HSC Science Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:
The equation whose roots are numerically equal but opposite in sign to the roots of 3x² − 5x − 7 = 0 is

Choose the correct alternative:
If 8 and 2 are the roots of x² + ax + c = 0 and 3, 3 are the roots of x² + dx + b = 0, then the roots of the equation x² + ax + b = 0 are

Choose the correct alternative:
If a and b are the real roots of the equation x² − kx + c = 0, then the distance between the points (a, 0) and (b, 0) is

Choose the correct alternative:
The number of roots of (x + 3)⁴ + (x + 5)⁴ = 16 is

Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`

Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`

Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

sin⁴x = sin²x

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 cos²x + 1 = – 3 cos x

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 sin²x + 1 = 3 sin x

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

cos 2x = 1 − 3 sin x

Solve the following equations:
sin 5x − sin x = cos 3

Solve the following equations:
2 cos²θ + 3 sin θ – 3 = θ

Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ

Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0

Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ

Solve the following equations:
sin θ + cos θ = `sqrt(2)`

Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1

Solve the following equations:
cot θ + cosec θ = `sqrt(3)`

Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`