Question

In 1502, the great explorer Christopher
Columbus visited the West Indies in a new
search for a sea-route to India. (a)
......
le
he was there, the natives told him of a mysterious
channel leading into the Pacific Ocean, (b)
ran across the present Panama Canal, joining
North America (c)
South America.
T
Columbus searched for this channel (d)
in vain. Nobody else attempted to do so (e)
1879, (P
a Frenchman set himself to
the task. (g)..... .... there were many difficulties
on the way (h)
they were overcome
with undaunted courage and hard work.
th
N
t
0
(i) While
() Though
(iv) Until
la) () As
(b) (i) as
(c) (i) till
mi) that
SO
(iv) how
M) and
(i) while
liv) or
d) () but
(m) yet
(1) and
1
le) (i) after since
(iv) although
(iv) until
(mi) because
1​

Answer 1

Answer:

Correct Question -

The circumference of two circle are in the ratio 2 : 3. Find the ratio of their areas.

Given -

Ratio of their circumference = 2:3

To find -

Ratio of their areas.

Formula used -

Circumference of circle

Area of circle.

Solution -

In the question, we are provided, with the ratios of the circumference of 2 circles, and we need to find the ratio of area of those circle, for that first we will use the formula of circumference of a circle, then we will use the formula of area of circles. We will be writing 1 equation in it too.

So -

Let the circumference of 2 circles be c1 and c2

According to question -

c1 : c2

Circumference of circle = 2πr

where -

π = $\tt\dfrac{22}{7}$

r = radius

On substituting the values -

c1 : c2 = 2 : 3

2πr1 : 2πr2 = 2 : 3

$\tt\dfrac{2\pi\:r\:1}{2\pi\:r\:2}$ = $\tt\dfrac{2}{3}$

$\tt\dfrac{r1}{r2}$ = $\tt\dfrac{2}{3}$$\longrightarrow$ [Equation 1]

Now -

Let the areas of both the circles be A1 and A2

Area of circle = πr²

So -

Area of both circles = πr1² : πr2²

On substituting the values -

A1 : A2 = πr1² : πr2²

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{(\pi\:r1)}{(\pi\:r2)}^{2}$

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{(r1)}{(r2)}^{2}$

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{(2)}{(3)}^{2}$ [From equation 1]

So -

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{4}{9}$

$\therefore$ The ratio of their areas is 4 : 9

______________________________________________________

Answer 2

Answer:

(a) While

(b) that

(c) and

(d) but

(e) until

(f) when

(g) Although

(h) yet

Hope it helped