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

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
of ‘I is

D:-None of the above
Correct Answer:- Option-A

Question49:-If *V* is a vector space with dim ‘V=n’ , then the dimension of the hyperspace of ` ` ऽ
Ae

Correct Answer:- Option-B
Question50:-Let ‘V* bea vector space of all 2 x 2 matrices over ‘R’ . Let ‘T be the linear mapping *T : V-> V* such that
*T (A)= AB-BA* where *B = [[2,1],[0,3]]* . Then the nullity of ‘T’ is
‏ا‎
‎8:-2
‎C:-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***, which of the following is not true?
is normal if ‘T’ is self-adjoint
is normal if ‘Tis unitary
: is self-adjoint if ‘T is normal
D:-None of the above
Correct Answer:- Option-C
Question55:-The equation of the normal at the point ‘(a sec Theta, b tanTheta)’ on the hyperbola *(x*2)/(a*2)- (y*2)/(b*2)
21“ 15
:-١ (00/(8) 560 77608 - (/)/(0) tan Theta = 1°
(x)/(a) sec Theta + (y)/(b) tan Theta = 1°
(ax)/(sec Theta) - (by)/(tan Theta) = a*2 + b*2°
:- ` (ax)/(sec Theta) + (by)/(tan Theta) = a*2 + b*2°
Correct Answer:- Option-D
Question56:-* lim_(x->00) (log x)/(x*n)* is
A:-‘00*
8:- -00`