Match the following.
Column –IColumn –II(i) If f(x) is a quadratic expressionin x and 6 dx =k f(1)…

Question

Match the following.
Column –IColumn –II(i) If f(x) is a quadratic expressionin x and 6  dx =k f(1) + f(0) + 4f(1/2), then k is[A] 1(ii) If the sum of the squaresof the intercepts on the axescut off by the tangents to the curve x1/3 + y1/3 = a1/3 (a > 0) at is 2, then a is[B] 4(iii) The distance of the point on y = x4 + 3x2 + 2x which is nearest to the line y = 2x – 1 is r, then  r is[C] 3(iv) If f(x) = –2 |sin x| +ae|x| + 5 |tan x|3 is differentiable at x = 0, then a is[D] 2

CGP EDU Academic Team · Accepted Answer

The correct answer is 6. Ans.
(i) [A]
(ii) [B]
(iii) [A]
(iv) [D]
Sol.
6  = 2a + 3b + 6c
= k (a + b + c) + c + 4 
∴ k = 1
 x –2/3 +  y –2/3  = 0
 = –1 at x =  , y = 
equation of tangent is y + x = 
∴ a = 4
 = 4x 3 + 6x + 2 = 2
2x 3 + 3x = 0 ⇒ x = 0, y = 0
∴ point on the curve at the least distance from the  line y = 2x – 1 is (0, 0)
least distance r = 
f ′ (0 + ) = f ′ (0 – ) ⇒ –2 + a = 2 – a ⇒ a = 2

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Column –I	Column –II
(i) If f(x) is a quadratic expression in x and 6 dx = k f(1) + f(0) + 4f(1/2), then k is	[A] 1
(ii) If the sum of the squares of the intercepts on the axes cut off by the tangents to the curve x1/3 + y1/3 = a1/3 (a > 0) at is 2, then a is	[B] 4
(iii) The distance of the point on y = x4 + 3x2 + 2x which is nearest to the line y = 2x – 1 is r, then r is	[C] 3
(iv) If f(x) = –2 \|sin x\| +ae\|x\| + 5 \|tan x\|3 is differentiable at x = 0, then a is	[D] 2

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