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

Choose the correct alternative:
According to the rational root theorem, which number is not possible rational root of 4x⁷ + 2x⁷ – 10x³ – 5?

Find all values of x such that – 6π ≤ x ≤ 6π and cos x = 0

Find all values of x such that – 5π ≤ x ≤ 5π and cos x = 1

State the reason for  `cos^-1 [cos(- pi/6)] ≠ - pi/6`

Is cos^–1(– x) = π – cos^–1 true? justify your answer

Find the principal value of `cos^-1 (1/2)`

Find the value of `2cos^-1 (1/2) + sin^-1 (1/2)`

Find the value of `cos^-1(1/2) + sin^-1( - 1)`

Find the value of `cos-1 [cos  pi/7 cos  pi/17 - sin  pi/7 sin  pi/17]`

Find the domain of `f(x) = sin^-1 ((|x| - 2)/3) + cos^-1 ((1 - |x|)/4)`

Find the domain of `g(x) = sin^-1x + cos^-1x`

For what value of x, the inequality `pi/2 < cos^-1 (3x - 1) < pi` holds?

Find the value of `cos[cos^-1 (4/5) + sin^-1(4/5)]`

Find the value of `cos^-1(cos((4pi)/3)) + cos^-1 (cos((5pi)/4))`. 

Find the equation of the parabola in the cases given below:

Focus (4, 0) and directrix x = – 4

Find the equation of the parabola in the cases given below:

Passes through (2, – 3) and symmetric about y-axis

Find the equation of the parabola in the cases given below:

Vertex (1, – 2) and Focus (4, – 2)

Find the equation of the parabola in the cases given below:

End points of latus rectum (4, – 8) and (4, 8)

Find the equation of the ellipse in the cases given below:

Foci `(+- 3, 0), "e"+ 1/2`

Find the equation of the ellipse in the cases given below:

Foci (0, ±4) and end points of major axis are (0, ±5)