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

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**JAM Question Paper 2019-20 MA (Mathematics)**

**JAM Question Paper 2019-20 MA (Mathematics)**

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**01. Let f(x) = |x^{2} – 25| for all x ∈ ℝ. The total number of points of ℝ at which f attains a local extremum (minimum or maximum) is**

- (A) 1
- (B) 2
- (C) 3
- (D) 4

**02. For a, b, c ∈ ℝ, if the differential equation**

(*ax*^{2} + *bxy* + *y*^{2}) *dx* + (2*x*^{2} + *cxy* + *y*^{2}) *dy* = 0

is exact, then

- (A) b = 2, c = 2a
- (B) b = 4, c = 2
- (C) b = 2, c = 4
- (D) b = 2, a = 2c

**03. Let G be a group of order 17. The total number of non-isomorphic subgroups of G is**

- (A) 1
- (B) 2
- (C) 3
- (D) 17

**04. Which one of the following is a subspace of the vector space ℝ ^{3}?**

- (A) {(x, y, z) ∈ ℝ
^{3}: x + 2y = 0, 2x + 3z = 0} - (B) {(x, y, z) ∈ ℝ
^{3}: 2x + 3y + 4z – 3 = 0, z = 0} - (C) {(x, y, z) ∈ ℝ
^{3}: x ≥ 0, y ≥ 0} - (D) {(x, y, z) ∈ ℝ
^{3}: x – 1 = 0, y = 0}

**05. Let G be a cyclic group of order 24. The total number of group isomarphisms of G onto itself is**

- (A) 7
- (B) 8
- (C) 17
- (D) 24

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