Legal Metrology • Physics Paper-III
The allowed energy of a particle of mass m confined in a cubic box with rigid walls is given by E = (h^2/8mL^2)(n1^2 + n2^2 + n3^2). How many numbers of states do we have with energy 6E_0?
A)
0
B)
1
C)
2
D)
3
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is '0' (Option A).
Legal Metrology • Physics Paper-III
A relaxation oscillator can produce
A)
Sine wave
B)
Cosine wave
C)
Solitonic wave
D)
Square wave
In the context of Electrical / Electronics Engineering, the most appropriate and technically accurate answer is 'Square wave' (Option D).
Legal Metrology • Physics Paper-III
A battery of 100 V is connected in series to a Zener diode and resistor of 10Ω. Assuming that the Zener diode is in reverse bias, what will be the voltage difference across the Zener diode if its breakdown voltage is 20 V?
A)
100 V
B)
80V
C)
20V
D)
0V
Once reverse bias voltage exceeds the Zener breakdown voltage (20V), the voltage across the diode remains clamped at 20V.
Legal Metrology • Physics Paper-III
The eigenvalues of Hermitian matrix are always
A)
Zero
B)
Real numbers
C)
Purely imaginary numbers
D)
Real even numbers
Hermitian matrices have real eigenvalues.
Legal Metrology • Physics Paper-III
The wave-function of a particle trapped inside a one-dimensional box of length L is given by ψ(x) = A sin(πx/L). The probability of finding the particle is maximum around
A)
x = 0
B)
x = L/2
C)
x = L/4
D)
x = L
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'x = L/4' (Option C).
Legal Metrology • Physics Paper-III
Fourier transforms of periodic even function contains
A)
Sine terms only
B)
A constant term only
C)
A constant and cosine terms only
D)
A constant and sine terms only
An even periodic function has no sine terms, so it contains a constant and cosine terms.
Legal Metrology • Physics Paper-III
What are the terminals of UJT?
A)
Collector, Base and Emitter
B)
Emitter, Base 1 and Base 2
C)
Emitter 1, Emitter 2 and Base
D)
Gate, Drain and Source
Based on established principles in Electrical / Electronics Engineering, the correct and most clinically/technically appropriate choice is 'Emitter 1, Emitter 2 and Base' (Option C).
Legal Metrology • Physics Paper-III
If h is the Planck’s constant, the de Broglie wavelength of a particle of momentum p is given by
A)
hp
B)
h/p
C)
p/h
D)
h^2/p
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'hp' (Option A).
Legal Metrology • Physics Paper-III
If there is no external force acting on two bodies except the force between them, then the centre of mass of the two bodies R_cm always satisfy
A)
R_cm = 0
B)
R_cm = Constant
C)
dR_cm/dt = 0
D)
d^2R_cm/dt^2 = 0
With no external net force, centre-of-mass acceleration is zero: d²R_cm/dt²=0.
Legal Metrology • Physics Paper-III
The Hall voltage is
A)
Parallel to applied current and perpendicular to applied magnetic field
B)
Perpendicular to applied current and parallel to applied magnetic field
C)
Parallel to both applied current and applied magnetic field
D)
Perpendicular to both applied current and applied magnetic field
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'Perpendicular to both applied current and applied magnetic field' (Option D).
Legal Metrology • Physics Paper-III
For a particle of mass m in a one-dimensional box of length L, the lowest energy is given by
A)
h^2/8mL^2
B)
h^2/4mL^2
C)
h^2/2mL^2
D)
h^2/mL^2
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'h^2/8mL^2' (Option A).
Legal Metrology • Physics Paper-III
The differential equation for the wave function of a particle of mass m and energy E in a potential V(x) is given by
A)
Option A
B)
Option B
C)
Option C
D)
Option D
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'Option A' (Option A).
Legal Metrology • Physics Paper-III
Which of the following is a periodic function?
A)
Option A
B)
log x
C)
sin x + 2 cos x
D)
x^2
sin x + 2 cos x is periodic with period 2π.
Legal Metrology • Physics Paper-III
If n and m are different integers, the value of the integral ∫ sin(nx) sin(mx) dx is
A)
π
B)
0
C)
2π
D)
π/nm
Different sine harmonics are orthogonal over a full common period, so the integral is zero.
Legal Metrology • Physics Paper-III
A battery of 10 V is connected in series to a diode and 5Ω resistor (assume that the diode is forward biased). If the forward bias resistance of the diode is zero and the voltage drop across the diode is 0.7 V, what is the current flowing through the circuit?
A)
0A
B)
1.86A
C)
2A
D)
0.14A
I=(10−0.7)/5=1.86 A.
Legal Metrology • Physics Paper-III
What is the output for the following rectifier circuit? (Refer to image in paper)
A)
Option A
B)
Option B
C)
Option C
D)
Option D
Based on established principles in Electrical / Electronics Engineering, the correct and most clinically/technically appropriate choice is 'Option B' (Option B).
Legal Metrology • Physics Paper-III
The matrix [[cos x, -sin x], [sin x, cos x]] is a
A)
Singular matrix
B)
Orthogonal matrix
C)
Symmetric matrix
D)
Skew-symmetric matrix
The rotation matrix [[cosx,-sinx],[sinx,cosx]] is orthogonal because AᵀA=I.
Legal Metrology • Physics Paper-III
Which of the following is a correct statement of the Heisenberg’s uncertainty principle
A)
ΔxΔp = 0
B)
ΔxΔp ≥ h/4π
C)
ΔxΔp < h/4π
D)
ΔxΔp = h/4π
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'ΔxΔp = h/4π' (Option D).
Legal Metrology • Physics Paper-III
The reduced mass of two masses 3 kg and 6 kg is
A)
2kg
B)
3kg
C)
4kg
D)
9kg
Reduced mass μ=m1m2/(m1+m2)=3×6/9=2 kg.
Legal Metrology • Physics Paper-III
Which is the normal operation mode of a transistor
A)
Emitter-base and collector-base are both forward biased
B)
Emitter-base and collector-base are both reverse biased
C)
Emitter-base is forward biased and collector-base is reverse biased
D)
Emitter-base is reverse biased and collector-base is forward biased
Based on established principles in Electrical / Electronics Engineering, the correct and most clinically/technically appropriate choice is 'Emitter-base is forward biased and collector-base is reverse biased' (Option C).
Legal Metrology • Physics Paper-III
If A and B are matrices, which of the following is not always satisfied?
A)
A + B = B + A
B)
AB = BA
C)
A A^T = (A A^T)^T
D)
A - B = -(B - A)
In the context of Quantitative Aptitude, the most appropriate and technically accurate answer is 'A + B = B + A' (Option A).
Legal Metrology • Physics Paper-III
Which of the following can be explained by the particle nature of light?
A)
Heisenberg’s uncertainty principle
B)
Photoelectric effect
C)
Interference of light
D)
Diffraction of light
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'Heisenberg’s uncertainty principle' (Option A).
Legal Metrology • Physics Paper-III
The existence of discrete energy levels (quantization of energy) for a particle confined in a box with rigid walls is due to
A)
Pauli’s exclusion principle
B)
Heisenberg uncertainty principle
C)
Confinement
D)
Spin-statistics principle
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'Pauli’s exclusion principle' (Option A).
Legal Metrology • Physics Paper-III
In NPN transistor in common emitter configuration, if 98% of the emitter current reach the collector, what is the current gain (β = I_C/I_B)?
A)
98
B)
2
C)
49
D)
102
Based on established principles in Electrical / Electronics Engineering, the correct and most clinically/technically appropriate choice is '2' (Option B).
Legal Metrology • Physics Paper-III
The equation which governs how the wave-function of a particle change with time is given by
A)
Option A
B)
Option B
C)
Option C
D)
Option D
In the context of Unmapped / long tail, the most appropriate and technically accurate answer is 'Option D' (Option D).
