JAM Mathematics (MA) Question Paper 2019 Download Free PDF

JAM Mathematics Question Paper 2019 Download Free PDF

Joint Admission Test for M.Sc. (JAM) 2019 Mathematics (MA) Question paper with answers JAM Mathematics 2019 Question with solution you can download it in FREE, if JAM Mathematics (MA) 2019 paper in text or pdf for JAM Mathematics 2019 Answer Keys you can download JAM 2019 page also just Go to menu bar, Click on File->then Save.

JAM MA (Mathematics) Question Paper 2019

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SAMPLE QUESTIONS

Q.1. Let 𝐺 be a noncyclic group of order 4. Consider the statements I and II:

I. There is NO injective (one-one) homomorphism from 𝐺 to β„€8
II. There is NO surjective (onto) homomorphism from β„€8 to 𝐺

Then

(A) I is true

(B) I is false

(C) II is true

(D) II is false

Q.2. Let 𝐺 be a nonabelian group, 𝑦 ∈ 𝐺, and let the maps 𝑓, 𝑔, β„Ž from 𝐺 to itself be defined by

𝑓(π‘₯) = 𝑦π‘₯𝑦 βˆ’1 , 𝑔(π‘₯) = π‘₯ βˆ’1 and β„Ž = 𝑔 ∘ 𝑔.

Then

(A) 𝑔 and β„Ž are homomorphisms and 𝑓 is not a homomorphism

(B) β„Ž is a homomorphism and 𝑔 is not a homomorphism

(C) 𝑓 is a homomorphism and 𝑔 is not a homomorphism

(D) 𝑓, 𝑔 and β„Ž are homomorphisms

Q.3. Let 𝑆 and 𝑇 be linear transformations from a finite dimensional vector space 𝑉 to itself such that 𝑆(𝑇(𝑣)) = 0 for all 𝑣 ∈ 𝑉. Then

(A) rank(𝑇) β‰₯ nullity(𝑆)

(B) rank(𝑆) β‰₯ nullity(𝑇)

(C) rank(𝑇) ≀ nullity(𝑆)

(D) rank(𝑆) ≀ nullity(𝑇)

Q.4. Let 𝐹⃗ and 𝐺⃗ be differentiable vector fields and let 𝑔 be a differentiable scalar function. Then

(A) βˆ‡ β‹… (𝐹⃗ Γ— 𝐺⃗) = 𝐺⃗ β‹… βˆ‡ Γ— 𝐹⃗ βˆ’ 𝐹⃗ β‹… βˆ‡ Γ— 𝐺⃗

(B) βˆ‡ β‹… (𝐹⃗ Γ— 𝐺⃗) = 𝐺⃗ β‹… βˆ‡ Γ— 𝐹⃗ + 𝐹⃗ β‹… βˆ‡ Γ— 𝐺⃗

(C) βˆ‡ β‹… (𝑔𝐹⃗) = π‘”βˆ‡ β‹… 𝐹⃗ βˆ’ βˆ‡g β‹… 𝐹⃗

(D) βˆ‡ β‹… (𝑔𝐹⃗) = π‘”βˆ‡ β‹… 𝐹⃗ + βˆ‡g β‹… 𝐹⃗

Q.5. Consider the intervals 𝑆 = (0, 2] and 𝑇 = [1, 3). Let π‘†βˆ˜ and π‘‡βˆ˜ be the sets of interior points of 𝑆 and 𝑇, respectively. Then the set of interior points of 𝑆 \ 𝑇 is equal to

(A) 𝑆 βˆ– π‘‡βˆ˜

(B) 𝑆 βˆ– 𝑇

(C) π‘†βˆ˜ βˆ– π‘‡βˆ˜

(D) π‘†βˆ˜ βˆ– 𝑇

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