Skip to content

Home
Subjects
Login
Register

Open test — no login required.

Physics — Unit 1 — Test 4

--:--

Cutoff (GEN): 70%

1/10

1

For f(x)=x on (−π,π), Fourier series contains

A

Both

B

Only sine terms

C

Only cosine terms

D

Diverges

2

Shift property: g(x)=f(x−x0) ⇒ G(ω)=

A

F(ω)+x0

B

e^{−iω x0} F(ω)

C

F(ω−x0)

D

e^{iω x0} F(ω)

3

Differentiation: F{f'}(ω) equals

A

F(ω)

B

ω^2 F(ω)

C

iω F(ω)

D

−iω F(ω)

4

General solution of y''−6y'+9y=0 is

A

C1 e^{9x}+C2

B

(C1+C2 x)e^{3x}

C

C1 e^{3x}+C2 e^{−3x}

D

C1 cos3x + C2 sin3x

5

For f(x)=cos(1x), complex Fourier coefficients c_n on (−π,π) are

A

All c_n=0

B

c_k=1, c_{−k}=0

C

c_{±k}=1

D

c_{±k}=1/2 and others 0

6

MGF of Poisson(λ) is

A

exp(λ t)

B

1/(1−λ t)

C

exp(t^2/2)

D

exp(λ(e^{t}−1))

7

For f(x)=cos(5x), complex Fourier coefficients c_n on (−π,π) are

A

c_k=1, c_{−k}=0

B

All c_n=0

C

c_{±k}=1/2 and others 0

D

c_{±k}=1

8

MGF of Poisson(λ) is

A

exp(t^2/2)

B

1/(1−λ t)

C

exp(λ(e^{t}−1))

D

exp(λ t)

9

For f(x)=cos(9x), complex Fourier coefficients c_n on (−π,π) are

A

c_k=1, c_{−k}=0

B

c_{±k}=1

C

c_{±k}=1/2 and others 0

D

All c_n=0

10

MGF of Poisson(λ) is

A

exp(λ t)

B

exp(λ(e^{t}−1))

C

exp(t^2/2)

D

1/(1−λ t)

Result

Loading…

Your Score

—

Percentage

—%

Cutoff

70%

Rank

—

Test Analysis

Your History

Loading…

Leaderboard

No scores yet.

View Explanations Retake Test

Select Community (affects cutoff):

Your Score

—

Percentage

—%

Cutoff

70%

Time Used

—

Attempt Analysis

Explanations

Detailed solutions for your latest run.

Loading…

Back to Result Retake Test

Explanation

Loading…