HSC Science (Electronics) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Convert the complex numbers in polar form and also in exponential form.

`(-3)/2 + (3sqrt(3))/2"i"`

Answer the following:

Find the coefficient of x⁶ in the expansion of e^2x using series expansion

In the following expansion, find the indicated coefficient.

x³ in `(x^2 + (3sqrt(2))/x)^9`

In the following expansion, find the indicated coefficient.

x⁸ in `(2x^5 - 5/x^3)^8`

In the following expansion, find the indicated coefficient.

x⁹ in `(1/x + x^2)^18`

In the following expansion, find the indicated coefficient.

x^–3 in `(x - 1/(2x))^5`

In the following expansion, find the indicated coefficient.

x^–20 in `(x^3 - 1/(2x^2))^15`

Show That C₀ + C₁ + C₂ + .... C₈ = 256

Show That C₀ + C₁ + C₂ + .... C₉ = 512

Show That C₁ + C₂ + C₃ + .... C₇ = 127

Show That C₁ + C₂ + C₃ + .... C₆ = 63

Show That C₀ + C₂ + C₄ + C₆ + C₈ = C₁ + C₃ + C₅ + C₇ = 128

Select the correct answer from the given alternatives.

The value ¹⁴C₁ + ¹⁴C₃ + ¹⁴C₅ + ..... + ¹⁴C₁₁ is

Select the correct answer from the given alternatives.

The value ¹¹C₂ + ¹¹C₄ + ¹¹C₆ + ¹¹C₈ is equal to

Expand (3x² + 2y)⁵ 

Answer the following:

If the coefficient of x¹⁶ in the expansion of (x² + ax)¹⁰ is 3360, find a

Evaluate the following limit : 

`lim_(x -> 0) [(9^x - 5^x)/(4^x - 1)]`

Evaluate the following limit : 

`lim_(x -> 0) [(5^x + 3^x - 2^x - 1)/x]`

Evaluate the following limit : 

`lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/sinx]`

Evaluate the following limit : 

`lim_(x -> 0) [(6^x + 5^x + 4^x - 3^(x + 1))/sinx]`