HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Answer the following:

Simplify: `("i"^65 + 1/"i"^145)`

Answer the following:

Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`

Answer the following:

Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`

Check whether the following sequence is G.P. If so, write t_n.

2, 6, 18, 54, …

Check whether the following sequence is G.P. If so, write t_n.

1, –5, 25, –125 …

Check whether the following sequence is G.P. If so, write t_n.

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...

Check whether the following sequence is G.P. If so, write t_n.

3, 4, 5, 6, …

Check whether the following sequence is G.P. If so, write t_n.

7, 14, 21, 28, …

For the G.P. if r = `1/3`, a = 9 find t₇

For the G.P. if a = `7/243`, r = 3 find t₆.

For the G.P. if r = − 3 and t₆ = 1701, find a.

For the G.P. if a = `2/3`, t₆ = 162, find r.

Which term of the G.P. 5, 25, 125, 625, … is 5¹⁰?

For what values of x, the terms `4/3`, x, `4/27` are in G.P.?

If for a sequence, t_n = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio

Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.

Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1

Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.

The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y² = xz

If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.