Let S = {x ∈ R : cos(x) + cos ( √2 x) < 2}. Then (A) S = ϕ (B

1.	Let S = {x ∈ R : cos(x) + cos ( √2 x) < 2}. Then (A) S = ϕ (B) S is a non-empty finite set (C) S is an infinite proper subset of R\{0} (D) S = R\{0}
Answer» Correct option (D) S = R\{0} Explanation: Cos x + cos( √2 x) will always be less than 2 except when both cos x = 1 & cos (√2 x) = 1 cos x = 1 ⇒ x = 2nπ cos ( √2 x) = 1 ⇒ x = √2 mπ both can simultaneously be 1 only when x = 0 ⇒ S = R – {0}

Let S = {x ∈ R : cos(x) + cos ( √2 x) < 2}. Then (A) S = ϕ (B) S is a non-empty finite set (C) S is an infinite proper subset of R\{0} (D) S = R\{0}

Answer»

Correct option (D) S = R\{0}

Explanation:

Cos x + cos( √2 x) will always be less than 2 except when both cos x = 1 & cos (√2 x) = 1

cos x = 1 ⇒ x = 2nπ

cos ( √2 x) = 1 ⇒ x = √2 mπ

both can simultaneously be 1 only when x = 0

⇒ S = R – {0}

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Let S = {x ∈ R : cos(x) + cos ( √2 x) &lt; 2}. Then (A) S = ϕ (B) S is a non-empty finite set (C) S is an infinite proper subset of R\{0} (D) S = R\{0}

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Let S = {x ∈ R : cos(x) + cos ( √2 x) < 2}. Then (A) S = ϕ (B) S is a non-empty finite set (C) S is an infinite proper subset of R\{0} (D) S = R\{0}