HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Choose the correct alternative:

If z is a non zero complex number, such that 2iz² = `bar(z)` then |z| is

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If |z – 2 + i| ≤ 2, then the greatest value of |z| is

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If (1 + i)(1 + 2i)(1 + 3i) ……. (l + ni) = x + iy, then 2.5.10 …… (1 + n²) is

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If α and β are the roots of x² + x + 1 = 0, then α²⁰²⁰ + β²⁰²⁰ is

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The value of `((1 + sqrt(3)"i")/(1 - sqrt(3)"i"))^10` is

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If f and g are polynomials of degrees m and n respectively, and if h(x) = (f o g)(x), then the degree of h is

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A polynomial equation in x of degree n always has

Find the domain of the following functions:

`tan^-1 (sqrt(9 - x^2))`

Find the domain of the following functions:

`1/2 tan^-1 (1 - x^2) - pi/4`

Find the value of `tan^-1(tan  (5pi)/4)`

Find the value of `tan^-1 (tan(- pi/6))`

Find the value of `tan(tan^-1((7pi)/4))`

Find the value of `tan(tan^-1(1947))`

Find the value of `tan(tan^-1(- 0.2021))`

Find the value of `tan(cos^-1 (1/2) - sin^-1 (- 1/2))`

Find the value of `sin(tan^-1 (1/2) - cos^-1 (4/5))`

Find the value of `cos(sin^-1 (4/5) - tan^-1 (3/4))`

Find the equation of the tangent at t = 2 to the parabola y² = 8x (Hint: use parametric form)

Find the equations of the tangent and normal to hyperbola 12x² – 9y² = 108 at θ = `pi/3`. (Hint: use parametric form)

If `vec"a" = hat"i"  - 2hat"j" + 3hat"k", vec"b" = 2hat"i" + hat"j" - 2hat"k", vec"c" = 3hat"i" + 2hat"j" + hat"k"`, find `(vec"a" xx vec"b") xx vec"c"`