HSC Science कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

If `(1 + z)/(1 - z)` = cos 2θ + i sin 2θ, show that z = i tan θ

If cos α + cos β + cos γ = sin α + sin β + sin γ = 0, show that cos 3α + cos 3β + cos 3γ = 3 cos (α + β + γ)

If cos α + cos β + cos γ = sin α + sin β + sin γ = 0. then show that sin 3α + sin 3β + sin 3γ = 3 sin(α + β + γ)

If z = x + iy and arg `((z - "i")/(z + 2)) = pi/4`, show that x² + y³ + 3x – 3y + 2 = 0 

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The solution of the equation |z| – z = 1 + 2i is

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If z is a complex number such that z ∈ C\R and `"z" + 1/"z"` ∈ R, then |z| is

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If `(z - 1)/(z + 1)` purely imaginary then |z| is

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The principal argument of `3/(-1 + "i")` is

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The principal argument of (sin 40° + i cos 40°)⁵ is

Solve the following equations
sin² x – 5 sin x + 4 = 0

Solve the following equations
12x³ + 8x = 29x² – 4 = 0

Examine for the rational roots of

2x³ – x² – 1 = 0

Examine for the rational roots of

x⁸ – 3x + 1 = 0

Solve: `8x^(3/(2"n")) - 8x^((-3)/(2"n"))` = 63

Solve: `2sqrt(x/"a") + 3sqrt("a"/x) = "b"/"a" + (6"a")/"b"`

Solve the equation
6x⁴ – 35x³ + 62x² – 35x + 6 = 0

Solve the equation
x⁴ + 3x³ – 3x – 1 = 0

Find all real numbers satisfying 4^x – 3(2^x+2) + 2⁵ = 0

Solve the equation 6x⁴ – 5x³ – 38x² – 5x + 6 = 0 if it is known that `1/3` is a solution

Choose the correct alternative:

If sin^–1x = 2sin^–1 α has a solution, then