HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If S_n, S_2n, S_3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that S_n (S_3n – S_2n) = (S_2n – S_n)².

Find: `sum_("r" = 1)^10(3 xx 2^"r")`

Find: `sum_("r" = 1)^10 5 xx 3^"r"`

The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)⁵ = 1.28, (1.05)⁶ = 1.34]

If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)⁵ = 1.47]

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

`1/2, 1/4, 1/8, 1/16,...`

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

`2, 4/3, 8/9, 16/27, ...`

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

`-3, 1, (-1)/3, 1/9, ...`

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"`