Given, AB =2, CD =1 and let BC = x

∴ Area of middle circle = Average of areas of other two circle

=

= BC

For the minimum wastage of sheet he has to cut the sheet in the given manner that length of the sheet consist diameter of two circle a circumference and breadth consist a diameter.

Total area of sheet required = length x breadth =

Area of sheet utilised =+

=

Area of wastage sheet = 4r²

=

Required ratio =

=

=

We can say that the bucket is in the form of frustum:

r = 3 cm and R = 6 cm, h = 7 cm

Now,

Volume of the frustum =

Hence, option b is the correct answer.

Let the other two numbers be  and .

Now, for the minimum value of  occurs when

Hence, option b is the correct answer.

HCF of A and B is 16

LCM (B, C) = 240

LCM (A, B) = 192

Let A be 16a and B be 16b

LCM of B and C is 240

B = 16b = 48

C = 20b = 60

LCM of A and B is 192

LCM (16a, 48) = 192

A = 16a = 64

LCM of A, B and C = LCM of 64, 48 and 60 = 960.

Hence, option b is the correct answer.

By Euler’s theorem

⇒ 222 X 185 denotes H.C.F. of 222 and 185

222 =

185 =

H.C.F. of 222 and 185 = 37

x @ y denotes LCM of x and y

37 @ 481 denotes LCM of 37 and 481

⇒

⇒

Hence, LCM of 37 and 481 = 481

So, answer will be 481.

The average

The savings of the company from 2001 to 2005 are 250, 400, 200, 150 and 350.

The savings percentage are

The average savings of year 2002, 2003 and 2004

The average savings of year 2001 and 2005

Required ratio,

Then required %age

Production by farmer F1 , F2 and F3 = 520 + 660 +550 = 1730

Required ratio = 1960 : 1730 = 196 : 173

Percentage of sales with respect to the production of F2 =

Percentage of sales with respect to the production of F3 =

Percentage of sales with respect to the production of F4 =

Clearly, Farmer F2 has lowest percentage of sales with respect to the production.

Production by famer F4 = 720 quintal

Difference = 720 quintal – 550 quintal = 170 quintal

Required percentage =

Given, the walking distance CD = 138 m.

Let the height of the monument AB = h meters

and

 and

=

We know that,

In triangle ABC,

 ….(i)

Now, in triangle ABD,

 (from equation (i))

Therefore, height of the monument is 42 meters.

Hence, option c is the correct answer.

Then in triangle ADE,

AD=DE=a

Applying sine rule in above triangle

In triangle ADE,

=

Hence option c is the correct answer.

We will use here

Then

 cos 35 +cos 85 +cos 155 = 2cos 60. cos 25 + cos(180-25)
                                      = cos25 -cos25
                                       =0

Since, the frequency is a straight line, so we take that all the classes have the same frequency, 10 each.

i. It is true that first and the last class have the same frequency of 10 each

ii. Both the middle class have frequency, 10+10 = 20

iii. Since, all have equal frequency, so we cannot determine the mode.

Therefore, only i and iii statements are correct.

Hence, option b is the correct answer.

We have to calculate

∴sum of the roots =

similarly product of roots =

=

we know the quadratic equation ⇒

⇒ =0