HSC Arts इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of P(A ∪ B)

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of `"P"("A" ∩ bar"B")`

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of `"P"(bar"A" ∩ "B")`

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. What is the probability that a fire engine is available when needed?

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. What is the probability that neither is available when needed?

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that it will get at least one of the two awards

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that it will get only one of the awards

Choose the correct alternative:

A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies `((x  - 10)(x - 50))/(x - 30) ≥ 0`, then P(A) is

Choose the correct alternative:

It is given that the events A and B are such that P(A) = `1/4`, P(A/B) = `1/2` and P(B/A) = `2/3`. Then P(B) is

Find the zeros of the polynomial function f(x) = 4x² − 25

If x = −2 is one root of x³ − x² − 17x = 22, then find the other roots of equation

Find the real roots of x⁴ = 16

Solve (2x + 1)² − (3x + 2)² = 0

Factorize: x⁴ + 1. (Hint: Try completing the square)

If x² + x + 1 is a factor of the polynomial 3x³ + 8x² + 8x + a, then find the value of a.

Choose the correct alternative:
If  `|x - 2|/(x - 2) ≥ 0`, then x belongs to

In a ∆ABC, if `sin"A"/sin"C" = (sin("A" - "B"))/(sin("B" - "C"))` prove that a², b², C² are in Arithmetic Progression

The angles of a triangle ABC, are in Arithmetic Progression and if b : c = `sqrt(3) : sqrt(2)`, find ∠A

In a ∆ABC, if cos C = `sin "A"/(2sin"B")` show that the triangle is isosceles

In a ∆ABC, prove that `sin "B"/sin "C" = ("c" - "a"cos "B")/("b" - "a" cos"C")`