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Objective Questions

Latest CUET PG Physics Exam Question (Objective Questions), MCQ in English

Subjects : Physics

Question Bank CUET PG Physics Exam - English
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Physics

Question 1Single Answer
The derivative of a function at a point geometrically represents:
  1. A
    Area under the curve
  2. B
    Slope of the tangent
  3. C
    Curvature only
  4. D
    Length of the curve
Question 2Single Answer
A function is differentiable at a point only if it is:
  1. A
    Discontinuous there
  2. B
    Periodic there
  3. C
    Continuous there
  4. D
    Even there
Question 3Single Answer
Continuity of a function at a point is:
  1. A
    Sufficient but not necessary for differentiability
  2. B
    Necessary but not sufficient for differentiability
  3. C
    Neither necessary nor sufficient
  4. D
    Equivalent to differentiability
Question 4Single Answer
A local maximum of a differentiable function at an interior point generally occurs where:
  1. A
    The function diverges
  2. B
    The first derivative vanishes
  3. C
    The independent variable vanishes
  4. D
    The function is discontinuous
Question 5Single Answer
At a stationary point, the:
  1. A
    Function must vanish
  2. B
    Second derivative always vanishes
  3. C
    First derivative vanishes
  4. D
    Function must be maximum
Question 6Single Answer
If the second derivative at a stationary point is positive, the point is generally a:
  1. A
    Local maximum
  2. B
    Local minimum
  3. C
    Point of discontinuity
  4. D
    Vertical asymptote
Question 7Single Answer
If the second derivative at a stationary point is negative, the point is generally a:
  1. A
    Local maximum
  2. B
    Local minimum
  3. C
    Saddle point necessarily
  4. D
    Point of inflection necessarily
Question 8Single Answer
A point of inflection is associated with a change in:
  1. A
    Concavity
  2. B
    Domain
  3. C
    Period
  4. D
    Range only
Question 9Single Answer
Rolle's theorem requires the function to have equal values at:
  1. A
    The two endpoints
  2. B
    Every point
  3. C
    The midpoint only
  4. D
    All stationary points
Question 10Single Answer
Rolle's theorem guarantees at least one interior point where:
  1. A
    The function vanishes
  2. B
    The second derivative vanishes
  3. C
    The derivative vanishes
  4. D
    The function is discontinuous
Question 11Single Answer
The Mean Value Theorem is applicable when a function is continuous on a closed interval and:
  1. A
    Periodic on the interval
  2. B
    Odd on the interval
  3. C
    Differentiable on its open interval
  4. D
    Bounded by unity
Question 12Single Answer
The fundamental theorem of calculus establishes a connection between:
  1. A
    Differentiation and integration
  2. B
    Matrices and determinants
  3. C
    Vectors and scalars
  4. D
    Fourier and Taylor series
Question 13Single Answer
An indefinite integral represents:
  1. A
    A single number only
  2. B
    A determinant
  3. C
    A family of antiderivatives
  4. D
    A vector field
Question 14Single Answer
The constant of integration appears in:
  1. A
    Definite integration only
  2. B
    Indefinite integration
  3. C
    Partial differentiation only
  4. D
    Matrix inversion
Question 15Single Answer
Integration by parts is based on the differentiation rule for:
  1. A
    A product
  2. B
    A quotient
  3. C
    An inverse
  4. D
    A determinant
Question 16Single Answer
Substitution in integration is closely related to the:
  1. A
    Chain rule
  2. B
    Product rule
  3. C
    Cramer's rule
  4. D
    Divergence theorem
Question 17Single Answer
An improper integral arises when:
  1. A
    Every limit is finite and the integrand is bounded
  2. B
    A limit is infinite or the integrand becomes unbounded
  3. C
    The function is polynomial
  4. D
    The integrand is constant
Question 18Single Answer
A convergent improper integral has:
  1. A
    No limiting value
  2. B
    An infinite determinant
  3. C
    A finite limiting value
  4. D
    A periodic derivative
Question 19Single Answer
For a function of two independent variables, the partial derivative with respect to one variable is obtained by:
  1. A
    Varying all variables equally
  2. B
    Holding the other variable fixed
  3. C
    Setting the other variable to zero
  4. D
    Integrating the other variable
Question 20Single Answer
A total differential accounts for changes in:
  1. A
    One independent variable only
  2. B
    All relevant independent variables
  3. C
    Dependent variables only
  4. D
    Constants only
Question 21Single Answer
For sufficiently smooth functions, mixed partial derivatives are:
  1. A
    Always unequal
  2. B
    Always zero
  3. C
    Equal under suitable continuity conditions
  4. D
    Undefined
Question 22Single Answer
The gradient of a scalar function of several variables is formed from its:
  1. A
    Integrals
  2. B
    First partial derivatives
  3. C
    Second integrals
  4. D
    Determinants only
Question 23Single Answer
A critical point of a function of two variables occurs when:
  1. A
    Its value is unity
  2. B
    Its integral diverges
  3. C
    Its mixed derivative alone vanishes
  4. D
    Its first partial derivatives vanish
Question 24Single Answer
The second derivative test for a function of two variables commonly uses:
  1. A
    The curl
  2. B
    The Hessian
  3. C
    The trace of a vector
  4. D
    Green's theorem
Question 25Single Answer
A saddle point is a point that behaves locally like:
  1. A
    A maximum in some directions and a minimum in others
  2. B
    A minimum in all directions
  3. C
    A maximum in all directions
  4. D
    A discontinuity in every direction
Question 26Single Answer
The Hessian matrix consists of:
  1. A
    First derivatives only
  2. B
    Vector products
  3. C
    Definite integrals
  4. D
    Second partial derivatives
Question 27Single Answer
The chain rule for multivariable functions is especially useful for:
  1. A
    Composite functions
  2. B
    Constant functions only
  3. C
    Singular matrices only
  4. D
    Divergence-free fields only
Question 28Single Answer
Lagrange multipliers are used mainly for finding:
  1. A
    Constrained extrema
  2. B
    Fourier coefficients
  3. C
    Matrix eigenvalues only
  4. D
    Complex conjugates
Question 29Single Answer
In the method of Lagrange multipliers, the gradient of the objective function at a constrained extremum is:
  1. A
    Parallel to the gradient of the constraint
  2. B
    Perpendicular to the gradient of the constraint
  3. C
    Always zero independently
  4. D
    Equal to the curl
Question 30Single Answer
A directional derivative describes the rate of change of a scalar field:
  1. A
    Over a closed surface
  2. B
    Only along the x-axis
  3. C
    Only along the normal
  4. D
    Along a specified direction
Question 31Single Answer
The largest directional derivative of a differentiable scalar field occurs in the direction of:
  1. A
    Curl
  2. B
    Divergence
  3. C
    Gradient
  4. D
    Laplacian
Question 32Single Answer
The gradient at a point is perpendicular to:
  1. A
    The corresponding level surface
  2. B
    Every coordinate axis
  3. C
    Every vector
  4. D
    The origin
Question 33Single Answer
The Laplacian of a scalar field involves:
  1. A
    First derivatives only
  2. B
    Line integrals only
  3. C
    Cross products only
  4. D
    Second spatial derivatives
Question 34Single Answer
A homogeneous function possesses a scaling property expressed by:
  1. A
    Cramer's rule
  2. B
    Green's theorem
  3. C
    Euler's theorem
  4. D
    Stokes' theorem
Question 35Single Answer
Euler's theorem for homogeneous functions relates the function to:
  1. A
    Its Fourier coefficients
  2. B
    Its determinant only
  3. C
    Its first partial derivatives
  4. D
    Its complex conjugate
Question 36Single Answer
A multivariable function is continuous at a point when its limit:
  1. A
    Depends on the path
  2. B
    Does not exist
  3. C
    Is infinite along one path
  4. D
    Is independent of the path and equals the function value
Question 37Single Answer
Path dependence of a multivariable limit indicates that the limit:
  1. A
    Exists
  2. B
    Must be unity
  3. C
    Must be zero
  4. D
    Does not exist
Question 38Single Answer
The differential of a differentiable multivariable function provides:
  1. A
    Its inverse matrix
  2. B
    An exact Fourier expansion
  3. C
    A linear approximation to its change
  4. D
    Its circulation
Question 39Single Answer
A double integral is commonly used to calculate:
  1. A
    Only quantities on a curve
  2. B
    Quantities distributed over an area
  3. C
    Only quantities at a point
  4. D
    Matrix rank
Question 40Single Answer
A triple integral is commonly associated with integration over:
  1. A
    A line
  2. B
    A volume
  3. C
    A surface only
  4. D
    A single point
Question 41Single Answer
Fubini's theorem allows a multiple integral to be evaluated as:
  1. A
    A vector product
  2. B
    A determinant only
  3. C
    A Fourier transform
  4. D
    Iterated integrals under suitable conditions
Question 42Single Answer
Changing the order of integration is often useful for:
  1. A
    Changing a scalar to a vector
  2. B
    Simplifying the integration region or integrand
  3. C
    Making the determinant singular
  4. D
    Eliminating all limits
Question 43Single Answer
In a change of variables for multiple integration, the scaling factor is provided by:
  1. A
    Curl
  2. B
    Trace
  3. C
    Jacobian
  4. D
    Eigenvector
Question 44Single Answer
The Jacobian is fundamentally a:
  1. A
    Line integral
  2. B
    Sum of second derivatives
  3. C
    Determinant of first partial derivatives
  4. D
    Vector cross product
Question 45Single Answer
A nonzero Jacobian near a point generally indicates that the coordinate transformation is:
  1. A
    Constant everywhere
  2. B
    Necessarily singular
  3. C
    Locally invertible
  4. D
    Divergence-free
Question 46Single Answer
For inverse coordinate transformations, the corresponding Jacobians are generally:
  1. A
    Equal to zero
  2. B
    Reciprocals when defined
  3. C
    Always identical
  4. D
    Always negative
Question 47Single Answer
The Jacobian becomes particularly important when:
  1. A
    Changing variables in multiple integrals
  2. B
    Finding only complex conjugates
  3. C
    Computing dot products
  4. D
    Solving only linear algebraic equations
Question 48Single Answer
A perfect differential is also called:
  1. A
    A singular differential
  2. B
    An exact differential
  3. C
    A Fourier differential
  4. D
    A vector differential
Question 49Single Answer
An exact differential is associated with:
  1. A
    A singular matrix
  2. B
    A non-conservative field necessarily
  3. C
    A well-defined scalar potential function
  4. D
    A divergent Fourier series
Question 50Single Answer
For an exact differential in two variables, an important condition involves equality of:
  1. A
    Appropriate cross partial derivatives
  2. B
    Both independent variables
  3. C
    All coefficients
  4. D
    Both integration limits
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