HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:

If p and q are the order and degree of the differential equation `y("d"y)/("d"x) + x^3 (("d"^2y)/("d"x^2)) + xy = cos x`, when

Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images

In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images

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