# JAM Question Paper 2019-20 MA (Mathematics)

JAM Question Paper 2019-20 MA (Mathematics).

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## JAM Question Paper 2019-20 MA (Mathematics).

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01. If {v1, v2, v3} 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) {v1 + v2 v3, 2v1 + v2 + 3v3, 5v1 + 4v2}
• (B) {v1v2, v2 v3, v3v1}
• (C) {v1 + v2 v3, v2 + v3 v1, v3 v1 + v2, v1 + v2 + v3}
• (D) {v1 + v2, v2 + 2v3, v3 + 3 v1}

02. Let U, V and W be finite dimensional real vector spaces, T:UV, S:V W and P:WU 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 → ℤ221 is a homomorphism implies f (g) ­ = 0, ∀g G. Then a possible group G is

• (A) ℤ21
• (B) ℤ51
• (C) ℤ91
• (D) ℤ119

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