Kerala PSC Previous Years Question Paper & Answer
Page:9
Below are the scanned copy of Kerala Public Service Commission (KPSC) Question Paper with answer keys of Exam Name 'HSST JUR MATHEMATICS NCA HIGHER SECONDARY EDUCATION' And exam conducted in the year 2015. And Question paper code was '315/2015'. Medium of question paper was in Malayalam or English . Booklet Alphacode was 'A'. Answer keys are given at the bottom, but we suggest you to try answering the questions yourself and compare the key along wih to check your performance. Because we would like you to do and practice by yourself.
B:-nonhomogeneous and inconsistent
C:-consistant and has unique solution
D:-consistant and has infinite solution
Correct Answer:- Option-D
Question75:-Which of the following map "T:RR~(3)->RR" is a linear functional 7
0:- 100४, 2) 9४16
Correct Answer:- Option-C
Question76:-Let V be a vector of dimension 15 over a fiekd F and W be a subspace of V. If dim W = 3, then “dim{v/W)="
ಹಿ
8:-5
نت
02
Correct Answer:- Option-D
Question77:-An “man” matrix is diagonalizable if
A:-all the eigen values are real and distinct
B:-all the eigen values are real and non-negative
C:-all the eigen values are real and non-zero
D:-all the eigen values are non-zero rational numbers
Correct Answer:- Option-A
Question78:-Let *1<=p
B:-Jensen's inequality
C:-Cauchy’s inequality
D:-Bessel's inequality
Correct Answer:- Option-B
Question79:-Which of the following is false 7
கிறு is a Hilbert space, where *1<=p<=00"
B:-Closed subspace of a Hilbert space is a Hilbert space
C:-The quotient of a Hilbert space by one of its closed subspace is again a Hilbert space
D:-A complete normed space with its norm satisfies the parallelogram law is a Hilbert space
Correct Answer:- Option-A
Question80:-Let A”in* BL{H} and A* be the adjoint of A. A is unitary if
D:-A¥= A
Correct Answer:- Option-C
Question81:-Which of the following is not a Banach space 7
A:-Finite dimensional normed spaces
6 (00)
0: *(6)(م)ا ೫॥[7 0 ೧೦೧7 ||. பனி where E is a Lebesgue measurable subset of 'RR* and *1<=p<=00"
Correct Answer:- Option-C
Question82:-Let X be an inner product space and let x, y "in” X. Then the parallelogram law 15
மினா (മുക മു”
[y~ @)+ eyl |~ =] x| |~ @)+ ]ly] [~ ()
தய
5: മുളി മുടി”
Correct Answer:- Option-A
Question83:-Let X and Y be normed spaces and F : X*->" Y be a linear map. The following conditions are equivalent except
one. Which of the following is not equivalent to others 7
A:-F is continuous at 0
B:-F is continuous on X
C:-a||x|[<=|[F{x}||", for all x'in’X and some a > 0
D:-F is uniformly continuous on X
Correct Answer:- Option-C