Test: Mathematical Physics - 2 - Physics MCQ

# Test: Mathematical Physics - 2 - Physics MCQ

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## 20 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Mathematical Physics - 2

Test: Mathematical Physics - 2 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The Test: Mathematical Physics - 2 questions and answers have been prepared according to the Physics exam syllabus.The Test: Mathematical Physics - 2 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Mathematical Physics - 2 below.
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Test: Mathematical Physics - 2 - Question 1

### For the function  at the point (1, 2, -1), find its rate of change with distance in the direction

Detailed Solution for Test: Mathematical Physics - 2 - Question 1

Therefore,
Therefore, rate of change with distance in the direction of

Test: Mathematical Physics - 2 - Question 2

### Evaluate the line integral  (exy + cos x sin y) dx + (ex + sin x cos y)dy, around the curve 'C'

Detailed Solution for Test: Mathematical Physics - 2 - Question 2

Note:  . then vector function is conservative and hence line integral (work clone) along a closed path is zero)

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Test: Mathematical Physics - 2 - Question 3

### If a unitary matrix U is written as A + iB, where A and B are Hermitian matrix with non degenerate eigenval­ ues. then

Detailed Solution for Test: Mathematical Physics - 2 - Question 3

Since. U is unitary matrix.

or (A + iB) (A - iB) = I  (since, A and B are Hermitian = B)
A2 + B2 + i(BA - AB) = I
Now. equating real and imaginary
Part. A2 + B2 = I and BA - AB = 0

Test: Mathematical Physics - 2 - Question 4

If (A)nxn is a square matrix, and elements of matrix A(aij) are such that

then value of det (eA) is equal to

Detailed Solution for Test: Mathematical Physics - 2 - Question 4

We know that, det (eA) = etrace A

*Answer can only contain numeric values
Test: Mathematical Physics - 2 - Question 5

If solution y(x), of the differential equation subjected to the boundary conditions y(0) = 2, y'(0) = 1 has the form y(x) = Ae-x + Bex + Ce2x, then the value of A + B - C is
(upto two decimal places)

Detailed Solution for Test: Mathematical Physics - 2 - Question 5

D2 - 3D + 2 = 0
(D - 2) (D - 1) = 0
Therefore, complementary function Bex + Ce2x and

*Answer can only contain numeric values
Test: Mathematical Physics - 2 - Question 6

The range of values ofz, for which the following complex power series converges, is Izl < A, then A is .................. (answer should be an integer)

Detailed Solution for Test: Mathematical Physics - 2 - Question 6

Test: Mathematical Physics - 2 - Question 7

If the matrix  can be diagonalised by a transformation of the form S* AS = A', where S has the normalized eigenvectors of A as its columns, then A' is

Detailed Solution for Test: Mathematical Physics - 2 - Question 7

A' will be a diagonal matrix, whose diagonal elements are the eigenvalues of A.
Therefore, to find eigenvalues of A.

Therefore, eigenvalues are λ = - 2, - 2, 4

Test: Mathematical Physics - 2 - Question 8

If  is the fourier transformation of  then the fourier trans form of f ' (t) is

Detailed Solution for Test: Mathematical Physics - 2 - Question 8

Fourier transfonn of f' (t)

Test: Mathematical Physics - 2 - Question 9

If a complex function f (z) lias a pole of order m at z = z0. then f'(z) has a pole of order

Detailed Solution for Test: Mathematical Physics - 2 - Question 9

where g is analytic at z0 and g(z0) ≠ 0
where h(z) = (z - z0) g'(z) - mg(z) is analytic at z = z0 and h(z0) = - mg (z0) ≠ 0
∴ f' (z) has a pole of order (m + 1) at z = z0.

Test: Mathematical Physics - 2 - Question 10

The inverse laplace transfonn of

Detailed Solution for Test: Mathematical Physics - 2 - Question 10

Using partial fraction.

*Answer can only contain numeric values
Test: Mathematical Physics - 2 - Question 11

If the fourier series for Isin θ| in the range -π < θ < π is given by  then the value of A is .........

Detailed Solution for Test: Mathematical Physics - 2 - Question 11

*Answer can only contain numeric values
Test: Mathematical Physics - 2 - Question 12

Value of the integral

Detailed Solution for Test: Mathematical Physics - 2 - Question 12

Poles are at z = + 2
Therefore, residue at 2 = 2

*Answer can only contain numeric values
Test: Mathematical Physics - 2 - Question 13

If the fourier expansion of   then the value of a2 if

Detailed Solution for Test: Mathematical Physics - 2 - Question 13

Test: Mathematical Physics - 2 - Question 14

If z = xy, where y = tan-1 t and x = sin t, then the value of dz/dt is equal to

Detailed Solution for Test: Mathematical Physics - 2 - Question 14

Test: Mathematical Physics - 2 - Question 15

If y (x) is the solution of the differential equation  with y(1) = -1, then

Detailed Solution for Test: Mathematical Physics - 2 - Question 15

Now, y (1) = -1, put x = 1, y = -1

∴ for y to be defined log x must be defined i.e.. x > 0
Also when log x - 1 = 0, log x = 1
So in the range 0 < x < 3 (option (b)). there will be a point x = 2.73 at whichy is not defined.
Also at x = e : y → ∞ (blow up).

Test: Mathematical Physics - 2 - Question 16

then the value of integral  where ‘S’ is the surface given by z = 12, x2 - y2 < 25 (taken anticlockwise), is

Detailed Solution for Test: Mathematical Physics - 2 - Question 16

∴

Test: Mathematical Physics - 2 - Question 17

The fourier complex transfoem of f(x), where

Detailed Solution for Test: Mathematical Physics - 2 - Question 17

Fourier transform of f (x)

(integrating by parts)

Test: Mathematical Physics - 2 - Question 18

then which of the following statements is true about A and B

Detailed Solution for Test: Mathematical Physics - 2 - Question 18

Since A is upper trinagular and B is lower triangular matrix. Hence, their eigenvalues are the principle diagonal elements.
Therefore, eigenvalues of A are 1, 0, 2 and eigenvalues of B are -1,1, 3
Since eigenvalues of A and B are all distinct, hence their corresponding eigenvectors will be linearly independent.
Hence, both A and B are digonalizable.

Test: Mathematical Physics - 2 - Question 19

The Laplace transform of f (t) = t2 cos at is

Detailed Solution for Test: Mathematical Physics - 2 - Question 19

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Test: Mathematical Physics - 2 - Question 20

The value of the integral  where C is closecl contour defined by the equation 2 |z - 1| - 3 = 0, traversed in the clockwise direction, is _______________________ (answer should be an integers)

Detailed Solution for Test: Mathematical Physics - 2 - Question 20

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