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

An urn contains 5 mangoes and 4 apples. Three fruits are taken at random. If the number of apples taken is a random variable, then find the values of the random variable and number of points in its inverse images

Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win ₹ 15 for each red ball selected and we lose ₹ 10 for each black ball selected. X denotes the winning amount, then find the values of X and number of points in its inverse images

A six sided die is marked ‘2’ on one face, ‘3’ on two of its faces, and ‘4’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images

Choose the correct alternative:

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

If z₁ = 1 – 3i, z₂ = – 4i, and z₃ = 5, show that (z₁ + z₂) + z₃ = z₁ + (z₂ + z₃)

If z₁ = 1 – 3i, z₂ = – 4i, and z₃ = 5, show that (z₁ z₂)z₃ = z₁(z₂ z₃)

If z₁ = 3, z₂ = 7i, and z₃ = 5 + 4i, show that z₁(z₂ + z₃) = z₁z₂ + z₁z₃

If z₁ = 3, z₂ = 7i, and z₃ = 5 + 4i, show that (z₁ + z₂)z₃ = z₁z₃ + z₂z₃

If z₁ = 2 + 5i, z₂ = – 3 – 4i, and z₃ = 1 + i, find the additive and multiplicative inverse of z₁, z₂ and z₃

Construct a cubic equation with roots 1, 2 and 3

Construct a cubic equation with roots 1, 1, and – 2

Construct a cubic equation with roots `2, 1/2, and 1`

If α, β and γ are the roots of the cubic equation x³ + 2x² + 3x + 4 = 0, form a cubic equation whose roots are 2α, 2β, 2γ

If α, β and γ are the roots of the cubic equation x³ + 2x² + 3x + 4 = 0, form a cubic equation whose roots are `1/alpha, 1/beta, 1/γ`

If α, β and γ are the roots of the cubic equation x³ + 2x² + 3x + 4 = 0, form a cubic equation whose roots are `- alpha, -beta, -γ`

Solve the equation 3x³ – 16x² + 23x – 6 = 0 if the product of two roots is 1

Find the sum of squares of roots of the equation `2x^4 - 8x^3 + 6x^2 - 3` = 0

Solve the equation x³ – 9x² + 14x + 24 = 0 if it is given that two of its roots are in the ratio 3 : 2

If α, β, and γ are the roots of the polynomial equation ax³ + bx² + cx + d = 0, find the value of `sum  alpha/(betaγ)` in terms of the coefficients

If α, β, γ and δ are the roots of the polynomial equation 2x⁴ + 5x³ – 7x² + 8 = 0, find a quadratic equation with integer coefficients whose roots are α + β + γ + δ and αβγδ