Page 70 - Mathematics Class - XII

Viva-Voce

1. What is the real life use of this given activity?
Ans. This activity is useful in preparing economical packages.
2. Is among the rectangles of given area, the square has maximum perimeter?
Ans. No, among the rectangles of given area, the square has minimum perimeter.

3. Find two numbers, whose sum is 32, and whose product is maximum.
Ans. Here, x + y = 32
Product (P) = xy

P = x (32 – x)
P = 32 x – x 2
dp x

dx 32 2
Now, dp = 0 then 2x = 32; x = 16
dx
dp
2
Again 2 ( ve)
dx 2
So, Product is maximum when, x = 16 and y = 16
4. If the radius of a circle is doubled, what effect does this have on the area of the circle? On the circumference?
Ans. If the radius of a circle is doubled, the area of the circle will be quadrupled and the circumference will also
be doubled.

MCQs

1. The side of an equilateral triangle is increasing at a rate of 2 cm/sec. The rate, at which area increases when
the side is 10, is

a) 10 cm /sec b) 10 cm /sec c) 3 cm /sec d) 10 3 cm /sec
2
2
2
2
3
2. If x increases at a rate of 2 m/sec at the instant when x = 3 m, y = 1 m, at what rate must y be changing in
order that the function 2 xy – 3 x y shall be neither increasing nor decreasing?
2
a) 32 m/sec, increasing b) 32 m/sec, decreasing
21 21
c) 8 m/sec, increasing d) 8 m/sec, decreasing
21 21
3. sin θ cos θ attains a maximum, when θ = ?
n
m
a) tan −1 m b) tan m c) tan( )n d) tan n
1

1

−1
n n m
Answers: 1. d) 10 3 cm /sec 2. b) 32 m/sec, decreasing 3. a) tan −1 m
2
21 n
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