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

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Let X have a Bernoulli distribution with a mean of 0.4, then the variance of (2X – 3) is

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If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is

Solve: `("d"y)/("d"x) = y sin 2x`

Write in polar form of the following complex numbers

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

Write in polar form of the following complex numbers

`3 - "i"sqrt(3)`

Write in polar form of the following complex numbers

– 2 – i2

Write in polar form of the following complex numbers

`("i" - 1)/(cos  pi/3 + "i" sin  pi/3)`

Find the rectangular form of the complex numbers

`(cos  pi/6  "i" sin  pi/6)(cos  pi/12 + "i" sin  pi/12)`

Find the rectangular form of the complex numbers

`(cos  pi/6 - "i" sin  pi/6)/(2(cos  pi/3 + "i" sin  pi/3))`

If (x₁ + iy₁)(x₂ + iy₂)(x₃ + iy₃) ... (x_n + iy_n) = a + ib, show that `(x_1^2 + y_1^2)(x_2^2 + y_2^2)(x_3^2 + y_3^2) ... (x_"n"^2 + y_"n"^2)` = a² + b² 

If (x₁ + iy₁)(x₂ + iy₂)(x₃ + iy₃) ... (x_n + iy_n) = a + ib, show that `sum_("r" = 1)^"n" tan^-1 (y_"r"/x_"r") = tan^-1 ("b"/"a") + 2"k"pi, "k" ∈ "z"`

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