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

The solutions to the differential equation dydx=xy+1 are a family of

Choices

Choice (4) Response

a.

Circles with different radii

b.

Circles with different centers

c.

Straight lines with different slopes

d.

Straight lines with different intercepts on the yaxis

Question number: 4

» 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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