8, IET:V -V isan orthogonal transformation on an inner product space V and if
(I) : Tis anisometry
(I1) : T takes orthonormal basis o orthonormal basis then

(A) (018 0೫೧ 0! (11) 19 10180 (0) (1) 15 false but (1) is true

(€) Both (I) and (11} are true (12) 8001 (1) and (11) are false
9. Let # be the cross product in the Euclidean space R3. Then

(A) *isassociative (ए) * is commutative

(C) + छ not associative (D) None of the above

10. Choose the linear mapping from the following :
(A) F:R?-> R? defined by F(x, y)= (2, ‏رق‎
‏٢‎ : 183 -> R? defined by F(x, ¥, z)= (v +2y— 3z, 4x—5y + 62)
(ಲ) F:R?— R? defined by F(x, y, 2) = (वि, y 1-2)
(D) 8:82, 87 000706 by F(x, y)= (xy, y)

11. Domain of the function y= 1 -2 ಗೆ;
(है) R (8) 0,1] (^) [-1,1] (0) (¢ 1)

12. ‏راد‎ = ೫2688:

3

(+) ० ® २ © 1 ठ ಇ
13. Laplace equation U, + ‏ور‎ 15;

(ക) வடி ‏رص‎ Parabolic © Hyperbolic (D) Noneof these
14. Number of different permutations of '’ items taken 'k’ at a time without repetition 1:

۸( ‏اھ‎ ध अ ‏اط‎ 2"

‎५५‏ 0۰7 1 بس لم
‎Every polynomial of degree 21 has ___ _ 2810.‏ .15

‎(A) exactly ೧೧೮ (B) infinitely many (C) atleast one (D) none of these

‎16. (लाः triangular matrices are :
(A) Matrices having non-zero entries above the main diagonal.
(B) Square matrices having non-zero entries above the main diagonal.
(€) Matrices having non-zero entries only on and above the main diagonal.
(D) Square matrices having non-zero entries only വ and above the main diagonal.

‎17. The Wronskian of functions sinx and cosx is :

‎त‏ )>( 1 © 8 )8( 1- ھ)
‎ An operator T on a Hilbert space I is normal, then it's adjoint T" is‏ .18

‎(A). a linear transformation (8) a polynomialin T

‎(C) orthogonal (D) none of these

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