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

Solve the following equations
sin² x – 5 sin x + 4 = 0

Solve the following equations
12x³ + 8x = 29x² – 4 = 0

Examine for the rational roots of

2x³ – x² – 1 = 0

Examine for the rational roots of

x⁸ – 3x + 1 = 0

Solve: `8x^(3/(2"n")) - 8x^((-3)/(2"n"))` = 63

Solve: `2sqrt(x/"a") + 3sqrt("a"/x) = "b"/"a" + (6"a")/"b"`

Solve the equation
6x⁴ – 35x³ + 62x² – 35x + 6 = 0

Solve the equation
x⁴ + 3x³ – 3x – 1 = 0

Find all real numbers satisfying 4^x – 3(2^x+2) + 2⁵ = 0

Solve the equation 6x⁴ – 5x³ – 38x² – 5x + 6 = 0 if it is known that `1/3` is a solution

Choose the correct alternative:

If sin^–1x = 2sin^–1 α has a solution, then

Choose the correct alternative:

If sin^-1 x + sin^-1 y + sin^-1 z = `(3pi)/2`, the value of show that `x^2017 + y^2018 + z^2019 - 9/(x^101 + y^101 + z^101)` is

A bridge has a parabolic arch that is 10 m high in the centre and 30 m wide at the bottom. Find the height of the arch 6m from the centre, on either sides

A tunnel through a mountain for a four-lane highway is to have a elliptical opening. The total width of the highway (not the opening) is to be 16 m, and the height at the edge of the road must be sufficient for a truck 4 m high to clear if the highest point of the opening is to be 5 m approximately. How wide must the opening be?

At a water fountain, water attains a maximum height of 4 m at horizontal distance of 0.5 m from its origin. If the path of water is a parabola, find the height of water at a horizontal distance of 0.75 m from the point of origin.

An engineer designs a satellite dish with a parabolic cross-section. The dish is  5m wide at the opening, and the focus is placed 1 2. m from the vertex. Position a coordinate system with the origin at the vertex and the x-axis on the parabola’s axis of symmetry and find an equation of the parabola

An engineer designs a satellite dish with a parabolic cross-section. The dish is 5 m wide at the opening and the focus is placed 1.2 m from the vertex. Find the depth of the satellite dish at the vertex

Parabolic cable of a 60 m portion of the roadbed of a suspension bridge are positioned as shown below. Vertical Cables are to be spaced every 6m along this portion of the roadbed. Calculate the lengths of first two of these vertical cables from the vertex.

Cross-section of a Nuclear cooling tower is in the shape of a hyperbola with equation `x^2/30^2 - y^2/44^2` = 1. The tower is 150 m tall and the distance from the top of the tower to the centre of the hyperbola is half the distance from the base of the tower to the centre of the hyperbola. Find the diameter of the top and base of the tower

A rod of length 1 2. m moves with its ends always touching the coordinate axes. The locus of a point P on the rod, which is 0 3. m from the end in contact with x-axis is an ellipse. Find the eccentricity