HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Express the following in the form a + ib, a, b ∈ R, using De Moivre's theorem:

`(1 - sqrt(3)"i")^4`

Express the following in the form a + ib, a, b ∈ R, using De Moivre's theorem:

`(-2sqrt(3) - 2"i")^5`

Select the correct answer from the given alternatives:

If z = r(cos θ + i sin θ), then the value of `"z"/bar("z") + bar("z")/"z"`

Evaluate the following :

`lim_(x -> ∞) [("a"x^3 + "b"x^2 + "c"x + "d")/("e"x^3 + "f"x^2 + "g"x + "h")]`

Evaluate the following :

`lim_(x -> ∞) [(x^3 + 3x + 2)/((x + 4)(x - 6)(x - 3))]`

Evaluate the following :

`lim_(x -> ∞) [(7x^2 + 5x - 3)/(8x^2 - 2x + 7)]`

Evaluate the following :

`lim_(x -> ∞) [(7x^2 + 2x - 3)/(sqrt(x^4 + x + 2))]`

Evaluate the following :

`lim_(x -> ∞) [sqrt(x^2 + 4x + 16) - sqrt(x^2 + 16)]`

Evaluate the following :

`lim_(x -> ∞) [sqrt(x^4 + 4x^2) - x^2]`

Evaluate the following :

`lim_(x -> ∞) [((3x^2 + 4)(4x^2 - 6)(5x^2 + 2))/(4x^6 + 2x^4 - 1)]`

Evaluate the following :

`lim_(x -> ∞) [((3x - 4)^3 (4x + 3)^4)/(3x + 2)^7]`

Evaluate the following :

`lim_(x -> ∞) [sqrt(x)(sqrt(x + 1) - sqrt(x))]`

Evaluate the following :

`lim_(x -> ∞) [((2x - 1)^20 (3x - 1)^30)/(2x + 1)^50]`

Evaluate the following :

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

Select the correct answer from the given alternatives.

`lim_(x -> ∞) [((2x + 3)^7 (x - 5)^3)/(2x - 5)^10]` =

Evaluate the following : 

`lim_(x -> ∞) [((2x + 1)^2*(7x - 3)^3)/(5x + 2)^5]`

Evaluate the following :

`lim_(x -> ∞) [(8x^2 + 5x + 3)/(2x^2 - 7x - 5)]^((4x + 3)/(8x - 1))`

If f(x) is a quadratic polynomial such that f(0) = 3, f'(2) = 2 and f'(3) = 12 then find f(x)

If f(x) = a sin x – b cos x, `"f'"(pi/4) = sqrt(2) and "f'"(pi/6)` = 2, then find f(x)

If f(2) = 4, f′(2) = 1 then find `lim_(x -> 2) [(x"f"(2) - 2"f"(x))/(x - 2)]`