Q.10 In a group G , the mapping f : G→ G , defined by f(x) = x⁻¹ for every XєG is an automorphism if G is ______________.Ans 1. cyclic2. alternating3. abelian4. sporadicCorrect Ans Provided: ...
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Q.9 Which is not the property of external direct product?Ans 1. (a,b )∉( G₁ × G₂)2. |G₁ × G₂| = | G₁|. |G₂|3. (a ,b ) ЄG₁ × G₂4. (e , e’) is identity element ...
Q.7 Every finite group G can be embedded in a symmetric group is ______________.Ans 1. Gauss divergence theorem2. Taylor’s theorem3. Cayley theorem4. Green’s theoremCorrect Ans Provided: 3
Q.8 Which of the following is not the property of continuous function if f(z) and g(z) are continuous on a region A, then ______________.Ans 1. (z) – g(z) is continuous on A .2. f(z) ∕g(z) is continuous ...
Q.16 A function f : A→ B between two metric spaces is uniformly continuous on A if for all Є >0 there exist ∂:Ans 1. d( x,y ) =∂2. d (x,y ) >∂3. d(x, y ) < ...
Q.19 Every open cover of a closed and bounded subset S of real numbers contains a finite subcover of S , i.e. , every closed and bounded subset of R is compact, is known as ______________.Ans 1. De ...
Q.17 Which of the following condition is correct for a mapping f : G→ G is called automorphism of G is ______________.Ans 1. f(a,b ) = 02. f(b,a) = f(a)3. f(a,b ) = f(b)4. f is a bijectionCorrect ...
Q.5 If A , B ⊂X and A × B ≅X, then we say that X is ______________.Ans 1. an internal direct product2. an external direct product3. cartesian product4. antisymmetric productCorrect Ans Provided: 2
Q.6 Which is the correct option for internal direct product?Ans 1. K₄ × Z₃2. H₁, H₂ ⊂G3. H₁ ⊂ H₂4. S₃× Z₄Correct Ans Provided: 2
Q.15 Find the power series representation for the following function- ...
