Question47:-The eigen values of the matrix `[[4.-2].[-2.1 are
:-1, 4

C:-0,5

D:-Cannot be determined

Correct Answer:- Option-C
Question48:-Let *V* be a finite dimensional vector space, *I" be the identity transformation on *V* , then the null space
07186

A

المج
‎D:-None of the above‏
‎Correct Answer:- Option-A‏
‎४ 15 2 vector space with dim "V=n" , then the dimension of the hyperspace of ഗ്‌ 5‏ ` :20650049
‎കന്‌‏
‎B:-'n-1"‏
‎ம்‌‏
‎D:-0‏
‎Correct Answer:- Option-B‏
‎Question50:-Let *V* 06 8 vector space of all 2 x 2 matrices over 'R” . Let *T" be the linear mapping *T: V-> V" such that‏
ئا ‎T (A)= AB-BA”™ where "B = [[2,1],[0,3]]' . Then the nullity of *T"‏
يم
2-:8
6:3
‎D:-4‏
‎Correct Answer:- Option-A‏
‎Question51:-Banach space is a‏
‎A:-Complete normed vector space‏
‎B:-Normed vector space‏
‎C:-Complete vector space‏
‎D:-None of the above‏
‎Correct Answer:- Option-A‏
‎Question52:-Which of the following is true?‏
‎A:-All normed spaces are inner product spaces‏
‎B:-All inner product spaces are normed spaces‏
‎C:-All inner product spaces are Banach spaces‏
‎D:-All inner product spaces are Hilbert spaces‏
‎Correct Answer:- Option-B‏
‎Question53:-Banach space is a Hilbert space if‏
‎A:-Pythagorean theorem holds‏
‎B:-Projection theorem holds‏
‎C:-Parallelogram law holds‏
‎D:-None of the above‏
‎Correct Answer:- Option-C‏
‎Question54:-If *T" is a bounded linear operator on a Hilbert space *H‏
‎കട? is normal ரி is self-adjoint‏
‎೧೦೧7೫೩1177 is unitary‏ 8 8:7
‎லோ கண்க is normal‏
‎D:-None of the above‏
‎Correct Answer:- Option-C‏
‎Question55:-The equation of the normal at the point ` (त sec Theta, b tanTheta)® on the hyperbola * (x~2)/(a”~2)- #^2)/{0^2)}‏
5ا ‎௨1‏
‎ക 00/(8) ടട൦ 15 - 00) (೫೧ 77608 ಎ 77‏
‎B:-*(x}/{a) sec Theta + (y}/(b) tan Theta = 1"‏
‎C:-*(ax}/(sec Theta) - (by)/(tan Theta} = a~2 + b~2"‏
‎D:-* (ax)/{(sec Theta) + (by)/(tan Theta) = a~2 + b~2"‏
‎Correct Answer:- Option-D‏
‎Question56:-"lim_{x->00} (log x}/(x~n}" is‏
‎കാ”‏
‏*00--:8

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