Match the column:
Column-IColumn-II(i) If x2 + y2 = 1, then minimum value of x + y is[A] -3 (ii) If…

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Match the column:
Column-IColumn-II(i) If x2 + y2 = 1, then minimum value of x + y is[A] -3 (ii) If maximum value of y = a cos(x) –  cos (3x) occurs when x = , then value of    'a' is[B] (iii) If f(x) = x – 2sin(x), 0 ≤ x ≤ 2π is increasing in interval (aπ, bπ) then (a + b) is[C]3(iv) If equation of tangent to the curve y = – e–x/2, where it crosses the y-axis is x/p + y/q = 1 then p – q is[D]2

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [B]; (ii) [D]; (iii) [D]; (iv) [C]. Ans.
(i) [B]
(ii) [D]
(iii) [D]
(iv) [C]
Sol.
x = sin θ & y = cos θ
x + y = sin θ + cos θ
=  sin ( θ + π /4) ⇒ min. value = – 
y = a cos x – 1/3 cos (3x)
y'( π /6) = 0 ⇒ – a sin π /6 + sin π /2 = –  + 1 = 0
⇒ a = 2
f '(x) = 1 – 2 cosx
f '(x) > 0 ⇒ cos(x) < 1/2 ⇒ x ∈ ( π /3, 5 π /3)
⇒ a = 1/3, b = 5/3 ⇒ a + b = 2
at x = 0, y = – e 0 = – 1
y' = 1/2 e –x/2 = y' (0) = ½
Equation of tangent y + 1 = ½ (x – 0)
⇒  ⇒ p = 2, q = – 1
So, p – q = 3

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Column-I	Column-II
(i) If x2 + y2 = 1, then minimum value of x + y is	[A] -3
(ii) If maximum value of y = a cos(x) – cos (3x) occurs when x = , then value of 'a' is	[B]
(iii) If f(x) = x – 2sin(x), 0 ≤ x ≤ 2π is increasing in interval (aπ, bπ) then (a + b) is	[C]3
(iv) If equation of tangent to the curve y = – e–x/2, where it crosses the y-axis is x/p + y/q = 1 then p – q is	[D]2

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