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

Resolve the following rational expressions into partial fractions

`(x^2 + x + 1)/(x^2 - 5x + 6)`

Resolve the following rational expressions into partial fractions

`(x^3 + 2x + 1)/(x^2 + 5x + 6)`

Resolve the following rational expressions into partial fractions

`(x + 12)/((x + 1)^2 (x - 2))`

Resolve the following rational expressions into partial fractions

`(6x^2 - x + 1)/(x^3 + x^2 + x + 1)`

Resolve the following rational expressions into partial fractions

`(2x^2 + 5x - 11)/(x^2 + 2x - 3)`

Resolve the following rational expressions into partial fractions

`(7 + x)/((1 + x)(1 + x^2))`

Determine the region in the plane determined by the inequalities:

x ≤ 3y, x ≥ y

Determine the region in the plane determined by the inequalities:

y ≥ 2x, −2x + 3y ≤ 6

Determine the region in the plane determined by the inequalities:

3x + 5y ≥ 45, x ≥ 0, y ≥ 0

Determine the region in the plane determined by the inequalities:

2x + 3y ≤ 35, y ≥ 2, x ≥ 5.

Determine the region in the plane determined by the inequalities:

2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0

Determine the region in the plane determined by the inequalities:

x − 2y ≥ 0, 2x − y ≤ −2, x ≥ 0, y ≥ 0

Determine the region in the plane determined by the inequalities:

2x + y ≥ 8, x + 2y ≥ 8, x + y ≤ 6

Choose the correct alternative:
The solution of 5x − 1 < 24 and 5x + 1 > −24 is

Choose the correct alternative:
The solution set of the following inequality |x − 1| ≥ |x − 3| is

Determine whether the following measurements produce one triangle, two triangles or no triangle:
∠B = 88°, a = 23, b = 2. Solve if solution exists

If the sides of a ∆ABC are a = 4, b = 6 and c = 8, then show that 4 cos B + 3 cos C = 2

In a ∆ABC, if a = `sqrt(3) - 1`, b = `sqrt(3) + 1` and C = 60° find the other side and other two angles

In any ∆ABC, prove that the area ∆ = `("b"^2 + "c"^2 - "a"^2)/(4 cot "A")`

In a ∆ABC, if a = 12 cm, b = 8 cm and C = 30°, then show that its area is 24 sq.cm