HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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

Answer the following:

Find approximate value of `1/4.08` upto four places of decimals

Evaluate the following :

`lim_(x -> pi/2) [("cosec"x - 1)/(pi/2 - x)^2]`

Evaluate the following :

`lim_(x -> "a") [(sinx - sin"a")/(root(5)(x) - root(5)("a"))]`

Evaluate the following :

`lim_(x -> pi) [(sqrt(5 + cosx) - 2)/(pi - x)^2]`

Evaluate the following :

`lim_(x -> pi/6) [(cos x - sqrt(3) sinx)/(pi - 6x)]`