 24 h, at a height 6R_E from the surface of earth. The time period of another satellite whose height is 2.5R_E from the surface will be:
a.
12/2.5 h
b.
6/2 h
c.
12√2 h
d.
24/2.5 h
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A circuit when connected to an AC source of 12 V gives a current of 0.2 A. The same circuit when connected to a DC source of 12 V, gives a current of 0.4 A. The circuit is:
a.
Series LCR
b.
Series LR
c.
Series RC
d.
Series LC
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A cycle wheel of radius 0.5 m is rotated with constant angular velocity of 10 rad/s in a region of magnetic field of 0.1 T which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is:
a.
Zero
b.
0.25 V
c.
0.125 V
d.
0.5 V
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For a transparent medium, relative permeability and permittivity, μ_r and ε_r are 1.0 and 1.44 respectively. The velocity of light in this medium would be:
a.
4.32 × 10^8 m/s
b.
2.5 × 10^8 m/s
c.
3 × 10^8 m/s
d.
2.08 × 10^8 m/s
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Two identical capacitors C1 and C2 of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C1 using a battery of emf V volt. Now disconnecting a and b, the terminals b and c are connected. Due to this, what will be the percentage loss of energy?
a.
25%
b.
75%
c.
0%
d.
50%
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Two identical capacitors C1 and C2 of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C1 using a battery of emf V volt. Now, after disconnecting a and b, the terminals b and c are connected. Due to this, what will be the percentage loss of energy?
a.
25%
b.
75%
c.
0%
d.
50%
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In a Young’s double slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has path difference
a.
11λ/2
b.
5λ/2
c.
10λ/2
d.
9λ/2
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A double convex lens has focal length 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii if the refractive index of the material of the lens is 1.5.
a.
50 cm, 100 cm
b.
100 cm, 50 cm
c.
25 cm, 50 cm
d.
18.75 cm, 37.5 cm
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Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m, with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m/s²)
a.
They will not collide
b.
After 2 s at a height of 180 m
c.
After 2 s at a height of 20 m
d.
After 4 s at a height of 120 m
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The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials X and Y are likely to be (respectively),
a.
Plastic and ductile
b.
Ductile and brittle
c.
Brittle and ductile
d.
Brittle and plastic
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A body of mass m is kept on a rough horizontal surface (coefficient of friction = μ). A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by F, where F is,
a.
F = mg
b.
F = mg + μmg
c.
F = μmg
d.
F ≤ mg\sqrt{1+μ^2}
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A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directions with speed v each. The energy released during the process is,
a.
4mv²/3
b.
2mv²/3
c.
2mv²/5
d.
2mv²/2
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A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directions with speed v each. The energy released during the process is,
a.
4mv²/3
b.
2mv²/5
c.
5mv²/3
d.
2mv²/3
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An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with x in the manner shown. The velocities of the object at the points x = 8 m and x = 12 m, would have the respective values of (nearly)
a.
18 m/s and 20.6 m/s
b.
18 m/s and 24.4 m/s
c.
23 m/s and 24.4 m/s
d.
23 m/s and 20.6 m/s
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An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with x in the manner shown. The velocities of the object at the points x = 8 m and x = 12 m would have the respective values of (nearly)
a.
18 m/s and 20.6 m/s
b.
18 m/s and 24.4 m/s
c.
23 m/s and 24.4 m/s
d.
23 m/s and 20.6 m/s
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A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination 30°. The centre of mass of the cylinder has speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be, [take g = 10 m/s²]
a.
2.4 m
b.
2.2 m
c.
1.6 m
d.
1.2 m
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