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Physics — Unit 1 — Test 3

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Cutoff (GEN): 70%

1/10

1

Stokes’ theorem requires

A

Oriented smooth surface S with boundary C and F of class C^1 near S

B

Only planar surfaces

C

Non-orientable surfaces allowed

D

∇·F=0

2

Gauss’ divergence theorem may fail if

A

Volume is bounded

B

F is C^1 on closure

C

F has non-integrable singularities inside volume

D

Boundary is piecewise smooth

3

For A=[[2,1],[0,2]], e^{At} equals

A

e^{2t}[[1,0],[t,1]]

B

[[e^{2t},t],[0,e^{2t}]]

C

[[e^{2t},0],[0,e^{2t}]]

D

e^{2t}[[1,t],[0,1]]

4

Real symmetric matrices are always

A

Defective

B

Diagonalizable by an orthogonal matrix

C

Only triangularizable

D

Diagonalizable only with distinct eigenvalues

5

For A=[[0,−1],[1,0]], eigenvalues are

A

±i

B

0,0

C

±1

D

i,2i

6

Γ(1/2) equals

A

√π

B

π

C

1

D

2

7

Beta–Gamma relation is

A

B(x,y)=Γ(x+y)

B

B(x,y)=Γ(x)Γ(y)

C

B(x,y)=Γ(x)Γ(y)/Γ(x+y)

D

B(x,y)=Γ(x)/Γ(y)

8

Order of pole of f(z)=e^{1/z}/z^3 at z=0 is

A

1

B

2

C

Essential singularity

D

3

9

Fourier transform of e^{−a x^2} (a>0) is

A

√(π/a) e^{−ω^2/(4a)}

B

(1/√a) e^{−ω^2}

C

√(a/π) e^{−ω^2/(4a)}

D

e^{−a ω^2}

10

For even f, its Fourier series has

A

Both nonzero generally

B

b_n=0

C

a_n=0

D

a_0=0

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#1	User 0	20%	September 9, 2025

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