९
ಬಯ ಹೂ

D:-1
Correct Answer:- Option-C
Question37:-For any arbitrary matrices ‘quadA* and ‘quadB* , the sum of ranks of \quadA’ and ‘quadB* is always
A:-less than rank ‘quad(A+B)°
B:-less than or equal to rank’ quad(A+B)°
C:-greater than rank quad(A+B)°
D:-greater than or equal to rank’ quad(A+B)°
Correct Answer:- Option-D
Question38:-Let ‘quadA* and ‘quadB* are ‘quadnxxn* square matrices. Then the eigen values of ‘quadAB* are same as
the eigen values of
A:-\quadA+B°

C:-‘quadB-A*

06: ۸۵7

Correct Answer:- Option-D
Question39:-The quadratic polynomial corresponds to the matrix ‘quadA=((1,0,1/2),(0,0,-1),(1/2,-1,0))° >> is

க: quadx*2+1/2xz-xy~

8:-` quadx* 2-2yz+xz>

C:-‘quadx*2+1/2yz-xy*

D:-* quadx*2+yz-2xz*

Correct Answer:- Option-B
Question40:-Let ‘quadP* be an ‘quadmxxm* orthogonal matrix, ‘quadQ* be an ‘quadnxxn* orthogonal matrix and ‘quadA*
any ‘quadmxxn* matrix. If *‘quadA*T denote the transpose of ‘quadA’ and ‘quadA*- denote the generalized inverse of
`ಓ, (೧6೧ the generalized inverse of ‘quadPAQ’ is

A: quadP*TA*{-}Q*°T°

B:-quadQ*TA*{-}P*T

@:- 4८०५१५८ {-}0`

0:-` १८०५0५^ {~}

Correct Answer:- Option-B
Question41:-If *quad{A_n}° is a sequence of events on a probability space (Q,‘quadA,P)* such that ‘quadA_n->A°
as ‘quadn->oo° , then what is the value of lim’ quadP(A_n)* ?

A:-zero

B:-one

C:-quadP(A)*

D:-need not exist

Correct Answer:- Option-C
Question42:-If ‘quadA* and ‘quadB* are mutually exclusive events, each with positive probabilities, then they are

A:-independent events

B:-dependent events

C:-equally likely events

D:-exhaustive events

Correct Answer:- Option-B
Question43:-If *quad{A_n}° is a sequence of events such that *quadsum_(k=1)*o0P(A_k)=o00" , then
*“quadP(lim"sup"A_n)=1* provided events are

A:-equally likely

B:-Mutually exclusive

C:-independent

D:-pair-wise mutually exclusive

Correct Answer:- Option-C
Question44:-Let ‘quad {A_n}° be a sequence of events such that ‘quadB_1=A_1° and ‘quadB_k=A*c_1
402...” “A _{k-1}*c Ak for ‘quadk>=2° , in which ‘quadA*c° is the complement of ‘quadA’ . Then the sequence of
events ‘quad{B_n}* are

A:-Pair-wise independent

B:-Mutually independent

C:-Mutually dependent

D:-Pair-wise mutually exclusive

Correct Answer:- Option-D