Match the column :
Column -I | Column-II |
(A) Number of solution of the equation sin x = – 1/6 in the interval [–7π, 5π] is | (P) 1 |
(B) (cos nπ)12, n ∈ I is equal to | (Q) 12 |
(C) If the equation sec2θ = –x2+ 14x – 23 is possible, then the greatest integral value of x, is | (R) 0 |
(D) Solution(s) of the equation 6.91/x – 13.61/x + 6.41/x = 0 is | (S) – 1 |
(T) 4 |
Text Solution
Verified by Experts(i) [B]; (ii) [A]; (iii) [B]; (iv) [A]; (i) [B]; (ii) [A]; (iii) [B]; (iv) [A]
Ans.
(i) [B]
(ii) [A]
(iii) [B]
(iv) [A], [D]
Sol. (i) ∴ sin x < 0 if x ∈ ( π , 2 π )
for x ∈ [–7 π , 5 π ] x can take 12 values
(ii) ∴ cos n π = ± 1, n ∈ I
∴ (± 1) 12 = 1
(iii) sec 2 θ = –x 2 + 14x – 23
∴ sec 2 θ ≥ 1 ⇒ –x 2 + 14x – 23 ≥ 1, x ∈ [2, 12]
(iv) 6.3 2/x – 13.3 1/x .2 1/x + 6.2 2/x = 0
Divide by 2 2/x ⇒ 6.(3/2)
2/x – 13(3/2) 1/x + 6 = 0
let (3/2) 2/x = t ⇒ 6t 2 – 13t + 6 = 0
⇒ 6t 2 – 9t – 4t + 6 = 0 ⇒ (3t – 2) (2t – 3) = 0
⇒ t = 2/3, 3/2 x = ± 1
Ans.
(i) [B]
(ii) [A]
(iii) [B]
(iv) [A], [D]
Sol. (i) ∴ sin x < 0 if x ∈ ( π , 2 π )
for x ∈ [–7 π , 5 π ] x can take 12 values
(ii) ∴ cos n π = ± 1, n ∈ I
∴ (± 1) 12 = 1
(iii) sec 2 θ = –x 2 + 14x – 23
∴ sec 2 θ ≥ 1 ⇒ –x 2 + 14x – 23 ≥ 1, x ∈ [2, 12]
(iv) 6.3 2/x – 13.3 1/x .2 1/x + 6.2 2/x = 0
Divide by 2 2/x ⇒ 6.(3/2)
2/x – 13(3/2) 1/x + 6 = 0
let (3/2) 2/x = t ⇒ 6t 2 – 13t + 6 = 0
⇒ 6t 2 – 9t – 4t + 6 = 0 ⇒ (3t – 2) (2t – 3) = 0
⇒ t = 2/3, 3/2 x = ± 1
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