A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is:
a.
13t/5
Correct Answer
b.
10t/13
c.
5t/13
d.
13t/10
Step-by-Step AI Explanation
Verified Method
Using Newton's Law of Cooling, (T1-T2)/t = K * ((T1+T2)/2 - Ts). For the first interval: (90-80)/t = K * (85-20) => 10/t = 65K. For the second: (80-60)/t' = K * (70-20) => 20/t' = 50K. Dividing the equations: (10/t)/(20/t') = 65/50 => t'/2t = 1.3 => t' = 2.6t = 13t/5.
Q1mcq
A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is:
a.
13/5 t
Correct Answer
b.
10/13 t
c.
5/13 t
d.
13/10 t
Step-by-Step AI Explanation
Verified Method
According to Newton's law of cooling: dT/dt = -k(T - T_surroundings). For 90 to 80: (90-80)/t = k[(90+80)/2 - 20] => 10/t = k(65). For 80 to 60: (80-60)/t' = k[(80+60)/2 - 20] => 20/t' = k(50). Dividing the equations: (10/t)/(20/t') = 65/50 => t'/2t = 13/10 => t' = 13t/5.
Q2mcq
Polar molecules are the molecules:
a.
acquire a dipole moment only in the presence of electric field due to displacement of charges.
b.
acquire a dipole moment only when magnetic field is absent.
c.
having a permanent electric dipole moment.
Correct Answer
d.
having zero dipole moment.
Step-by-Step AI Explanation
Verified Method
Polar molecules are those in which the center of positive and negative charges do not coincide, resulting in a permanent electric dipole moment.
Q2mcq
Polar molecules are the molecules :
a.
acquire a dipole moment only in the presence of electric field due to displacement of charges.
b.
acquire a dipole moment only when magnetic field is absent.
c.
having a permanent electric dipole moment.
Correct Answer
d.
having zero dipole moment.
Step-by-Step AI Explanation
Verified Method
Polar molecules are those in which the centres of positive and negative charges do not coincide, resulting in a permanent electric dipole moment.
Q3mcq
A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is :
a.
9.4 MeV
b.
804 MeV
c.
216 MeV
Correct Answer
d.
0.9 MeV
Step-by-Step AI Explanation
Verified Method
Initial Binding Energy = 240 * 7.6 MeV = 1824 MeV. Final Binding Energy = (120 * 8.5) * 2 = 2040 MeV. Gain = 2040 - 1824 = 216 MeV.
Q3mcq
A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is:
a.
9.4 MeV
b.
804 MeV
c.
216 MeV
Correct Answer
d.
0.9 MeV
Step-by-Step AI Explanation
Verified Method
Total BE before = 240 * 7.6 = 1824 MeV. Total BE after = 2 * (120 * 8.5) = 2 * 1020 = 2040 MeV. Gain = 2040 - 1824 = 216 MeV.
Q4mcq
An electromagnetic wave of wavelength ‘λ’ is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength λ_d, then :
a.
λ = (2mc/h) * λ_d^2
Correct Answer
b.
λ_d = (2mc/h) * λ^2
c.
λ_d = (2h/mc) * λ^2
d.
λ_d = (2m/hc) * λ^2
Step-by-Step AI Explanation
Verified Method
Energy of photon E = hc/λ. Kinetic Energy of emitted photoelectron K = E = hc/λ. Also K = p^2/2m = (h/λ_d)^2 / 2m. Equating: hc/λ = h^2 / (2m * λ_d^2). Therefore λ = (2mc/h) * λ_d^2.
Q5mcq
A radioactive nucleus X(A, Z) undergoes spontaneous decay in the sequence X(A,Z) -> B(A, Z-1) -> C(A-4, Z-3) -> D(A-4, Z-2), where Z is the atomic number of element X. The possible decay particles in the sequence are:
a.
α, β+, β-
b.
β+, α, β-
Correct Answer
c.
β-, α, β+
d.
α, β-, β+
Step-by-Step AI Explanation
Verified Method
X(A,Z) -> B(A,Z-1) implies β+ emission (or EC). B(A,Z-1) -> C(A-4,Z-3) implies α emission (A decreases by 4, Z by 2). C(A-4,Z-3) -> D(A-4,Z-2) implies β- emission (Z increases by 1).
Q6mcq
Match Column - I with Column - II for physical terms associated with current flow.
a.
(A)-(R), (B)-(S), (C)-(Q), (D)-(P)
b.
(A)-(R), (B)-(P), (C)-(S), (D)-(Q)
c.
(A)-(R), (B)-(Q), (C)-(S), (D)-(P)
d.
(A)-(R), (B)-(S), (C)-(P), (D)-(Q)
Correct Answer
Step-by-Step AI Explanation
Verified Method
Drift velocity (vd) = eEτ/m (R). Resistivity (ρ) = m/(ne^2τ) (S). Relaxation period is implied as inverse of scattering/resistance metrics. Current density (J) = nev (Q). Based on standard relations provided: A-R, B-S, C-P, D-Q.
Q7mcq
In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs?
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be:
a.
Mg
b.
3Mg/2
c.
2Mg
d.
Mg/2
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Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g=10 m/s^2)
a.
8.1 kW
b.
12.3 kW
c.
7.0 kW
d.
10.2 kW
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The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series?
a.
0.5 Ω
b.
1 Ω
c.
4 Ω
d.
0.25 Ω
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A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively:
a.
S/4, sqrt(3gS/2)
b.
S/2, sqrt(3gS/2)
c.
S/4, sqrt(3gS)
d.
S/4, sqrt(3gS/2)
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A particle is released from height S from the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively:
a.
S/4, 3gS/2
b.
S/2, 3gS/2
c.
S/4, sqrt(3gS)/2
d.
S/4, sqrt(3gS)/2
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A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be:
a.
15
b.
50
c.
30
d.
25
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A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be:
a.
15
b.
50
c.
30
d.
25
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A capacitor of capacitance ‘C’ is connected across an ac source of voltage V, given by V = V0 sin(ωt). The displacement current between the plates of the capacitor would then be given by:
a.
Id = (V0/ωC) cos(ωt)
b.
Id = (V0/ωC) sin(ωt)
c.
Id = V0ωC sin(ωt)
d.
Id = V0ωC cos(ωt)
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The electron concentration in an n-type semiconductor is the same as hole concentration in a p-type semiconductor. An external electric field is applied across each of them. Compare the currents in them.
a.
current in p-type > current in n-type.
b.
current in n-type > current in p-type.
c.
No current will flow in p-type, current will only flow in n-type.
d.
current in n-type = current in p-type.
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The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3×10^-3 watt will be: (h=6.6×10^-34 Js)
a.
10^17
b.
10^16
c.
10^15
d.
10^18
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For a plane electromagnetic wave propagating in x-direction, which one of the following combinations gives the correct possible directions for electric field (E) and magnetic field (B) respectively?
a.
-j + k, j + k
b.
+j - k, -j + k
c.
-j + k, -j + k
d.
+j + k, j + k
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A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is: (ε0 = permittivity of free space)
a.
ε0EAd
b.
1/2 ε0 E^2 Ad
c.
E^2 Ad / ε0
d.
1/2 ε0 E^2
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Consider the following statements (A) and (B) and identify the correct answer: (A) A zener diode is connected in reverse bias, when used as a voltage regulator. (B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.
a.
(A) and (B) both are incorrect.
b.
(A) is correct and (B) is incorrect.
c.
(A) is incorrect but (B) is correct.
d.
(A) and (B) both are correct.
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Consider the following statements (A) and (B) and identify the correct answer. (A) A zener diode is connected in reverse bias, when used as a voltage regulator. (B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.
a.
(A) and (B) both are incorrect.
b.
(A) is correct and (B) is incorrect.
c.
(A) is incorrect but (B) is correct.
d.
(A) and (B) both are correct.
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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.
0.026 cm
b.
0.26 cm
c.
0.052 cm
d.
0.52 cm
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A small block slides down on a smooth inclined plane, starting from rest at time t=0. Let Sn be the distance travelled by the block in the interval t=n-1 to t=n. Then, the ratio Sn / Sn+1 is:
a.
(2n-1)/(2n+1)
b.
(2n+1)/(2n-1)
c.
2n/(2n-1)
d.
(2n-1)/2n
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The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is:
a.
2 v
b.
3 v
c.
4 v
d.
v
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A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
a.
0.4 A
b.
2 A
c.
4 A
d.
0.2 A
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Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:
a.
R1/R2
b.
R1^2/R2
c.
R2^2/R1
d.
R1/R2^2
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Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:
a.
R1/R2
b.
R1^2/R2
c.
R2^2/R1
d.
R1/R2^2
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A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g=10 m/s^2) nearly:
a.
4.2 kg m/s
b.
2.1 kg m/s
c.
1.4 kg m/s
d.
0 kg m/s
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A car starts from rest and accelerates at 5 m/s^2. At t=4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6 s? (Take g=10 m/s^2)
a.
20 m/s, 0
b.
20√2 m/s, 0
c.
20√2 m/s, 10 m/s^2
d.
20 m/s, 5 m/s^2
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From a circular ring of mass ‘M’ and radius ‘R’ an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is ‘K’ times ‘MR^2’. Then the value of ‘K’ is:
a.
7/8
b.
1/4
c.
1/8
d.
3/4
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A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light, c=3.0×10^8 ms^-1]
a.
219.2 m
b.
2192 m
c.
21.92 cm
d.
219.3 m
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Choose the correct option for the total pressure (in atm.) in a mixture of 4 g O2 and 2 g H2 confined in a total volume of one litre at 0°C. [Given R=0.082 L atm mol⁻¹ K⁻¹, T=273 K]
a.
2.602
b.
25.18
c.
26.02
d.
2.518
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