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 ?
A:-T(x, y) = (2x + y, x + >(L)/(2)y)
B:-T(x, y) = (2x +y, ` (1)/(2)> + #)
C:-T(x, y) = (x + °(1)/(2)'y, 2x + y)
D:-T(x, y) = (x+y, x+y)
Correct Answer:- Option-B
Question49:-If the characteristic polynomial of the linear transformation T : *RR*(9)* *->RR*(9)° is *x*(9)° + 4x + 1, then
det (T- 1) is

Option-A

00001
00010
45 [10000
01000

0 00100, 55
Question50:-If , then which is true ?

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245)
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Correct Answer:- Option-D

Question51:-Which is the following normed linear space is strictly convex ?

1
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മ

മിട

D:-None of these

Correct Answer:- Option-B
Question52:-Which of the following is false ?

A:-A - B is self adjoint if A and B are so

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 ?

4: 1^ (1).

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D:-None of these
Correct Answer:- Option-B
Question54:-Let f(x, y)= * {((x*(3))/(x*(3)+y*(2)) if (x, y)!=(0, 0)), (0 if (x, y)=(0, 0)):}°
Then which is not true ?
A:-f is 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 + 2) + 3k, 4i + 5j + 6k and 5i + mj + 9k are coplanar, then the value of m is
‏7ھ‎
‎8:-6
‎C:-5