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HPCL Officer Number Theory: related Quantitative Aptitude practice

The practice bank below covers broader Quantitative Aptitude topics; a dedicated Number Theory lesson is not available yet.

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Quantitative Aptitude 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
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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._

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

  1. 50
  2. 125
  3. 250
  4. 75
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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._

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

  1. 2
  2. √3 − 2
  3. 2√3
  4. 4
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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._

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More Quantitative Aptitude topics

MultiplicationNumber PropertiesSquares And RootsRatio and ProportionProfit and LossTime and WorkProfit LossSpeed Distance