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Indian Navy MR Permcomb — practice questions

Explore 52 free Permcomb questions in Indian Navy MR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Permcomb questions and exercises with answers

Showing questions 1–30 of 52.

$\sin(180° - \theta)$ equals:Read the answer and worked solution →For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →Median of an odd-length sorted data set is:Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →

Worked practice questions

$\sin(180° - \theta)$ equals:

  1. $-\cos\theta$
  2. $-\sin\theta$
  3. $\sin\theta$
  4. $\cos\theta$
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Correct answer: C. $\sin\theta$

Supplementary-angle identity: $\sin(180° - \theta) = \sin\theta$. Reason: sine is positive in the second quadrant (where $180° - \theta$ lies for $0° < \theta < 180°$), and the reference angle is $\theta$. Companion identities: - $\cos(180° - \theta) = -\cos\theta$ - $\tan(180° - \theta) = -\tan\theta$

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For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:

  1. $1$
  2. $0$
  3. $2.0$
  4. $1.25$
Show answer and solution

Correct answer: D. $1.25$

$F(0.5) = 3(0.5) - 2(0.5)^3 = 1.5 - 2(0.125) = 1.5 - 0.25 = 1.25$. (Note: this exceeds 1, which signals a problem with the source p.d.f. — but the question is purely about evaluating the given $F$ formula.)

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sin(A + B) equals:

  1. cosA cosB - sinA sinB
  2. sinA cosB - cosA sinB
  3. sinA cosB + cosA sinB
  4. sinA + sinB
Show answer and solution

Correct answer: C. sinA cosB + cosA sinB

**Compound angle formula:** sin(A + B) = sinA cosB + cosA sinB. (And sin(A - B) = sinA cosB - cosA sinB.)

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