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Objective Questions

Latest BEL Probationary Engineer Electronics Exam Question (Objective Questions), MCQ in English

Subjects : Technical Subject (Electronics), General Aptitude and Reasoning

Question Bank BEL Probationary Engineer (Electronics) Exam - English
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Technical Subject (Electronics)

Question 1Single Answer
The determinant of an identity matrix of any order is:
  1. A
    1
  2. B
    0
  3. C
    −1
  4. D
    Depends on order
Question 2Single Answer
The eigenvalues of a triangular matrix are its:
  1. A
    Row sums
  2. B
    Column sums
  3. C
    Determinants
  4. D
    Diagonal elements
Question 3Single Answer
If A is an orthogonal matrix, then:
  1. A
    A² = 0
  2. B
    AᵀA = I
  3. C
    Aᵀ = 0
  4. D
    det(
Question 4Single Answer
The trace of a matrix is the sum of its:
  1. A
    Eigenvectors
  2. B
    Rows
  3. C
    Diagonal elements
  4. D
    Columns
Question 5Single Answer
The inverse of a matrix exists only when the matrix is:
  1. A
    Non-singular
  2. B
    Singular
  3. C
    Rectangular
  4. D
    Zero
Question 6Single Answer
For a symmetric matrix A:
  1. A
    Aᵀ = −A
  2. B
    det(
  3. C
    A² = I
  4. D
    Aᵀ = A
Question 7Single Answer
The rank of an n × n identity matrix is:
  1. A
    0
  2. B
    n
  3. C
    1
  4. D
    n − 1
Question 8Single Answer
If λ is an eigenvalue of A, then an eigenvalue of A² is:
  1. A
    λ
  2. B
    2λ
  3. C
    √λ
  4. D
    λ²
Question 9Single Answer
A matrix whose transpose is equal to its negative is called:
  1. A
    Symmetric
  2. B
    Skew-symmetric
  3. C
    Orthogonal
  4. D
    Hermitian
Question 10Single Answer
The diagonal elements of a real skew-symmetric matrix are:
  1. A
    1
  2. B
    0
  3. C
    −1
  4. D
    Arbitrary
Question 11Single Answer
The determinant of an orthogonal matrix is:
  1. A
    Either +1 or −1
  2. B
    Always 1
  3. C
    Always 0
  4. D
    Any real number
Question 12Single Answer
The rank of a zero matrix is:
  1. A
    0
  2. B
    1
  3. C
    n
  4. D
    Infinite
Question 13Single Answer
The derivative of sin x is:
  1. A
    −sin x
  2. B
    tan x
  3. C
    −cos x
  4. D
    cos x
Question 14Single Answer
The derivative of eˣ is:
  1. A
    eˣ
  2. B
    xeˣ
  3. C
    e⁻ˣ
  4. D
    ln x
Question 15Single Answer
The derivative of ln x is:
  1. A
    x
  2. B
    1/x
  3. C
    ln x
  4. D
    eˣ
Question 16Single Answer
∫ cos x dx equals:
  1. A
    −sin x + C
  2. B
    cos x + C
  3. C
    sin x + C
  4. D
    tan x + C
Question 17Single Answer
∫ eˣ dx equals:
  1. A
    xeˣ
  2. B
    eˣ + C
  3. C
    e⁻ˣ + C
  4. D
    ln x + C
Question 18Single Answer
The derivative of xⁿ is:
  1. A
    nxⁿ
  2. B
    n²x
  3. C
    xⁿ⁻¹
  4. D
    nxⁿ⁻¹
Question 19Single Answer
∫ xⁿ dx for n ≠ −1 is:
  1. A
    xⁿ⁺¹/(n + 1) + C
  2. B
    nxⁿ⁻¹ + C
  3. C
    ln x + C
  4. D
    xⁿ/n + C
Question 20Single Answer
The derivative of tan x is:
  1. A
    cot x
  2. B
    cosec²x
  3. C
    sec²x
  4. D
    cos²x
Question 21Single Answer
The derivative of cos x is:
  1. A
    sin x
  2. B
    −sin x
  3. C
    cos x
  4. D
    −cos x
Question 22Single Answer
A function is at a local maximum when its first derivative changes from:
  1. A
    Negative to positive
  2. B
    Zero to positive
  3. C
    Positive to negative
  4. D
    Zero to zero
Question 23Single Answer
The order of d²y/dx² + 3dy/dx + y = 0 is:
  1. A
    1
  2. B
    0
  3. C
    3
  4. D
    2
Question 24Single Answer
The degree of (d²y/dx²)³ + y = 0 is:
  1. A
    3
  2. B
    2
  3. C
    1
  4. D
    6
Question 25Single Answer
The general solution of dy/dx = 0 is:
  1. A
    y = x
  2. B
    y = x²
  3. C
    y = eˣ
  4. D
    y = C
Question 26Single Answer
The solution of dy/dx = ky is:
  1. A
    y = C + kx
  2. B
    y = Ceᵏˣ
  3. C
    y = Cxᵏ
  4. D
    y = k/x
Question 27Single Answer
A first-order linear differential equation has the standard form:
  1. A
    y² + x² = 1
  2. B
    d²y/dx² + y = 0
  3. C
    dy/dx + Py =
  4. D
    dy/dx = y² only
Question 28Single Answer
The integrating factor for dy/dx + Py = is:
  1. A
    e^(∫P dx)
  2. B
    e^(∫ dx)
  3. C
    P/
  4. D
    /P
Question 29Single Answer
A second-order differential equation requires how many independent initial conditions for a unique solution?
  1. A
    1
  2. B
    4
  3. C
    3
  4. D
    2
Question 30Single Answer
The complementary solution of y″ + ω²y = 0 contains:
  1. A
    Sinusoidal functions
  2. B
    Exponential growth only
  3. C
    Polynomial functions only
  4. D
    Logarithmic functions
Question 31Single Answer
Euler's formula is:
  1. A
    eʲˣ = cos x + j sin x
  2. B
    eˣ = cos x
  3. C
    eʲˣ = sin x
  4. D
    eˣ = jx
Question 32Single Answer
The magnitude of 3 + j4 is:
  1. A
    3
  2. B
    5
  3. C
    4
  4. D
    7
Question 33Single Answer
The imaginary unit j satisfies:
  1. A
    j² = −1
  2. B
    j² = 1
  3. C
    j = 0
  4. D
    j³ = 1
Question 34Single Answer
The complex conjugate of 3 + j4 is:
  1. A
    3 − j4
  2. B
    −3 − j4
  3. C
    −3 + j4
  4. D
    4 + j3
Question 35Single Answer
The modulus of a complex number z = x + jy is:
  1. A
    √(x² + y²)
  2. B
    x + y
  3. C
    x² + y²
  4. D
    x − y
Question 36Single Answer
The argument of 1 + j is:
  1. A
    0°
  2. B
    45°
  3. C
    30°
  4. D
    90°
Question 37Single Answer
j³ equals:
  1. A
    −j
  2. B
    −1
  3. C
    j
  4. D
    1
Question 38Single Answer
The probability of a certain event is:
  1. A
    0
  2. B
    0.5
  3. C
    1
  4. D
    Infinity
Question 39Single Answer
The probability of an impossible event is:
  1. A
    0.5
  2. B
    1
  3. C
    −1
  4. D
    0
Question 40Single Answer
The mean of a random variable is also called its:
  1. A
    Variance
  2. B
    Range
  3. C
    Mode only
  4. D
    Expectation
Question 41Single Answer
Variance is always:
  1. A
    Negative
  2. B
    Less than −1
  3. C
    Imaginary
  4. D
    Non-negative
Question 42Single Answer
Standard deviation is the:
  1. A
    Square of variance
  2. B
    Mean of variance
  3. C
    Reciprocal of variance
  4. D
    Square root of variance
Question 43Single Answer
The total probability over all outcomes of a sample space is:
  1. A
    1
  2. B
    0.5
  3. C
    0
  4. D
    2
Question 44Single Answer
For a fair coin, probability of getting a head is:
  1. A
    0
  2. B
    1/4
  3. C
    1/2
  4. D
    1
Question 45Single Answer
For a fair six-sided die, probability of getting 6 is:
  1. A
    1/6
  2. B
    1/3
  3. C
    1/2
  4. D
    1/12
Question 46Single Answer
The mean of a Gaussian distribution determines its:
  1. A
    Width
  2. B
    Center
  3. C
    Skewness only
  4. D
    Tail direction
Question 47Single Answer
For a normal distribution, mean, median, and mode are:
  1. A
    Always different
  2. B
    Zero only
  3. C
    Equal
  4. D
    Infinite
Question 48Single Answer
The binomial distribution applies to:
  1. A
    Continuous infinite outcomes
  2. B
    Sinusoidal signals
  3. C
    Deterministic systems
  4. D
    Repeated independent Bernoulli trials
Question 49Single Answer
Poisson distribution is often used to model:
  1. A
    Differential equations
  2. B
    Matrix eigenvalues
  3. C
    Complex angles
  4. D
    Number of events in an interval
Question 50Single Answer
The value of sin²x + cos²x is:
  1. A
    0
  2. B
    1
  3. C
    2
  4. D
    x
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