11 Official GATE PH Questions with Verified Solutions & Answer Keys
The inverse Laplace transform $\mathcal{L}^{-1}\left\{ \frac{s}{s^2 + 4} \right\}$ is...
for x < 3, ihen the Laplace transform of f(x) is 11 () =fx-3 forx23, (A) 833 (B) s'e" (C) 52 (D) 5*e-"...
Which of the following pairs of the given function F(t) and its Laplace transform f (s) is NOT CORRECT?...
For a free electron gas in two dimensions, the variation of the density of states, 𝑁𝑁(𝐸𝐸) as a function of energy E, is best represented by (A) (B) (C) (D) N(E) E N(E) E N(E) E...
f+1 fort> 0 The Heaviside function is defined as H (t) = 1-1 fort <0 - 21/c. The Fourier transform of - 1(1+1/2) - 17(1-1/2) is and its Fourier transform is given by (A) (0) sin(;)...
A periodic function f (x) of period 2m is defined in the interval (-n < x < 1t) as: F(x) =51:-0≤*500 0 <X<П The appropriate Fourier series expansion for f (x) is...
As shown in the figure, X-ray diffraction pattern is obtained from a diatomic chain of atoms P and Q. The diffraction condition is given by a cos 0 = n2, where n is the order of th...
Consider a spinS - /z particle in the state lp) - 117 . The probability that a measurement finds the state with Sx = +h/2 is (A) | 5/18 (B) | 11/18 (C) | 15/18 (D) 17/18...
A function f(t) is defined only for t ≥ 0. The Laplace transform of f(t) is £(f;s) = e-st f(t) dt whereas the Fourier transform of f(t) is f(a) = Jo F(t) e it dt. The correct state...
If g(k) is the Fourier transform of f(x), then which of the following are true?...
The Fourier transform and its inverse transform are respectively defined as f ̃ (\omega) = 1 √2𝜋 ∫ f(x)ei\omegaxdx +∞ -∞ and f(x) = 1 √2𝜋 ∫ f ̃ (\omega)e-i\omegaxd\omega +∞ -∞ . ...