Mathematical Physics-Linear Vector Space (GATE Physics): Questions 1 - 3 of 4

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Question number: 1

» Mathematical Physics » Linear Vector Space » Orthogonality and Completeness

Appeared in Year: 2012

MCQ▾

Question

Identify the correct statement for the vectors a=3i^+2j^ and b=i^+2j^

Choices

Choice (4) Response

a.

The vectors a and b linearly dependent

b.

The vectors a and b are orthogonal

c.

The vectors a and b are normalized

d.

The vectors a and b are linearly independent

Question number: 2

» Mathematical Physics » Linear Vector Space » Basis

Appeared in Year: 2013

MCQ▾

Question

Γ(n+12) is equal to –

[Given Γ(n+1)=nΓ(n) and Γ(12)=π ]

Choices

Choice (4) Response

a.

n!22nπ

b.

2n!n!22nπ

c.

2n!n!2nπ

d.

n!2nπ

Question number: 3

» Mathematical Physics » Linear Vector Space » Basis

Appeared in Year: 2011

MCQ▾

Question

Consider a cylinder of height h and radius a , closed at both ends, centered at the origin, Let r=i^x+j^y+k^z be the position vector and n^ a unit vector normal to the surface. The surface integral srn^ds over the closed surface of the cylinder is

Ellipse c Ellipse c: Ellipse with foci A, B passing through CEllipse c_1 Ellipse c_1: Ellipse with foci A_1, B_1 passing through C_1Segment f Segment f: Segment [A, A_1] Segment g Segment g: Segment [B, B_1] Vector u Vector u: Vector [D, E] Vector u Vector u: Vector [D, E] Vector v Vector v: Vector [D, F] Vector v Vector v: Vector [D, F] Vector w Vector w: Vector [D, G] Vector w Vector w: Vector [D, G] Z text1 = “Z”Y text1_1 = “Y”X text1_2 = “X”O text1_3 = “O”

a Cylinder of Closed Ends

In figure a cylinder of height h and radius a, closed at both ends, centered at the origin.

Choices

Choice (4) Response

a.

3πa2h

b.

Zero

c.

2πa2h

d.

2πa2(a+h)

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