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

If S₁, S₂ and S₃ are the sums of first n natural numbers, their squares and their cubes respectively then show that - 9S₂² = S₃ (1 + 8 S₁) 

Answer the following:

Find 2 + 22 + 222 + 2222 + ... upto n terms

Answer the following:

Find `sum_("r" = 1)^"n" (5"r"^2 + 4"r" - 3)`

Answer the following:

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

Answer the following:

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

Answer the following:

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

Answer the following:

Find 2 × 6 + 4 × 9 + 6 × 12 + ... upto n terms

Answer the following:

Find 2 × 5 × 8 + 4 × 7 × 10 + 6 × 9 × 12 + ... upto n terms

Answer the following:

Find `1^2/1 + (1^2 + 2^2)/2 + (1^2 + 2^2 + 3^2)/3 + ...` upto n terms

Answer the following:

Find 12² + 13² + 14² + 15² + ... 20² 

Answer the following:

If `(1 + 2 + 3 + 4 + 5 + ...  "upto n terms")/(1 xx 2 + 2 xx3 + 3 xx 4 + 4 xx5 + ...  "upto n terms") = 3/22` Find the value of n 

Answer the following:

Find (50² – 49²) + (48² – 47²) + (46² – 45²) + ... + (2² – 1²)

Answer the following:

If  `(1 xx 3 + 2 xx 5 + 3 xx 7 + ...  "upto n terms")/(1^3 + 2^3 + 3^3 + ...  "upto n terms") = 5/9`, find the value of n

Answer the following:

If p, q, r are in G.P. and `"p"^(1/x) = "q"^(1/y) = "r"^(1/z)`, verify whether x, y, z are in A.P. or G.P. or neither.

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 + x)⁻⁴

State, by writing first four terms, the expansion of the following, where |x| < 1

`(1 - x)^(1/3)`

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 – x²)^–3

State, by writing first four terms, the expansion of the following, where |x| < 1

`(1 + x)^(-1/5)`

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 + x²)^–1

State, by writing first four terms, the expansion of the following, where |b| < |a|

(a − b)⁻³