Match the column:
Column-IColumn-II(i) If an edge of a cube increases by 1% then percentage increas…

Question

Match the column:
Column-IColumn-II(i) If an edge of a cube increases by 1% then percentage increase in volume is[A]15(ii) If langrange's mean value theorem is satisfied for f(x) = and C ∈ (1, 5), then the value of C2 is[B]1/4(iii) The maximum value attained by y = 10 – |x – 10|, is –1 ≤ x ≤ 3, is[C]3(iv) Let F(x) =  and F(0) = 0 if F() = λ, then λ =[D]2

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [C]; (ii) [A]; (iii) [C]; (iv) [B]. Ans.
(i) [C]
(ii) [A]
(iii) [C]
(iv) [B]
Sol.
Let x is the edge of cube then volume V is given by V = x 3 ⇒ dV = 3x 2 dx.
given that  = 
 =  = 3.  = 
So % increase in volume = 3.
f ' = 
⇒  = 
 =  =  ⇒ 4C 2 = 150 – 6C 2 C
2 = 15
y = 10 – |x – 10| =

So max. of y for x ∈ [–1, 3] is 3.
f(x) = 
= 
= 
 F(0) = 0 so C = 0
F(  ) = 
=  =  =

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Column-I	Column-II
(i) If an edge of a cube increases by 1% then percentage increase in volume is	[A]15
(ii) If langrange's mean value theorem is satisfied for f(x) = and C ∈ (1, 5), then the value of C2 is	[B]1/4
(iii) The maximum value attained by y = 10 – \|x – 10\|, is –1 ≤ x ≤ 3, is	[C]3
(iv) Let F(x) = and F(0) = 0 if F() = λ, then λ =	[D]2

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