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

If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos² B + cos² C = 1

If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin² B + sin² C = 1

If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos  "B"/2  sin  "C"/2`

Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` = 

Choose the correct alternative:
If cos 28° + sin 28° = k³, then cos 17° is equal to

Choose the correct alternative:
`(1 + cos  pi/8) (1 + cos  (3pi)/8) (1 + cos  (5pi)/8) (1 + cos  (7pi)/8)` =

Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to

Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =

Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f₄(x) − f₆(x) = 

Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is 

If `""^(("n"  – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n

If `""^10"P"_("r" - 1)` = 2 × ⁶Pr, find r

Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?

Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?

Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?

A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?

A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?

A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?

A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

What is the maximum number of different answers can the students give?

A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

How will the answer change if each question may have more than one correct answers?