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

If `(cos^4alpha)/(cos^2beta) + (sin^4alpha)/(sin^2beta)` = 1, prove that `(cos^4beta)/(cos^2alpha) + (sin^4beta)/(sin^2alpha)` = 1

If y = `(2sinalpha)/(1 + cosalpha + sinalpha)`, then prove that `(1 - cosalpha + sinalpha)/(1 + sinalpha)` = y

If x = `sum_("n" = 0)^oo cos^(2"n") theta, y = sum_("n" = 0)^oo sin^(2"n") theta` and z = `sum_("n" = 0)^oo cos^(2"n") theta, sin^(2"n") theta, 0 < theta < pi/2`, then show that xyz = x + y + z. [Hint: Use the formula 1 + x + x² + x³ + . . . = `1/(1 - x), where |x| < 1]

If tan² θ = 1 – k², show that sec θ + tan³ θ cosec θ = (2 – k²)^3/2. Also, find the values of k for which this result holds

If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p

If cot θ(1 + sin θ) = 4m and cot θ(1 – sin θ) = 4n then prove that (m² – n²)² = m

If cosec θ – sin θ = a³ and sec θ – cos θ = b³, then prove that a²b² (a² + b²) = 1

Eliminate θ from the equations a sec θ – c tan θ = b and b sec θ + d tan θ = c

Choose the correct alternative:
The maximum value of `4sin^2x + 3cos^2x + sin   x/2 + cos  x/2` is

Choose the correct alternative:
Which of the following is not true?

A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?

There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?

How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?

Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?

In how many ways 5 persons can be seated in a row?

A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?

Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?

Four children are running a race:
In how many ways can the first two places be filled?

Four children are running a race:
In how many different ways could they finish the race?

Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is allowed