KEE Model Question

KARUNYA ENTRANCE EXAMINATION - 2025 (KEE’25) SAMPLE Question Paper For the candidates who have studied Mathematics in +2 Mathematics Physics Chemistry English General Aptitude

For the candidates who have not studied Mathematics in +2 Biology Physics Chemistry English General Aptitude

PART A(1) - MATHEMATICS 1. The number of elements in the set 𝑆 = {(𝑥, 𝑦, 𝑧): 𝑥, 𝑦, 𝑧 ∈ 𝑧, 𝑥 + 2𝑦 + 3𝑧 = 42, 𝑥, 𝑦, 𝑧 ≥ 0} is equal to (a) 170 (c) 150

(b) 169 (d) 154

2. Let 𝐴 = {𝑛 ∈ 𝑁: 𝐻𝐶𝐹 (𝑛, 45) = 1} and 𝐵 = {2𝑘: 𝑘 ∈ {1,2,3, … .100}}. The sum of all the elements of 𝐴 ∩ 𝐵 is (a) 5264 (b) 5260 (c) 5280 (d) 5296 1+𝑥

2𝑥

3. If 𝑓(𝑥) = log (1−𝑥), then 𝑓 (1+𝑥 2 ) is equal to (a) (𝑓(𝑥)) (b) 2𝑓(𝑥)

2

4𝑥+3

(b) (𝑓(𝑥)) (d) 3𝑓(𝑥) 2

3

2

2

4. If 𝑓(𝑥) = 6𝑥−4 , 𝑥 ≠ 3 and (𝑓𝑜𝑓)(𝑥) = 𝑔(𝑥), where 𝑔: 𝑅 − {3} → 𝑅 − {3}, then (𝑔𝑜𝑔𝑜𝑔)(4) is equal to 19 19 (a) − 20 (b) 20 (c) -4 (d) 4 cos4 𝛼

sin4 𝛼

5. If cos2 𝛽 + sin2 𝛽 = 1 then sin4 𝛼 + sin4 𝛽 is equal to (a) sin2 𝛼 sin2 𝛽 (c) 2sin2 𝛼 sin2 𝛽

KEE’25 Model Question Paper

(b) cos2 𝛼 cos2 𝛽 (d) 2cos 2 𝛼 cos 2 𝛽

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