*JAM Question Paper 2018 MA (Mathematics).*

*JAM MA – Mathematics 2018 Question Paper test papers will be fully objective type. This JAM MA – Mathematics 2018 Question will help all the students for their exam preparation, here the question type is MCQ i.e multiple choice question answers, if this JAM MA – Mathematics 2018 question paper in pdf file for IIT JAM MA – Mathematics you can download it in FREE, if Joint Entrance Examination (JAM) 2018 paper in text for JAM you can download JAM 2018 page also just Go to menu bar, Click on File->then Save.*

**JAM Question Paper 2018 MA (Mathematics).**

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**01. If {v _{1}, v_{2}, v_{3}} is a linearly independent set of vectors in a vector space over ℝ, then which one of the following sets is also linearly independent**?

- (A) {
*v*_{1}+*v*_{2 }–*v*_{3}, 2*v*_{1}+*v*_{2 }+ 3*v*_{3}, 5*v*_{1}+ 4*v*_{2}} - (B) {
*v*_{1}–*v*_{2},*v*_{2 }–*v*_{3},*v*_{3}–*v*_{1}} - (C) {
*v*_{1}+*v*_{2 }–*v*_{3},*v*_{2 }+*v*_{3 }–*v*_{1},*v*_{3 }–*v*_{1 }+*v*_{2},*v*_{1}+*v*_{2 }+*v*_{3}} - (D) {
*v*_{1}+*v*_{2},*v*_{2}+ 2*v*_{3},*v*_{3 }+ 3*v*_{1}}

**02. Let U, V and W be finite dimensional real vector spaces, T:U → V, S:V → W and P:W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is TRUE?**

- (A) nullity of
*T*= nullity of*S* - (B) dimension U ≠ of dimension of
*W* - (C) If dimension of
*V*= 3, dimension of*U*= 4, then*P*is not identically zero - (D) If dimension of
*V*= 4, dimension of*U*= 3, and*T*is one-one, then*P*is identically zero

**03. Let G be a group satisfying the property that f:G → ℤ_{221 }is a homomorphism implies f (g) = 0, ∀g ∈ G. Then a possible group G is**

- (A) ℤ
_{21} - (B) ℤ
_{51} - (C) ℤ
_{91} - (D) ℤ
_{119}

**04. Let H be the quotient group ℚ/ ℤ. Consider the following statements**

**I.** Every cyclic subgroup of *H* is finite.

**II.** Every finite cyclic group is isomorphic to a subgroup of *H*.

Which one of the following holds?

- (A) I is TRUE but II is FALSE
- (B) II is TRUE but I is FALSE
- (C) both I and II are TRUE
- (D) neither I nor II is TRUE

**05. Let P and Q be two non-empty disjoint subsets of ℝ. Which of the following is (are) FALSE?**

- (A) If
*P*and*Q*are compact, then*P*∪*Q*is also compact - (B) If
*P*and*Q*are not connected, then*P*∪*Q*is also not connected - (C) If
*P*∪*Q*and*P*are closed, then*Q*is closed - (D) If
*P*∪*Q*and*P*are open, then*Q*is open

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