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

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)`

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

`root(4)(16.08)`

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

(1.02)^–5 

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

(0.98)^–3 

Show That C₁ + C₂ + C₃ + .... C_n = 2ⁿ − 1

Show That C₀ + 2C₁ + 3C₂ + 4C₃ + ... + (n + 1)C_n = (n + 2)2ⁿ⁻¹

Answer the following:

Expand `((2x)/3 - 3/(2x))^4`

Answer the following:

Using binomial theorem, find the value of `root(3)(995)` upto four places of decimals