HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

9, 8.1, 7.29, ...

Express the following recurring decimal as a rational number:

`0.bar(7)`

Express the following recurring decimal as a rational number:

`2.bar(4)`

Express the following recurring decimal as a rational number:

`2.3bar(5)`

Express the following recurring decimal as a rational number:

`51.0bar(2)`

If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term

If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio.

The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.

Find : `sum_("r" = 1)^oo 4(0.5)^"r"`

Find : `sum_("r" = 1)^oo (-1/3)^"r"`

Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"` 

Find : `sum_("n" = 1)^oo 0.4^"n"`

The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares

The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the perimeters of all the squares

A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball

Find GM of two positive numbers whose A.M. and H.M. are 75 and 48

Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.

If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.

Select the correct answer from the given alternative.

The common ratio for the G.P. 0.12, 0.24, 0.48, is –