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

Simplify `1/(3 - sqrt(8)) - 1/(sqrt(8) - sqrt(7)) + 1/(sqrt(7) - sqrt(6)) - 1/(sqrt(6) - sqrt(5)) + 1/(sqrt(5) - 2)`

If x = `sqrt(2) + sqrt(3)` find `(x^2 + 1)/(x^2 - 2)`

Find the principal value of `sin^-1  1/sqrt(2)`

Find the principal value of `cos^-1  sqrt(3)/2`

Find the principal value of cosec^–1(– 1)

Find the principal value of `sec^-1 (- sqrt(2))`.

Find the principal value of `tan^-1 (sqrt(3))`

Choose the correct alternative:
cos 2θ cos 2ϕ+ sin² (θ – ϕ) – sin² (θ + ϕ) is equal to

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it. if the ball is black, what is the probability that it is from the first urn?

The chances of A, B and C becoming manager of a certain company are 5 : 3 : 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?

Let b > 0 and b ≠ 1. Express y = b^x in logarithmic form. Also state the domain and range of the logarithmic function

Compute log₉ 27 – log₂₇ 9

Solve log₈x + log₄x + log₂x = 11

Solve log₄ 2^8x = 2^log₂8 

If a² + b² = 7ab, show that `log  ("a" + "b")/3 = 1/2(log"a" + log "b")`

Prove `log  "a"^2/"bc" + log  "b"^2/"ca" + log  "c"^2/"ab"` = 0

Prove that `log 2 + 16log  16/15 + 12log  25/24 + 7log  81/80` = 1

Prove that log_a² a + log_b² b + log_c² c = `1/8`

Prove log a + log a² + log a³ + · · · + log aⁿ = `("n"("n" + 1))/2 log "a"`

If `log x/(y - z) = logy/(z - x) = logz/(x - y)`, then prove that xyz = 1