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

Solve for x quantity demanded if 16x − 4 = 68 + 7x.

Classify each element of `{sqrt(7), (-1)/4, 0, 3, 1, 4, 4, 22/7}` as a member of N, Q, R − Q or Z

Prove that `sqrt(3)` is an irrational number.
(Hint: Follow the method that we have used to prove `sqrt(2)` ∉ Q)

Are there two distinct irrational numbers such that their difference is a rational number? Justify

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

Find a positive number smaller than `1/2^1000`. Justify

Choose the correct alternative:
Given that x, y and b are real numbers x < y, b > 0, then

Identify the quadrant in which an angle given measure lies
25°

Identify the quadrant in which an angle given measure lies
825°

Identify the quadrant in which an angle given measure lies
– 55°

Identify the quadrant in which an angle given measure lies
328°

Identify the quadrant in which an angle given measure lies
– 230°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
395°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
525°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
1150°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 270°

For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 450°

If a cos θ − b sin θ = c, show that a sin θ + b cos θ = `+-  sqrt("a"^2 + "b"^2 - "c"^2)`

If sin θ + cos θ = m, show that cos⁶θ + sin⁶θ = `(4 - 3("m"^2 - 1)^2)/4`, where m² ≤ 2

If `(cos^4α)/(cos^2β) + (sin^4α)/(sin^2β)` = 1, prove that sin⁴α + sin⁴β = 2 sin²α sin²β