HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

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")`

In an ∆ABC, prove that a cos A + b cos B + c cos C = 2a sin B sin C

In a ∆ABC, ∠A = 60°. Prove that b + c = `2"a" cos (("B" - "C")/2)`

In an ∆ABC, prove the following, `"a"sin ("A"/2 + "B") = ("b" + "c") sin  "A"/2`

In a ∆ABC, prove the following, a(cos B + cos C) = `2("b" + "c") sin^2  "A"/2`

In a ∆ABC, prove the following, `("a"^2 - "c"^2)/"b"^2 = (sin ("A" - "C"))/(sin("A" + "C"))`

In a ∆ABC, prove the following, `("a"sin("B" - "C"))/("b"^2 - "c"^2) = ("b"sin("C" - "A"))/("c"^2 - "a"^2) = ("c"sin("A" - "B"))/("a"^2 - "b"^2)`

In a ∆ABC, prove the following, `("a"+ "b")/("a" - "b") = tan(("A" + "B")/2) cot(("A" - "B")/2)`