A4
B:-3
6-2
0-1
Correct Answer:- Option-C
Question37:-For any arbitrary matrices ` १५५४ ३१५ ` १८१५९. , 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 *quadmoin’ square matrices. Then the eigen values of *quadAB’ are same as
the eigen values of
A:-"quadA+B®
B:-'quadA-B®
C:-'quadB-A*
‏٭-:0‎ 7
Correct Answer:- Option-D
Question39:-The quadratic polynomial corresponds to the matrix “quadA=((1,0,1/2),(0,0,-1},(12,-1,0}) ``
&:- १५२५४८८ 2411262४
B:-'quadx™2-2yz+xz®
C:-"quadx~2+1/2yz-xy*
‏ری ری نکد‎
Correct Answer:- Option-B
Question40:-Let *quadP’ be an “quadmxxm® orthogonal matrix, *quadQ" be an “quadmon’ orthogonal matrix and ` १८६५५
any “quadmxn’ matrix. If *quadA~T" denote the transpose of *quadA’ and “quadA~-* denote the generalized inverse of
A", then the generalized inverse of “quadPAQ’ is
കന്‌
५५०7५ {-)?^
:- १५०५०५८ {-}0`
0:- १८५३५०५ {-}?`
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->00" , then what is the value of lim'quadP(A_n)" 7
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
Question: ` १८५३५६९ n}" is a sequence of events such that “quadsum_{k=1)"0oP(A k)=00" , 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
-Let “quad{A_n}" be a sequence of events such that “quadB_1=A 1" and "quadB_k=A"c_1
: 2... A {k-1}*c A k' for quadk>=2", in ೫01೧೧ ` 02687೧ 15 the complement of *quadA™ . Then the sequence of
வலா *quad{B_n}" are
A:-Pair-wise independent
B:-Mutually independent
C:-Mutually dependent
D:-Pair-wise mutually exclusive
Correct Answer:- Option-D