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

Simplify: `(3^-6)^(1/3)`

Simplify: `(27^((-2)/3))/(27^((-1)/3))`

Evaluate `[((256)^(-1/2))^((-1)/4)]^3`

If `(x^(1/2) + x^(- 1/2))^2 = 9/2` then find the value of `(x^(1/2) - x^(-1/2))` for x >1

Simplify and hence find the value of n:

`(3^(2"n")*9^2*3^(-"n"))/(3^(3"n"))` = 27

Find the radius of the spherical tank whose volume is `(32pi)/3` units

. Simplify by rationalising the denominator `(7 + sqrt(6))/(3 - sqrt(2))`

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