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

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 

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

(a + b)⁻⁴ 

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

`("a" + "b")^(1/4)`

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

`("a" - "b")^(-1/4)`

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

`("a" + "b")^(-1/3)`

Simplify first three terms in the expansion of the following

(1 + 2x)^–4 

Simplify first three terms in the expansion of the following

`(1 + 3x)^(-1/2)`

Simplify first three terms in the expansion of the following

`(2 - 3x)^(1/3)`

Simplify first three terms in the expansion of the following

`(5 + 4x)^(-1/2)`

Simplify first three terms in the expansion of the following

`(5 - 3x)^(-1/3)`

Use binomial theorem to evaluate the following upto four places of decimal

`sqrt(99)`

Use binomial theorem to evaluate the following upto four places of decimal

`root(3)(126)`