HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

2i

Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

− 3i

Answer the following:

Find the modulus and argument of a complex number and express it in the polar form.

`1/sqrt(2) + 1/sqrt(2)"i"`

Answer the following:

Represent 1 + 2i, 2 − i, −3 − 2i, −2 + 3i by points in Argand's diagram.

Answer the following:

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

z = `(2 + 6sqrt(3)"i")/(5 + sqrt(3)"i")`

Answer the following:

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

z = `-6 + sqrt(2)"i"`

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