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Match the items in Column-I with those in Column-II and select the correct option.
Column-I Column-II
a) A Circular plate is expanded by heat from radius 6 cm to 6.06 cm. Approximate increase in the area is. p) 5
b) If an edge of a cube increases by 2%,then the percentage increase in its volume is q) 0.72 $π$
c) If the rate of decrease of $\frac{x^{2}}{2} - 2 x + 5$ is thrice the rate of decrease of x, then x is
equal to (rate of decrease is non-zero)
r) 6
d) The rate of increase in the area of an equilateral triangle of side 30 cm, when each side increase at the rate of 0.1 cm/s is s) $\frac{3 \sqrt{3}}{2}$

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$a \to s, b \to r, c \to q, d \to p$

$a \to r, b \to q, c \to s, d \to p$

$a \to p, b \to s, c \to q, d \to r$

$a \to q, b \to r, c \to p, d \to s$

answer is A.

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Detailed Solution

A) $r = 6 c m$ , $δ r = 0.06, A = π r^{2} \Rightarrow δ A = 2 π r δ r = 2 π (6) (0.06) = 0.72 π$

b) $v = x^{3}, δ v = 3 x^{2} δ x ∴ \frac{δ v}{v} \times 100 = 3. \frac{δ x}{x} \times 100 = 3 \times 2 = 6$

c) $(x - 2) \frac{d x}{d t} = 3. \frac{d x}{d t} \Rightarrow x = 5$

d) $A = \frac{\sqrt{3}}{4} x^{2} \Rightarrow \frac{d A}{d t} = \frac{\sqrt{3}}{2} (x . \frac{d x}{d t}) = \frac{\sqrt{3}}{2} \times 30 \times \frac{1}{10} = \frac{3 \sqrt{3}}{2}$

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