A radioactive nucleus Z^A X undergoes spontaneous decay in the sequence Z^A X -> Z-1^A B -> Z-3^A C -> Z-2^A D, where Z is the atomic number of element X. The possible decay particles in the sequence are:
a.
β^+, α, β^-
b.
β^-, α, β^+
c.
α, β^-, β^+
d.
α, β^+, β^-
Correct Answer
Step-by-Step AI Explanation
Verified Method
Z-1^A (β^+), then Z-3^A (α decay reduces Z by 2, mass by 4), then Z-2^A (β^- decay increases Z by 1).
Q1mcq
A radioactive nucleus Z X^A undergoes spontaneous decay in the sequence Z X^A -> Z-1 B^A -> Z-3 C^A -> Z-2 D^A, where Z is the atomic number of element X. The possible decay particles in the sequence are:
a.
β+, α, β-
Correct Answer
b.
β-, α, β+
c.
α, β-, β+
d.
α, β+, β-
Step-by-Step AI Explanation
Verified Method
In the first step, Z goes to Z-1 (β+ decay). In the second step, Z-1 goes to Z-3 (α decay, reduces Z by 2). In the third step, Z-3 goes to Z-2 (β- decay, increases Z by 1). Thus, the sequence is β+, α, β-.
Q2mcq
Polar molecules are the molecules:
a.
acquire a dipole moment only when magnetic field is absent.
b.
having a permanent electric dipole moment.
Correct Answer
c.
having zero dipole moment.
d.
acquire a dipole moment only in the presence of electric field due to displacement of charges.
Step-by-Step AI Explanation
Verified Method
Polar molecules are those in which the centres of positive and negative charges do not coincide even in the absence of an external electric field, resulting in a permanent electric dipole moment.
Q2mcq
Polar molecules are the molecules:
a.
acquire a dipole moment only when magnetic field is absent.
b.
having a permanent electric dipole moment.
Correct Answer
c.
having zero dipole moment.
d.
acquire a dipole moment only in the presence of electric field due to displacement of charges.
Step-by-Step AI Explanation
Verified Method
Polar molecules have centers of positive and negative charges separated even in the absence of an external electric field, thus possessing a permanent dipole moment.
Q3mcq
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.
1 Ω
b.
4 Ω
Correct Answer
c.
0.25 Ω
d.
0.5 Ω
Step-by-Step AI Explanation
Verified Method
Let resistance of each wire be R. In parallel, 1/Rp = 1/R + 1/R + 1/R + 1/R = 4/R. Given Rp = 0.25 Ω, so R/4 = 0.25, meaning R = 1 Ω. In series, Rs = R + R + R + R = 4R = 4(1) = 4 Ω.
Q3mcq
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.
1 Ω
b.
4 Ω
Correct Answer
c.
0.25 Ω
d.
0.5 Ω
Step-by-Step AI Explanation
Verified Method
If each wire has resistance R, then R/4 = 0.25, so R = 1 Ω. In series, total resistance = 4R = 4 Ω.
Q4mcq
Match Column-I (Physical terms) with Column-II (Mathematical relations): (A) Drift Velocity (B) Electrical Resistivity (C) Relaxation Period (D) Current Density. Column-II: (P) m/(ne^2τ), (Q) nev_d, (R) eEτ/m, (S) E/J
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?
a.
64 cm
b.
62 cm
c.
60 cm
Correct Answer
d.
21.6 cm
Step-by-Step AI Explanation
Verified Method
Using E1/E2 = L1/L2: 1.5/2.5 = 36/L2 => L2 = 36 * (2.5/1.5) = 60 cm.
Q7mcq
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.
3 v
b.
4 v
c.
v
d.
2 v
Correct Answer
Step-by-Step AI Explanation
Verified Method
Escape velocity v = sqrt(2GM/R) = sqrt(2G(4/3πR^3ρ)/R) = R*sqrt(8/3Gπρ). Since ρ is same, v is proportional to R. As radius is 4 times, velocity is 4 times? Wait, V proportional to R, so 4 times. Rechecking: v = R * const. If R becomes 4R, then v' = 4v.
Q9mcq
A capacitor of capacitance ‘C’ is connected across an ac source of voltage V, given by V = V_0 sinωt. The displacement current between the plates of the capacitor would then be:
a.
I_d = (V_0/ωC) sinωt
b.
I_d = V_0 ωC sinωt
c.
I_d = V_0 ωC cosωt
Correct Answer
d.
I_d = (V_0/ωC) cosωt
Step-by-Step AI Explanation
Verified Method
I_d = dQ/dt = d(CV)/dt = C * d/dt(V_0 sinωt) = C * V_0 * ω * cosωt.
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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.
50
b.
30
c.
25
d.
15
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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.
50
b.
30
c.
25
d.
15
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An infinitely long straight conductor carries a current of 5 A. An electron is moving with a speed of 10^5 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm. Calculate the magnitude of the force experienced by the electron.
a.
4π×10^-20 N
b.
8×10^-20 N
c.
4×10^-20 N
d.
8π×10^-20 N
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The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant. If the density of glycerine is d/2, then the viscous force acting on the ball will be:
a.
3Mg/2
b.
2Mg
c.
Mg/2
d.
Mg
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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 field (electric) is applied across each of them. Compare the currents in them.
a.
current in n-type > current in p-type.
b.
No current will flow in p-type, current will only flow in n-type.
c.
current in n-type = current in p-type.
d.
current in p-type > current in n-type.
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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 is:
a.
0.26 cm
b.
0.052 cm
c.
0.52 cm
d.
0.026 cm
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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.
10^16
b.
10^15
c.
10^18
d.
10^17
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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.
12.3 kW
b.
7.0 kW
c.
10.2 kW
d.
8.1 kW
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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 λd, then:
a.
λ = (2mc/h) * λd^2
b.
λ = (2h/mc) * λd^2
c.
λ = (2m/hc) * λd^2
d.
λ = (h/2mc) * λd^2
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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.
804 MeV
b.
216 MeV
c.
0.9 MeV
d.
9.4 MeV
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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.
804 MeV
b.
216 MeV
c.
0.9 MeV
d.
9.4 MeV
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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.
1/2 * ε0 * E^2 * Ad
b.
ε0 * E^2 * Ad
c.
1/2 * ε0 * E^2
d.
ε0 * EAd
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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.
(1/2)ε₀E²Ad
b.
ε₀E²Ad
c.
(1/2)ε₀E²
d.
ε₀EAd
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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) is correct and (B) is incorrect.
b.
(A) is incorrect but (B) is correct.
c.
(A) and (B) both are correct.
d.
(A) and (B) both are incorrect.
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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 'MR²'. Then the value of 'K' is:
a.
1/4
b.
1/8
c.
3/4
d.
7/8
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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.
2 A
b.
4 A
c.
0.2 A
d.
0.4 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.
R1^2 / R2
b.
R2^2 / R1
c.
R1 / R2
d.
R2 / R1
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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.
R1^2 / R2
b.
R2^2 / R1
c.
R1 / R2^2
d.
R1^2 / R2^2
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A particle of mass ‘m’ is projected with a velocity v=kVe (k < 1) from the surface of the earth (Ve = escape velocity). The maximum height above the surface reached by the particle is:
a.
R * k^2 / (1 - k^2)
b.
R * k^2 / (1 + k^2)
c.
R / (1 - k^2)
d.
R / (1 + k^2)
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A particle of mass 'm' is projected with a velocity v=kV_e (k < 1) from the surface of the earth (V_e = escape velocity). The maximum height above the surface reached by the particle is:
a.
R * k² / (1 + k²)
b.
R * k² / (1 - k²)
c.
R * k² / (1 - k)
d.
R * k² / (1 + k)
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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/s2) nearly:
a.
2.1 kg m/s
b.
1.4 kg m/s
c.
0 kg m/s
d.
4.2 kg m/s
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A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz. The wavelength of the electromagnetic radiation emitted by the transmitter is (c=3.0×10^8 ms^-1):
a.
2192 m
b.
21.92 cm
c.
219.3 m
d.
219.2 m
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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.
2192 m
b.
21.92 cm
c.
219.3 m
d.
219.2 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 273 K is :
[Given R=0.082 L atm mol-1 K-1, T=273 K]
a.
25.18
b.
26.02
c.
2.518
d.
2.602
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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.
25.18
b.
26.02
c.
2.518
d.
2.602
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