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

Solve the cubic equations:

2x³ – 9x² + 10x = 3

Solve the cubic equations:

8x³ – 2x² – 7x + 3 = 0

Solve the equation:

x⁴ – 14x² + 45 = 0

Solve: (x – 5)(x – 7) (x + 6)(x + 4) = 504

Solve: (x – 4)(x – 2)(x- 7)(x + 1) = 16

Solve: (2x – 1)(x + 3)(x – 2)(2x + 3) + 20 = 0

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A zero of x³ + 64 is

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If α, β and γ are the zeros of x³ + px² + qx + r, then `sum 1/alpha` is

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The polynomial x³ – kx² + 9x has three real roots if and only if, k satisfies

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If x³ + 12x² + 10ax + 1999 definitely has a positive zero, if and only if 

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The polynomial x³ + 2x + 3 has

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The number of positive roots of the polynomials `sum_("j" = 0)^"n"  ""^"n""C"_"r" (- 1)^"r" x^"r"` is

Find the equations of the two tangents that can be drawn from (5, 2) to the ellipse 2x² + 7y² = 14

Find the equations of tangents to the hyperbola `x^2/16 - y^2/64` = 1 which are parallel to10x − 3y + 9 = 0

Show that the line x – y + 4 = 0 is a tangent to the ellipse x² + 3y² = 12. Also find the coordinates of the point of contact

Find the equation of the tangent to the parabola y² = 16x perpendicular to 2x + 2y + 3 = 0

Prove that the point of intersection of the tangents at ‘t₁‘ and t₂’ on the parabola y² = 4ax is [at₁ t₂, a (t₁ + t₂)]

If the normal at the point ‘t₁‘ on the parabola y² = 4ax meets the parabola again at the point ‘t₂‘, then prove that t₂ = `- ("t"_1 + 2/"t"_1)`

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The ellipse E₁ : `x^2/9 + y^2/4` = 1 is inscribed in a rectangle R whose sides are parallel to the co-ordinate axes. Another ellipse E₂ passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse is

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Tangents are drawn to, the, hyperbola `x^2/9 - y^2/4` = 1 parallel to the straight line 2x – y – 1. One of the points of contact of tangents on the hyperbola is