Methods of Mathematical Physics-I - Quanta: BS/MSc Physics Books

1: What is the magnitude of unit vector

a. It has no magnitude

b. Zero

c. Constant but not zero

d. Unity

2: Flying a bird is the example of

a. Collinear vector

b. Multiplication of vector

c. Addition of vector

d. Composition of vector

3: Cross product is the mathematical operation performed between

a. 2 scaler numbers

b. A scaler and a vector

c. 2 vectors

d. Any 2 numbers

4: The mathematical perception of the gradient is said to be

a.Tangent

b. Chord

c. Slope

d. Arc

5: Gauss theorem uses which of the following operations

a. Gradient

b. Divergence

c. Laplacian

d. Curl

6: Which of the following operation uses the curl operation

a. Greens theorem

b. Gauss divergence theorem

c. Stoke’s theorem

d. Maxwell equation

7: Find the curl of A=(ycosax)i+(y+e^x)k

a. $2i-exj-cosaxk$

b. $\mathbf{i-exj-cosaxk}$

c. $2i-exj+cosaxk$

d. $i-exj+cosaxk$

8: Mathematically the function in the green theorem will be

a. Continuous derivative

b. Discrete derivative

c. Continuous partial derivatives

d. Discrete partial derivatives

9: The first member in ordered pair is considered as

a. Mantissa

b. Cartesian coordinates

c. Abscissa

d. Ordinate

10: Example of spherical system in the following is

a. Charge in space

b. Charge in box

c. Charge in dielectric

d. Uncharged system

11: Tensor are associated with

a. Magnitude only

b. Magnitude and direction

c. Magnitude and two or more than two directions

d. Magnitude and two directions

12: Which of the following quantity is example of vector quantity

a. Temperature

b. Velocity

c. Volume

d. Mass

13: Kronecker delta is usually a function of two

a. Positive integer

b. Non negative integer

c. Both a & b

d. One negative and one positive integer

14: In probability theory and statistics, the Kronecker delta and Dirac delta function both are used to represent

a. Variable distribution

b. Discrete distribution

c. Uniform distribution

d. None of these

15: The example of symmetric tensor is

a. Einstein tensor

b. Metric tensor

c. Ricci tensor

d. All of these

16: Anti symmetrization tensor is denoted by

a. ()

b. {}

c. []

d. II

17: Multiplying or dividing vector by scalers results in

a. Vectors if multiplied or scalers if divided

b. scaler if multiplied scalers

c. Scalers

d. Vectors

18: The coordinates $(x\prime,\ y\prime,\ z \prime)$ & $(x,\ y,\ z)$ of any point relative to two system of coordinates axis can be written in form of each other using

a. Sines

b. Cosines

c. Direction cosines

d. Direction sines

19: If A_ijk and B_pq two tensors of rank 3 and 2 respectively then their inner product is a tensor of rank

a. 2

b. 5

c. 3

d. 1

20: Which symbol represents substitution operator

a. $\mathbf{\delta_{ij}}$

b. $\epsilon_{ij}$

c. $\epsilon_{ijk}$

d. None of these

21: Matrix is a · · · word which means place in which something develops or originates

a. Latin

b. Arabic

c. Greek

d. German

22: Who introduce term Matrix

a. James Sylvester

b. Arthur Cayley

c. Girolamo cardano

d. Paul erodes

23: The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along

a. Leading diagonal

b. Last column

c. Last row

d. Non leading diagonal

24: In Jacobi’s identity Sum of the cyclic permutation of the double poison bracket of three function is

a. Positive integer

b. Non negative integer

c. Both a & b

d. Zero

25: if we multiply any matrix A with identity matrix the we get the , · · · matrix

a. Identity Matrix

b. Scaling Matrix

c. Original Matrix

d. Translation Matrix

26: The transformation that changes the coordinate position of an object along a circular path is called · · ·

a. Translation

b. Scaling

c. Rotation

d. Reflection

27: Which of the following property of matrix multiplication is correct

a. Multiplication is not commutative in general

b. Multiplication is distributive over addition

c. Multiplication is associative

d. All of these

29: What is Eigen value

a. A vector obtains from coordinates

b. A matric determined from algebraic equation

c. A scaler associated with a given linear transformation

d. It is the inverse of the transform

30: if A and B are two matrices, then which from the following is true

a. $A+B\neq B+A$

b. $\left(A^t\right)^t\neq A$

c. $\mathbf{AB\neq BA}$

d. All are true

31: The monoid is a

a. Groupoid

b. A non-abelian group

c. Group

d. A commutative group

32: How many properties can be held by a group

a. 2

b. 3

c. 5

d. 4

33: A homomorphism which is one to one and onto is called

a. Endomorphism

b. Monomorphism

c. Isomorphism

d. Epimorphism

34: If f: $G\ \rightarrow\ G^\prime$ is onto homomorphism then

a. $G^\prime\ is\ image\ of\ G$

b. $G\ is\ image\ of\ G\prime$

c. $\mathbf{G^\prime}$ is homomorphic image of

d. G’ is isomorphic image of

35: Every homomorphic image of a group G is isomorphic to a quotient group of G, it is called

a. 1st theorem of homomorphism

b. 2nd theorem of homomorphism

c. 3rd theorem of homomorphism

d. 1st theorem of isomorphism

36: An isomorphism of a group onto itself is called

a. Isomorphism

b. Automorphism

c. Equimorphism

d. Homomorphism

37: What is an inverse of -i in the multiplicative group if 1, -1, i, -i is

a. −1

b. 1

c. i

d. None of these

38: The orthogonal matrix is denoted by

a. O

b. A

c. O₂

d. None of these

39: The transpose of the orthogonal matrix is

a. Octahedral matrix

b. Diagonal Matrix

c. Unitary Matrix

d. Orthogonal

40: The product of a matrix and its transpose gives the identity value is called

a. Unitary matrix

b. Diagonal Matrix

c. Octahedral Matrix

d. Orthogonal

41: The value of $\sqrt{(-16)}$ is

a. -4i

b. 4i

c. -2i

d. 2i

42: Let Z be a complex number such that $\mathbf{|Z|=4\ and\ arg(Z)=\frac{5\pi}{6}, }$ , then

a. $-2\sqrt3+2i$

b. $2\sqrt3+2i$

c. $2\sqrt3-2i$

d. $-\sqrt3+i$

43: A function which is analytic, is also called

a. Holomorphic function

b. Harmonic function

c. Differential function

d. None of these

44: An analytic function with constant argument is

a. Not constant

b. Constant

c. Analytic

d. None of these

45: The elementary functions are not closed under

a. Parenthesis

b. Integration

c. Differentiation

d. Brackets

46: If e^ax cos y is harmonic, then a is

b. 0

c. −1

d. 2

47: The harmonic conjugate of $2x-x^3+3xy^2$ is

a. $x-3x^2y+y^3$

b. $\mathbf{2y-3x^2y+y^3}$

c. $y+3x^2y+y^3$

d. $2y+3x^2y-y^3$

48: The Taylor series expansion of $\mathbf{\frac{1}{Z-2}, |Z| <}$ is

a. $-\frac{1}{2}\ (1\ -\frac{Z}{2}+\frac{Z^2}{4}-\frac{Z^3}{8})$

b. $\mathbf{-\frac{1}{2}\ (1\ +\frac{Z}{2}\ +\frac{Z^2}{4}+\frac{Z^3}{8})}$

c. $-\frac{1}{2}\ (1-\frac{Z}{2}-\frac{Z^2}{4}+\frac{Z^3}{8})$

d. $x\ -\frac{1}{2}\ (1+\frac{Z}{2}-\frac{Z^2}{4}-\frac{Z^3}{8})$

49: If principle part of the Laurent’s series vanishes, then the Laurent’s series reduces to

a. Cauchy series

b. Maclaurin’s series

c. Taylor’s series

d. None of these

50: Residue at $z=2 \ of \ f \left(Z\right)=\frac{2Z+1}{Z^2-Z-2}$ is

a. $\frac{\mathbf{5}}{\mathbf{3}}$

b. $\frac{1}{3}$

c. $\frac{3}{5}$

d. $\frac{2}{3}$

MCQ's with Answers

1: What is the magnitude of unit vector

2: Flying a bird is the example of

3: Cross product is the mathematical operation performed between

4: The mathematical perception of the gradient is said to be

5: Gauss theorem uses which of the following operations

6: Which of the following operation uses the curl operation

7: Find the curl of A=(ycosax)i+(y+ex)k

8: Mathematically the function in the green theorem will be

9: The first member in ordered pair is considered as

10: Example of spherical system in the following is

11: Tensor are associated with

12: Which of the following quantity is example of vector quantity

13: Kronecker delta is usually a function of two

14: In probability theory and statistics, the Kronecker delta and Dirac delta function both are used to represent

15: The example of symmetric tensor is

16: Anti symmetrization tensor is denoted by

17: Multiplying or dividing vector by scalers results in

19: If Aijk and Bpq two tensors of rank 3 and 2 respectively then their inner product is a tensor of rank

20: Which symbol represents substitution operator

21: Matrix is a · · · word which means place in which something develops or originates

22: Who introduce term Matrix

23: The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeroes along

24: In Jacobi’s identity Sum of the cyclic permutation of the double poison bracket of three function is

25: if we multiply any matrix A with identity matrix the we get the , · · · matrix

26: The transformation that changes the coordinate position of an object along a circular path is called · · ·

27: Which of the following property of matrix multiplication is correct

29: What is Eigen value

30: if A and B are two matrices, then which from the following is true

31: The monoid is a

32: How many properties can be held by a group

33: A homomorphism which is one to one and onto is called

35: Every homomorphic image of a group G is isomorphic to a quotient group of G, it is called

36: An isomorphism of a group onto itself is called

37: What is an inverse of -i in the multiplicative group if 1, -1, i, -i is

38: The orthogonal matrix is denoted by

39: The transpose of the orthogonal matrix is

40: The product of a matrix and its transpose gives the identity value is called

43: A function which is analytic, is also called

44: An analytic function with constant argument is

45: The elementary functions are not closed under

46: If eax cos y is harmonic, then a is

49: If principle part of the Laurent’s series vanishes, then the Laurent’s series reduces to

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7: Find the curl of A=(ycosax)i+(y+e^x)k

19: If A_ijk and B_pq two tensors of rank 3 and 2 respectively then their inner product is a tensor of rank

46: If e^ax cos y is harmonic, then a is