Correct Answer:- Option-C
Question72:-Let G = (V, E} be a simple graph. Choose the wrong statement from below :
A:-G is bipartite implies G has a perfect matching
B:-Any plane Graph has a dual graph
C:-Two isomorphic graphs are having the same degree sequence
D:-Any Hamiltonian graph is 2-connected
Correct Answer:- Option-A
Question73:-Let (X, d} be a metric space and ` (८ 7) ` be a sequence in X. Choose the correct statement from the following :
கோரி *(x_n}" is a Cauchy sequence, then it converges.
B:-If *(x_n)* converges in X, any subsequence converges to the same limit.
ना *(x_n)" is bounded, then it has a convergent subsequence.
D:-If *(x_n})" is unbounded, then it cannot have a convergent subsequence.
Correct Answer:- Option-B
Question74:-Let *X = R*2". From the following maps from X to X, choose the one which is a linear homeomorphism :
AF(x 1, x2)=(x1-x2,x2-x1)
8:- (x_1,x 2} = (2x_1-x_2,0)
(८ 1, + 2) = (3൨, മധ്‌
0: {^ @ 1, ८ 2) = {x_1-x_2, x_1+x_2)"
Correct Answer:- Option-D
Question75:-Let E = { x “epsi* R: x is rational, 0 "<=" x "<=" 2}. The Lebesgue measure of E is :
A2
B:-1
C:-not Lebesgue measurable
0:-0
Correct Answer:- Option-D
Question76:-Among the following equations, choose the exact differential equation :
A" 12X 2ydx+4x " 3dy=
B:-* (x+y)dx+3x~ 2ydy=0"
©" (५0/00) 5 0250”
D" (4X~2+3y)dx-+6x 2y~ 2dy=0"
Correct Answer:- Option-A
Question77:-Let X = ("C*2 ", *||.]|_1"). Let A’in*B L (X} be defined by A*(x_1, x_2)=(2x_2, x_1)." Then [4 5
ಹಿ
8:-3/2*
6-2
0-1
Correct Answer:- Option-C
Question78:-Let *mu’ denote the Mobius function then *mu’ (75} is :
Al
B:-0
C:-15
0:--1
Correct Answer:- Option-B
Question79:-Consider the vector field defined by X *(x_1, x_2) = (x_1, x 2, - x_2, x_1)." Choose an integral curve of X from
the following :
கலட்ட ` (€^, €^)
6:0 (-'sint, cos t}
வர்ற = (cos t, sin t}
D:-"alpha’ {t) = " {t, t~2)"
Correct Answer:-Question Cancelled
0५650080: `) ( = 2^2, ` # = {@ 0) : x ടി” R} where, *||.||_1" is defired on X. Letg: Y ->" R be defined by 90%
0))=x. From the following choose a Hahn-Banach extension of g :
&:- (८ 1, 2) = (1 + 262
छः (41, + 2) = (५1 + 3 2\/2)"
¢ 0८ 1, 3८ 2} = 61 -2( 2`
0:- (८ 1, + 2) = 3८ 1 + 4 2
Correct Answer:- Option-C
Question81:-Which of the following is not a solution of the two-dimensional Laplace equation :
കടലാടി