Out of 180 students in a class 7 students failed in all the three subjects viz, Physics, Chemistry, Maths. only 144 students pass in only one subject and 21 students pass in only two subjects.
(a) How many studens passed in all the three subjects?
(b) How many students passed in atleast two subjects?
(c) How many students passed in at most two subjects but atleast in one subject?

8, 25, 150

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8, 29, 145

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8, 29, 165

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8, 25, 130

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Solution

The correct option is C 8, 29, 165
$α = a + b + c = 144 β = x + y + z = 21 α + β + γ = 180 - 7 = 173 γ = (α + β + γ) - (α + β) γ = (173) - (144 + 21) \Rightarrow γ = 8 (γ = k) (a) 8$
(b) Atleast two subjects
$= β + γ = 21 + 8 = 29$
(c) Atleast one subject but
atmost two subjects
$= α + β = 144 + 21 = 165.$

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The correct option is C 8, 29, 165α=a+b+c=144β=x+y+z=21α+β+γ=180−7=173γ=(α+β+γ)−(α+β)γ=(173)−(144+21)⇒γ=8(γ=k)(a)8 (b) Atleast two subjects =β+γ=21+8=29 (c) Atleast one subject but atmost two subjects =α+β=144+21=165.