Engineering Physics · all questions

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Q41

Open question

The points, where the series solution of the Legendre differential equation

(1 - x^{2}) \frac{d ^{2} y}{d x ^{2}} - 2 x \frac{d y}{d x} + \frac{3}{2} (\frac{3}{2} + 1) y = 0

will diverge, are located at

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Q42

Open question

All solutions of the equation e^z = -3 are

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Q43

Open question

The solution of the system of differential equations

\frac{d y}{d x} = y - z

and

\frac{d z}{d x} = - 4 y + z

is given by (for A and B are arbitrary constants)

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Q44

Open question

The value of the integral

C \int \frac{e ^{z}}{z ^{2} - 3 z + 2} d z,

where the contour C is the circle

∣ z ∣ = \frac{3}{2}

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Q45

Open question

Inverse Laplace transform of

\frac{s + 1}{s ^{2} - 4}

is .

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Q46

Open question

Consider the Bessel equation

(v = 0), \frac{d ^{2} y}{d z ^{2}} + \frac{1}{z} \frac{d y}{d z} + y = 0.

Which one of the following statements is correct?

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Q47

Open question

F [f (x)] = \int_{- \infty}^{\infty} f (x) e^{- ik x} d x,

then

F^^{2} [f (x)]

is equal to

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Q48

Open question

The value of the integral

C \int z^{10} d z,

where C is the unit circle with the origin as the centre is

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Q49

Open question

If u (x, y, z, t) = f(x + iβy - vt) + g(x - iβy - vt), where f and g are arbitrary and twice differentiable functions, is a solution of the wave equation

\frac{\partial u ^{2}}{\partial x ^{2}} = \frac{\partial ^{2} u}{\partial y ^{2}} = \frac{1}{c ^{2}} \frac{\partial ^{2} u}{\partial t ^{2}}

then β is

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Q50

Open question

The average of the function f(x) = sin x in the interval (0, π) is

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Q51

Open question

For a physical system, two observables O₁ and O₂ are known to be compatible. Choose the correct implication from amongst those given below.

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Q52

Open question

A vector

A = (5 x + 2 y) i^+ (3 y - z) j^+ (2 x - a z) k^

is solenoidal, if the constant a has a value

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Q53

Open question

The Fourier transform of the function f(x) is

F (k) = \int e^{ik x} f (x) d x .

The Fourier transform of

\frac{df ( x )}{d x}

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Q54

Open question

The solution of the differential equation

(1 + x) \frac{d ^{2} y ( x )}{d x ^{2}} + x \frac{d y ( x )}{d x} - y (x) = 0

is
where A and B are constants

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Q55

Open question

A 3 × 3 matrix has eigen values 0, 2 + i and 2 - i. Which one of the following statement is correct?

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Q56

Open question

The value of the residue of

\frac{sin z}{z ^{6}}

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Q57

Open question

Which one of the following curves gives the solution of the differential equation

k_{1} \frac{d x}{d t} + k_{2} x = k_{3},

where k₁, k₂ and k₃ are positive constant with initial conditions x = 0 and t = 0?

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Q58

Open question

The eigen values and eigen vectors of the matrix

\left[ {\begin{array}{*{20}{c}} 5&4 \\ 1&2 \end{array}} \right]

are

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Q59

Open question

If a force

F

is derivable from a potential function V(r), where r is the distance from the origin of the coordinate system, it follows that

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Q60

Open question

If two matrices A and B can be diagonalized simultaneously, which of the following is true?

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Mathematical Physicspractice.

Mathematical Physics
practice.