Mathematical Physics-Linear Vector Space (GATE Physics): Questions 4 - 5 of 5

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Question number: 4

» Mathematical Physics » Linear Vector Space » Orthogonality and Completeness

Appeared in Year: 2010

MCQ▾

Question

Given the recurrence relation for the Legendre polynomials (2n+1)xPn(x)=(n+1)Pn+1(x)+nPn1(x) , which of the following integrals has a non – zero value?

Choices

Choice (4) Response

a.

1+1xPn(x)Pn+2(x)dx

b.

1+1x2Pn(x)Pn+2(x)dx

c.

1+1x2Pn(x)Pn+1(x)dx

d.

1+1x[Pn(x)]2dx

Question number: 5

» Mathematical Physics » Linear Vector Space » Basis

Appeared in Year: 2007

MCQ▾

Question

Consider a vector p=2i^+3j^+2k^ in the coordinate system (i^,j^,k^) . The axes are rotated anti – clock wise about the Y axis by an angle of 60° . The vector p in the rotate coordinate system (i^,j^,k^) is –

Choices

Choice (4) Response

a.

(13)i^+3j^+(1+3)k^

b.

(1+3)i^+3j^+(13)k^

c.

(13)i^+(33)j^+2k^

d.

(13)i^+(3+3)j^+2k^

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