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Objective Questions

Latest UP PGT Physical Science Exam Question (Objective Questions), MCQ in English

Subjects : Physical Science, General Studies

Question Bank UP PGT Physical Science Exam - English
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Physical Science

Question 1Single Answer
Which mathematical operation gives the direction of the maximum increase of a scalar field?
  1. A
    Divergence
  2. B
    Gradient
  3. C
    Curl
  4. D
    Circulation
Question 2Single Answer
The gradient of a scalar field is fundamentally what type of quantity?
  1. A
    Scalar
  2. B
    Constant
  3. C
    Matrix
  4. D
    Vector
Question 3Single Answer
Which vector calculus operation measures the net outward flow of a vector field from an infinitesimal region?
  1. A
    Gradient
  2. B
    Curl
  3. C
    Divergence
  4. D
    Directional derivative
Question 4Single Answer
The divergence of a vector field produces which type of quantity?
  1. A
    Scalar
  2. B
    Vector
  3. C
    Matrix
  4. D
    Complex vector
Question 5Single Answer
Which vector calculus operation measures the local rotational tendency of a vector field?
  1. A
    Gradient
  2. B
    Divergence
  3. C
    Curl
  4. D
    Flux
Question 6Single Answer
The curl of a vector field is generally what type of quantity?
  1. A
    Scalar
  2. B
    Eigenvalue
  3. C
    Determinant
  4. D
    Vector
Question 7Single Answer
A vector field whose divergence vanishes everywhere is known as what?
  1. A
    Conservative field
  2. B
    Singular field
  3. C
    Solenoidal field
  4. D
    Scalar field
Question 8Single Answer
A vector field whose curl vanishes everywhere in a region is called what?
  1. A
    Rotational field
  2. B
    Solenoidal field
  3. C
    Irrotational field
  4. D
    Divergent field
Question 9Single Answer
Which theorem converts a volume integral involving divergence into a surface integral?
  1. A
    Gauss's divergence theorem
  2. B
    Stokes' theorem
  3. C
    Cauchy's theorem
  4. D
    Cayley-Hamilton theorem
Question 10Single Answer
Gauss's divergence theorem applies to which type of surface?
  1. A
    Open surface only
  2. B
    Closed surface
  3. C
    Plane curve only
  4. D
    Infinite line only
Question 11Single Answer
Which theorem relates a surface integral of curl to a line integral around the boundary?
  1. A
    Green's theorem
  2. B
    Taylor's theorem
  3. C
    Gauss's theorem
  4. D
    Stokes' theorem
Question 12Single Answer
Stokes' theorem is most directly associated with which pair of concepts?
  1. A
    Flux and divergence
  2. B
    Eigenvalue and eigenvector
  3. C
    Gradient and potential
  4. D
    Circulation and curl
Question 13Single Answer
Green's theorem is primarily formulated for a region in how many dimensions?
  1. A
    One
  2. B
    Infinite
  3. C
    Four
  4. D
    Two
Question 14Single Answer
Which theorem may be regarded as a two-dimensional analogue of Stokes' theorem?
  1. A
    Green's theorem
  2. B
    Residue theorem
  3. C
    Binomial theorem
  4. D
    Cayley-Hamilton theorem
Question 15Single Answer
For a sufficiently smooth vector field, the divergence of its curl has what value?
  1. A
    One
  2. B
    It is always negative
  3. C
    Infinity
  4. D
    Zero
Question 16Single Answer
For a sufficiently smooth scalar field, the curl of its gradient has what value?
  1. A
    It depends only on coordinates
  2. B
    Unity
  3. C
    Infinity
  4. D
    Zero
Question 17Single Answer
Which property is generally associated with a conservative vector field in a simply connected domain?
  1. A
    Nonzero curl everywhere
  2. B
    Infinite divergence
  3. C
    Zero curl
  4. D
    Discontinuous potential
Question 18Single Answer
What is the value of a closed-loop line integral of a conservative vector field?
  1. A
    One
  2. B
    Zero
  3. C
    Always positive
  4. D
    Always infinite
Question 19Single Answer
In a conservative vector field, the line integral between two points depends primarily on what?
  1. A
    Shape of the path
  2. B
    Length of the path
  3. C
    Number of intermediate points
  4. D
    End points
Question 20Single Answer
A scalar potential can most naturally be associated with which type of vector field?
  1. A
    Random field
  2. B
    Conservative field
  3. C
    Singular matrix field
  4. D
    Non-differentiable field
Question 21Single Answer
Which quantity describes the flux per unit volume emerging from a point in a vector field?
  1. A
    Curl
  2. B
    Divergence
  3. C
    Gradient
  4. D
    Circulation
Question 22Single Answer
A positive divergence at a point generally indicates what behavior?
  1. A
    Source-like behavior
  2. B
    Sink-like behavior
  3. C
    Pure rotation only
  4. D
    Zero flux
Question 23Single Answer
A negative divergence at a point generally represents what?
  1. A
    Source
  2. B
    Zero circulation
  3. C
    Constant potential
  4. D
    Sink
Question 24Single Answer
Which operation is most useful for identifying local circulation in a fluid velocity field?
  1. A
    Gradient
  2. B
    Laplace transform
  3. C
    Divergence
  4. D
    Curl
Question 25Single Answer
A fluid velocity field with zero divergence is commonly described as what?
  1. A
    Compressible
  2. B
    Incompressible
  3. C
    Singular
  4. D
    Irregular
Question 26Single Answer
Which product of two vectors results in a scalar quantity?
  1. A
    Cross product
  2. B
    Curl product
  3. C
    Tensor product only
  4. D
    Dot product
Question 27Single Answer
The dot product of two perpendicular vectors has what value?
  1. A
    One
  2. B
    Zero
  3. C
    Maximum positive value
  4. D
    Infinity
Question 28Single Answer
Which product of two vectors produces a vector perpendicular to the plane containing them?
  1. A
    Scalar product
  2. B
    Cross product
  3. C
    Dot product
  4. D
    Inner scalar sum
Question 29Single Answer
The cross product of two parallel vectors has what magnitude?
  1. A
    Infinite
  2. B
    Unity
  3. C
    Maximum
  4. D
    Zero
Question 30Single Answer
Which rule determines the direction of the cross product of two vectors?
  1. A
    Left-hand rule only
  2. B
    Simpson's rule
  3. C
    Lenz's rule
  4. D
    Right-hand rule
Question 31Single Answer
What geometrical quantity is represented by the magnitude of the cross product of two vectors?
  1. A
    Volume of a sphere
  2. B
    Area of a parallelogram
  3. C
    Length of a diagonal
  4. D
    Curvature of a circle
Question 32Single Answer
The scalar triple product of three vectors geometrically represents what?
  1. A
    Area of a triangle
  2. B
    Length of a vector
  3. C
    Volume of a parallelepiped
  4. D
    Angle between two planes only
Question 33Single Answer
If the scalar triple product of three nonzero vectors vanishes, the vectors are what?
  1. A
    Mutually perpendicular
  2. B
    Coplanar
  3. C
    Necessarily parallel
  4. D
    Unit vectors
Question 34Single Answer
Which property does the vector triple product generally possess?
  1. A
    It is associative
  2. B
    It is always scalar
  3. C
    It always vanishes
  4. D
    It is not associative
Question 35Single Answer
Which coordinate system is particularly suitable for problems possessing spherical symmetry?
  1. A
    Cartesian coordinates
  2. B
    Spherical polar coordinates
  3. C
    Plane polar coordinates only
  4. D
    Rectangular matrix coordinates
Question 36Single Answer
Which coordinate system is especially convenient for systems possessing cylindrical symmetry?
  1. A
    Matrix coordinates
  2. B
    Cartesian coordinates only
  3. C
    Complex coordinates
  4. D
    Cylindrical coordinates
Question 37Single Answer
The directional derivative of a scalar field is greatest along which direction?
  1. A
    Opposite to its gradient
  2. B
    Along its gradient
  3. C
    Perpendicular to its gradient
  4. D
    Along every direction equally
Question 38Single Answer
A surface on which a scalar field has a constant value is commonly called what?
  1. A
    Equipotential surface
  2. B
    Rotational surface
  3. C
    Divergence surface
  4. D
    Singular surface
Question 39Single Answer
The gradient of a scalar field is oriented how with respect to its constant-value surfaces?
  1. A
    Tangentially
  2. B
    Parallel to every tangent
  3. C
    Randomly
  4. D
    Normally
Question 40Single Answer
Which theorem is most suitable for calculating the total outward flux through a closed surface using information inside the volume?
  1. A
    Cauchy's theorem
  2. B
    Green's theorem
  3. C
    Gauss's divergence theorem
  4. D
    Residue theorem
Question 41Single Answer
Which mathematical object is an arrangement of elements in rows and columns?
  1. A
    Distribution
  2. B
    Vector field
  3. C
    Contour
  4. D
    Matrix
Question 42Single Answer
A matrix having the same number of rows and columns is called what?
  1. A
    Rectangular matrix
  2. B
    Column matrix
  3. C
    Row matrix
  4. D
    Square matrix
Question 43Single Answer
A matrix whose elements outside the main diagonal are zero is known as what?
  1. A
    Rectangular matrix
  2. B
    Singular matrix
  3. C
    Diagonal matrix
  4. D
    Antisymmetric matrix only
Question 44Single Answer
Which matrix has unity as every diagonal element and zero elsewhere?
  1. A
    Identity matrix
  2. B
    Null matrix
  3. C
    Singular matrix
  4. D
    Antisymmetric matrix
Question 45Single Answer
A square matrix with zero determinant is called what?
  1. A
    Orthogonal matrix
  2. B
    Singular matrix
  3. C
    Identity matrix
  4. D
    Unitary matrix
Question 46Single Answer
Which condition is necessary for an ordinary square matrix to possess a unique inverse?
  1. A
    Its determinant must vanish
  2. B
    Its trace must vanish
  3. C
    Its determinant must be nonzero
  4. D
    Every element must be positive
Question 47Single Answer
The transpose of a matrix is obtained by performing which operation?
  1. A
    Taking every reciprocal
  2. B
    Changing every sign
  3. C
    Interchanging rows and columns
  4. D
    Reversing diagonal elements only
Question 48Single Answer
A real square matrix equal to its transpose is called what?
  1. A
    Antisymmetric matrix
  2. B
    Symmetric matrix
  3. C
    Singular matrix
  4. D
    Nilpotent matrix
Question 49Single Answer
A real square matrix whose transpose equals its negative is known as what?
  1. A
    Symmetric matrix
  2. B
    Skew-symmetric matrix
  3. C
    Identity matrix
  4. D
    Diagonal matrix
Question 50Single Answer
What must the diagonal elements of a real skew-symmetric matrix be?
  1. A
    Unity
  2. B
    Zero
  3. C
    Positive integers
  4. D
    Purely arbitrary nonzero numbers
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