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

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

If p and q are the roots of the equation lx² + nx + n = 0, show that `sqrt("p"/"q") + sqrt("q"/"p") + sqrt("n"/l)` = 0

If the equations x² + px + q = 0 and x² + p’x + q’ = 0 have a common root, show that it must be equal to `("pq'" - "p'q")/("q" - "q")` or `("q" - "q'")/("p'" - "P")`

A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was left standing

Find the value of `sin^-1(sin((2pi)/3))`