Start learning →

Indian Coast Guard Yantrik Permutations and Combinations — practice questions

Explore 3 free Permutations and Combinations questions in Indian Coast Guard Yantrik Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

Practise Permutations and Combinations with Quill →

Permutations and Combinations questions and exercises with answers

Showing questions 1–3 of 3.

If tan α = √5 - 2, then the value of tan α - cot α is:Read the answer and worked solution →Given 10 sin⁴α + 15 cos⁴α = 6, find the value of 27 cosec⁶α + 8 sec⁶α.Read the answer and worked solution →If tan α = √3 + 2, then the value of tan α − cot α is:Read the answer and worked solution →

Worked practice questions

If tan α = √5 - 2, then the value of tan α - cot α is:

  1. -2
  2. √5 + 2
  3. 2√5
  4. -4
Show answer and solution

Correct answer: D. -4

1. cot α = 1 / tan α = 1 / (√5 - 2). 2. Rationalise: 1/(√5 - 2) = (√5 + 2)/((√5)² - 2²) = (√5 + 2)/1 = √5 + 2. 3. tan α - cot α = (√5 - 2) - (√5 + 2) = -4. _Source: RRB Group D CEN-02/2018 PYQ, Q.39._

Open this question →

Given 10 sin⁴α + 15 cos⁴α = 6, find the value of 27 cosec⁶α + 8 sec⁶α.

  1. 50
  2. 125
  3. 250
  4. 75
Show answer and solution

Correct answer: C. 250

1. Let s = sin²α, c = cos²α with s + c = 1. The condition 10s² + 15c² = 6 is solved by s = 3/5, c = 2/5 (since 10·9/25 + 15·4/25 = 90/25 + 60/25 = 6). 2. cosec⁶α = 1/s³ = (5/3)³ = 125/27, so 27 cosec⁶α = 125; sec⁶α = 1/c³ = (5/2)³ = 125/8, so 8 sec⁶α = 125. 3. Sum = 125 + 125 = 250. _Source: RRB Group D CEN-02/2018 PYQ, Q.49._

Open this question →

If tan α = √3 + 2, then the value of tan α − cot α is:

  1. 2
  2. √3 − 2
  3. 2√3
  4. 4
Show answer and solution

Correct answer: C. 2√3

1. cot α = 1 / (√3 + 2). Rationalise: multiply by (√3 − 2)/(√3 − 2); denominator = 3 − 4 = −1. 2. So cot α = −(√3 − 2) = 2 − √3. 3. tan α − cot α = (√3 + 2) − (2 − √3) = 2√3. _Source: RRB Group D CEN-02/2018 PYQ, Q.25._

Open this question →

How to practise

  1. Choose a Permutations and Combinations question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Quantitative Aptitude topics

MensurationMultiplicationNumber PropertiesSimple InterestSquares And RootsPercentagesNumber SystemRatio and Proportion