HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

Answer the following:

Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`

Answer the following:

For a G.P. a = `4/3` and t₇ = `243/1024`, find the value of r

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For a sequence , if t_n = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.

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Find three numbers in G.P. such that their sum is 35 and their product is 1000

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Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.

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For a sequence S_n = 4(7ⁿ – 1) verify that the sequence is a G.P.

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Find the n^th term of the sequence 0.6, 0.66, 0.666, 0.6666, ...

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For a G.P. if t₂ = 7, t₄ = 1575 find a

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If for a G.P. t₃ = `1/3`, t₆ = `1/81` find r

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Find `sum_("r" = 1)^"n" (2/3)^"r"`

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Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.

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If for a G.P. first term is (27)² and seventh term is (8)², find S⁸ 

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If p^th, q^th and r^th terms of a G.P. are x, y, z respectively. Find the value of x^q–r .y^r–p .z^p–q

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Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.

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If a, b, c are in G.P. and ax² + 2bx + c = 0 and px² + 2qx + r = 0 have common roots then verify that pb² – 2qba + ra² = 0

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If p, q, r, s are in G.P., show that (p² + q² + r²) (q² + r² + s²) = (pq + qr + rs)²   

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If p, q, r, s are in G.P., show that (pⁿ + qⁿ), (qⁿ + rⁿ) , (rⁿ + sⁿ) are also in G.P.

Answer the following:

Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`

Evaluate: 8!

Evaluate: 10!