Plus One Maths (Commerce) Public Exam Answer Key

Plus One Maths(Com) QP March 2025 - Answer Key

Section 1 (Questions 1-8, 3 scores each)

Question 1

(i) (c) A - B
(ii) Subsets of A = {-1, 0, 1}:
∅, {-1}, {0}, {1}, {-1,0}, {-1,1}, {0,1}, {-1,0,1}

Question 2

(i) x = 3, y = -1
(ii) A × A × A = {(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1)}

Question 3

Total arrangements: 11!/(2!2!2!) = 4,989,600
Arrangements starting with H: 10!/(2!2!) = 907,200

Question 4

(i) Octant: XOYZ' (or 4th octant)
(ii) Distance AB = √[(4-2)² + (3-3)² + (1-5)²] = √(4+0+16) = √20 = 2√5

Section 2 (Questions 9-16, 4 scores each)

Question 9

(i) Λ ∪ Λ' = U (universal set)
(ii) Verification:
(Λ ∪ B) = {2,3,4,6}, (Λ ∪ B)' = {1,5}
Λ' = {1,5,6}, B' = {1,2,5}
Λ' ∩ B' = {1,5}
Thus, (Λ ∪ B)' = Λ' ∩ B'

Question 10

(i) Graph of f(x) = |x-2|: V-shaped with vertex at (2,0)
(ii) Domain: x ∈ ℝ, x ≠ 4
Range: y ∈ ℝ, y ≠ 1

Question 11

(i) sin²(π/6) + cos²(π/3) - tan²(π/4) = (1/2)² + (1/2)² - 1² = 1/4 + 1/4 - 1 = -1/2
(ii) Proof:
(cos7x + cos5x)/(sin7x - sin5x) = [2cos6xcosx]/[2cos6xsinx] = cotx

Question 12

(i) Multiplicative inverse of 3-4i: (3+4i)/25
(ii) (1+i)/(1-i) = i

Question 13

(i) Solution: x ≥ 2
(ii) Real line representation: Closed circle at 2 with shading to the right

Question 14

(i) (b) n!/(r!(n-r)!)
(ii) Number of teams: C(5,4)×C(12,7) = 5×792 = 3,960

Question 15

(i) (d) n+1
(ii) (x/3 - 1/x)⁵ = (x/3)⁵ - 5(x/3)⁴(1/x) + 10(x/3)³(1/x)² - 10(x/3)²(1/x)³ + 5(x/3)(1/x)⁴ - (1/x)⁵

Question 16

(i) Minor axis length: 24
(ii) Latus rectum: 288/13, Eccentricity: 5/13
(iii) Equation: x²/169 + y²/144 = 1

Section 3 (Questions 17-20, 6 scores each)

Question 17

(i) n = 4 terms
(ii) Proof: Let first term = a, common ratio = r
p = ar⁴, q = ar⁷, s = ar¹⁰
ps = a²r¹⁴ = q²
(iii) Sum to infinity: 2

Question 18

(i) (d) y = 0
(ii) Equation: y-3 = (5/1)(x-2) → y = 5x-7
(iii) Distance = |8+3-1|/5 = 2 units

Question 19

(i) Mean: 63
(ii) Variance: 204
(iii) Standard Deviation: √204 ≈ 14.28

Question 20

(i) P(A∪B) = 2/5 + 1/2 - 1/5 = 7/10
(ii)
(a) P(3 white) = C(5,3)/C(13,3) = 10/286
(b) P(3 red) = C(8,3)/C(13,3) = 56/286
(c) P(1 red, 2 white) = C(8,1)×C(5,2)/C(13,3) = 80/286