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Objective Questions

Latest IOCL JE Instrumentation Exam Question (Objective Questions), MCQ in English

Subjects : Domain Knowledge, Quantitative Aptitude, Logical Reasoning, Verbal Ability of English Language

Question Bank IOCL Junior Engineer (Instrumentation) Exam - English
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Domain Knowledge

Question 1Single Answer
A matrix having the same number of rows and columns is called:
  1. A
    Square matrix
  2. B
    Rectangular matrix
  3. C
    Row matrix
  4. D
    Column matrix
Question 2Single Answer
A matrix in which all elements are zero is known as:
  1. A
    Identity matrix
  2. B
    Null matrix
  3. C
    Scalar matrix
  4. D
    Diagonal matrix
Question 3Single Answer
In an identity matrix, the principal diagonal elements are:
  1. A
    All zero
  2. B
    All negative
  3. C
    All one
  4. D
    Arbitrary
Question 4Single Answer
A diagonal matrix is necessarily a:
  1. A
    Square matrix
  2. B
    Row matrix
  3. C
    Rectangular matrix
  4. D
    Column matrix
Question 5Single Answer
A matrix whose transpose is equal to itself is called:
  1. A
    Skew-symmetric matrix
  2. B
    Singular matrix
  3. C
    Symmetric matrix
  4. D
    Orthogonal matrix
Question 6Single Answer
In a skew-symmetric matrix, the diagonal elements are always:
  1. A
    One
  2. B
    Positive
  3. C
    Zero
  4. D
    Negative
Question 7Single Answer
A square matrix having zero determinant is called:
  1. A
    Singular matrix
  2. B
    Non-singular matrix
  3. C
    Identity matrix
  4. D
    Orthogonal matrix
Question 8Single Answer
A non-singular matrix always possesses:
  1. A
    Zero determinant
  2. B
    Zero eigenvalues only
  3. C
    An inverse
  4. D
    Identical rows
Question 9Single Answer
The rank of a matrix represents the maximum number of:
  1. A
    Zero elements
  2. B
    Linearly independent rows or columns
  3. C
    Diagonal elements
  4. D
    Eigenvalues equal to zero
Question 10Single Answer
Elementary row operations on a matrix:
  1. A
    Always change its rank
  2. B
    Make its rank zero
  3. C
    Preserve its rank
  4. D
    Make it singular in every case
Question 11Single Answer
A homogeneous system of linear equations always has:
  1. A
    At least the trivial solution
  2. B
    No solution
  3. C
    Only infinitely many nonzero solutions
  4. D
    Exactly two solutions
Question 12Single Answer
A system of linear equations is called consistent if it has:
  1. A
    Only a zero determinant
  2. B
    No solution
  3. C
    At least one solution
  4. D
    Only complex solutions
Question 13Single Answer
Two vectors are linearly dependent if:
  1. A
    Neither can be represented using the other vectors
  2. B
    At least one can be expressed as a linear combination of the others
  3. C
    They are always perpendicular
  4. D
    Their magnitudes are equal
Question 14Single Answer
An eigenvector of a matrix is a nonzero vector whose direction under the matrix transformation:
  1. A
    Necessarily becomes perpendicular
  2. B
    Always becomes zero
  3. C
    Remains unchanged apart from scaling
  4. D
    Changes randomly
Question 15Single Answer
The scalar associated with an eigenvector is called:
  1. A
    Eigenvalue
  2. B
    Rank
  3. C
    Determinant
  4. D
    Trace vector
Question 16Single Answer
The sum of the eigenvalues of a square matrix, counting multiplicities, equals its:
  1. A
    Rank
  2. B
    Order
  3. C
    Nullity
  4. D
    Trace
Question 17Single Answer
The product of the eigenvalues of a square matrix, counting multiplicities, equals its:
  1. A
    Trace
  2. B
    Rank
  3. C
    Determinant
  4. D
    Nullity
Question 18Single Answer
Eigenvectors corresponding to distinct eigenvalues of a real symmetric matrix are:
  1. A
    Parallel
  2. B
    Identical
  3. C
    Orthogonal
  4. D
    Zero vectors
Question 19Single Answer
A real symmetric matrix has eigenvalues that are always:
  1. A
    Purely imaginary
  2. B
    Real
  3. C
    Zero
  4. D
    Positive only
Question 20Single Answer
The process of transforming a matrix into a diagonal matrix using a suitable similarity transformation is called:
  1. A
    Differentiation
  2. B
    Normalization
  3. C
    Integration
  4. D
    Diagonalization
Question 21Single Answer
Rolle's theorem is applicable when a function is continuous on a closed interval and differentiable on the corresponding:
  1. A
    Closed interval only
  2. B
    Infinite interval
  3. C
    Open interval
  4. D
    Discrete set
Question 22Single Answer
An additional condition required by Rolle's theorem is that the function values at the two endpoints must be:
  1. A
    Equal
  2. B
    Opposite
  3. C
    Zero individually
  4. D
    Infinite
Question 23Single Answer
Lagrange's Mean Value Theorem geometrically relates the slope of a secant line to the slope of a:
  1. A
    Normal
  2. B
    Vertical line
  3. C
    Tangent
  4. D
    Coordinate axis
Question 24Single Answer
Rolle's theorem may be regarded as a special case of:
  1. A
    Green's theorem
  2. B
    Stokes' theorem
  3. C
    Lagrange's Mean Value Theorem
  4. D
    Gauss' theorem
Question 25Single Answer
The Fundamental Theorem of Calculus establishes a fundamental connection between:
  1. A
    Differentiation and integration
  2. B
    Matrices and vectors
  3. C
    Probability and statistics
  4. D
    Complex numbers and matrices
Question 26Single Answer
A partial derivative measures the change in a multivariable function with respect to:
  1. A
    All variables simultaneously
  2. B
    One variable while the others are held constant
  3. C
    No independent variable
  4. D
    Only time
Question 27Single Answer
The gradient of a scalar field points in the direction of:
  1. A
    Maximum decrease only
  2. B
    Maximum increase
  3. C
    Zero change always
  4. D
    Constant curvature
Question 28Single Answer
At a differentiable local maximum or minimum occurring at an interior point, a necessary condition is generally that the:
  1. A
    Function becomes infinite
  2. B
    Function is discontinuous
  3. C
    First derivative vanishes
  4. D
    Integral becomes zero
Question 29Single Answer
A stationary point of a differentiable single-variable function is a point where:
  1. A
    The function must be zero
  2. B
    Its second derivative must be zero
  3. C
    Its first derivative is zero
  4. D
    The function is discontinuous
Question 30Single Answer
A saddle point of a function of two variables is generally a stationary point that is:
  1. A
    Always a local maximum
  2. B
    Always a local minimum
  3. C
    Neither a local maximum nor a local minimum
  4. D
    Always discontinuous
Question 31Single Answer
A double integral is commonly used to integrate a function over a:
  1. A
    Curve
  2. B
    Single point
  3. C
    Two-dimensional region
  4. D
    Sequence
Question 32Single Answer
A triple integral is commonly associated with integration over a:
  1. A
    Line segment
  2. B
    Three-dimensional region
  3. C
    Single coordinate axis
  4. D
    Finite sequence
Question 33Single Answer
Fourier series represent suitable periodic functions in terms of:
  1. A
    Polynomials only
  2. B
    Sine and cosine functions
  3. C
    Matrices only
  4. D
    Logarithmic functions only
Question 34Single Answer
For an even function represented by a Fourier series over a symmetric interval, which terms generally vanish?
  1. A
    Cosine terms
  2. B
    All terms
  3. C
    Constant term
  4. D
    Sine terms
Question 35Single Answer
For an odd function represented by a Fourier series over a symmetric interval, which terms generally vanish?
  1. A
    Sine terms
  2. B
    All harmonic terms
  3. C
    Cosine terms including the constant component
  4. D
    Only higher harmonics
Question 36Single Answer
The divergence of a vector field produces a:
  1. A
    Tensor of fixed rank two only
  2. B
    Vector field
  3. C
    Matrix field
  4. D
    Scalar field
Question 37Single Answer
The curl of a three-dimensional vector field produces a:
  1. A
    Vector
  2. B
    Scalar
  3. C
    Matrix
  4. D
    Constant only
Question 38Single Answer
The divergence of the curl of a sufficiently smooth vector field is:
  1. A
    Always one
  2. B
    Always zero
  3. C
    Always infinite
  4. D
    Equal to its gradient
Question 39Single Answer
The curl of the gradient of a sufficiently smooth scalar field is:
  1. A
    Zero
  2. B
    Unity
  3. C
    Infinite
  4. D
    Equal to its divergence
Question 40Single Answer
A line integral is evaluated along a:
  1. A
    Surface
  2. B
    Volume only
  3. C
    Curve or path
  4. D
    Matrix
Question 41Single Answer
A surface integral is evaluated over a:
  1. A
    Curve
  2. B
    Single point
  3. C
    Surface
  4. D
    Sequence
Question 42Single Answer
The divergence theorem connects a volume integral with a:
  1. A
    Closed surface integral
  2. B
    Fourier series
  3. C
    Line integral only
  4. D
    Matrix determinant
Question 43Single Answer
Stokes' theorem relates a surface integral involving curl to a:
  1. A
    Volume integral
  2. B
    Line integral around the boundary
  3. C
    Matrix equation
  4. D
    Probability distribution
Question 44Single Answer
Green's theorem is primarily applicable to:
  1. A
    Matrix spaces only
  2. B
    Four-dimensional regions
  3. C
    Plane regions
  4. D
    Probability distributions
Question 45Single Answer
A conservative vector field has the important property that its line integral between two fixed points is:
  1. A
    Path dependent
  2. B
    Always negative
  3. C
    Always infinite
  4. D
    Path independent
Question 46Single Answer
The order of a differential equation is determined by the:
  1. A
    Lowest derivative present
  2. B
    Number of variables only
  3. C
    Highest-order derivative present
  4. D
    Number of constants
Question 47Single Answer
The degree of a differential equation is defined with respect to the:
  1. A
    Number of boundary conditions
  2. B
    Independent variable only
  3. C
    Number of terms
  4. D
    Highest-order derivative after the equation is made polynomial in derivatives
Question 48Single Answer
A first-order differential equation contains derivatives of order:
  1. A
    Two as the highest order
  2. B
    One as the highest order
  3. C
    Three as the highest order
  4. D
    Zero only
Question 49Single Answer
A linear differential equation is one in which the dependent variable and its derivatives occur:
  1. A
    Only as trigonometric functions
  2. B
    Only to the first power and are not multiplied together
  3. C
    Only as exponential functions
  4. D
    In arbitrary nonlinear combinations
Question 50Single Answer
A nonlinear differential equation may contain:
  1. A
    Only constant coefficients
  2. B
    Only first-degree polynomial terms
  3. C
    No derivatives
  4. D
    Nonlinear functions or products of the dependent variable and its derivatives
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