JAM Mathematics Question Paper 2019 Download Free PDF
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JAM MA (Mathematics) Question Paper 2019
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SAMPLE QUESTIONS
Q.1. Let πΊ be a noncyclic group of order 4. Consider the statements I and II:
I. There is NO injective (one-one) homomorphism from πΊ to β€8
II. There is NO surjective (onto) homomorphism from β€8 to πΊ
Then
(A) I is true
(B) I is false
(C) II is true
(D) II is false
Q.2. Let πΊ be a nonabelian group, π¦ β πΊ, and let the maps π, π, β from πΊ to itself be defined by
π(π₯) = π¦π₯π¦ β1 , π(π₯) = π₯ β1 and β = π β π.
Then
(A) π and β are homomorphisms and π is not a homomorphism
(B) β is a homomorphism and π is not a homomorphism
(C) π is a homomorphism and π is not a homomorphism
(D) π, π and β are homomorphisms
Q.3. Let π and π be linear transformations from a finite dimensional vector space π to itself such that π(π(π£)) = 0 for all π£ β π. Then
(A) rank(π) β₯ nullity(π)
(B) rank(π) β₯ nullity(π)
(C) rank(π) β€ nullity(π)
(D) rank(π) β€ nullity(π)
Q.4. Let πΉβ and πΊβ be differentiable vector fields and let π be a differentiable scalar function. Then
(A) β β (πΉβ Γ πΊβ) = πΊβ β β Γ πΉβ β πΉβ β β Γ πΊβ
(B) β β (πΉβ Γ πΊβ) = πΊβ β β Γ πΉβ + πΉβ β β Γ πΊβ
(C) β β (ππΉβ) = πβ β πΉβ β βg β πΉβ
(D) β β (ππΉβ) = πβ β πΉβ + βg β πΉβ
Q.5. Consider the intervals π = (0, 2] and π = [1, 3). Let πβ and πβ be the sets of interior points of π and π, respectively. Then the set of interior points of π \ π is equal to
(A) π β πβ
(B) π β π
(C) πβ β πβ
(D) πβ β π
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