A:-There exists a vector space of 81 elements
B:-There exists a vector space of 81 elements over a field of 3 elements
C:-There exists a vector space of 81 elements over a field of 9 elements
D:-There exists a vector space of 81 elements over a field of 27 elements
Correct Answer:- Option-D
Question48:-Which of the following linear transformation is invertible 7
கண்ல ப ய ४}
8ः-(८ ४) = (22८ த யப
6:0५ ४) = ® + ` (1)/(2} ४ 26 + ४}
0:70 ४) = 00+ ४, + ४)
Correct Answer:- Option-B
Question49:-If the characteristic polynomial of the linear transformation T : 9)” ` ->22^(9)` 65 `^ {9}` + 4८ + 1, पौलो
det(T- 5

A:-—6
8:--9
C—1
0-1

Correct Answer:- Option-A

/00 0 0 1Y
00010
45 |160000
01000

Question50:-If 0 00109 9/ then which is true 7

കടക =1
8:-4^ (4) = ॥
മു്‌ ಎ|
5:26 5
Correct Answer:- Option-D
Question51:-Which is the following normed linear space is strictly convex 7
|| |
o L ‏ا‎
‎உணடு!
‎டாட with | ட
D:-None of these
Correct Answer:- Option-B
Question52:-Which of the following is false 7
A:-A — B is self adjoint if A and B are 50
B:-Every unitary operator is normal
C:-Every normal operator is self adjoint
D:-A + B is self adjoint if A and B are so
Correct Answer:- Option-C
Question53:-Which of the following is a Hilbert space 7
A1)
B:- 172
(ல்‌
D:-None of these
Correct Answer:- Option-B
Question54:-Let f(x, y)= " {{(x* B3O 3y~ (2)) if (x, y!=(0, 0), (010500, O}):}"
Then which is not true 7
‏ا اعنم‎ continuous at (0, 0)
B:-Partial derivatives exists at (0, 0)
C:-Directional derivatives exists at (0, 0)
D:-Partial derivatives are not bounded functions on *RR™(2)"
Correct Answer:- Option-D
Question55:-If the vectors i + ‏ز2‎ + 3k, 4i + 5j + 6k and 5i + mj + 9k are coplanar, then the value of mis
A7
B:-6
5