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Indian Navy SSR Linear Programming — practice questions

Explore 77 free Linear Programming questions in Indian Navy SSR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Programming questions and exercises with answers

Showing questions 1–30 of 77.

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:Read the answer and worked solution →$\cos 3\theta$ 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 →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →Find the midpoint of A(2, −3) and B(8, 5).Read the answer and worked solution →The angle 90° in radians 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

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:

  1. $\dfrac{1}{2}$
  2. $1$
  3. $0$
  4. $-1$
Show answer and solution

Correct answer: C. $0$

Square both sides of $\sin\theta + \cos\theta = 1$: $(\sin\theta + \cos\theta)^2 = 1^2$ $\sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta = 1$ Using $\sin^2 + \cos^2 = 1$: $1 + 2\sin\theta\cos\theta = 1$ $\sin\theta \cos\theta = 0$. Verify: the original equation holds only when $\theta = 0°$ (so $\sin = 0$, $\cos = 1$) or $\theta = 90°$ (so $\sin = 1$, $\cos = 0$). In both cases the product is 0. ✓

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$\cos 3\theta$ equals:

  1. $3\sin\theta - 4\sin^3\theta$
  2. $3\cos\theta - 4\cos^3\theta$
  3. $4\sin^3\theta - 3\sin\theta$
  4. $4\cos^3\theta - 3\cos\theta$
Show answer and solution

Correct answer: D. $4\cos^3\theta - 3\cos\theta$

Triple-angle for cosine: $\cos 3\theta = 4\cos^3\theta - 3\cos\theta$. Derivation: $\cos 3\theta = \cos(2\theta + \theta) = \cos 2\theta \cos\theta - \sin 2\theta \sin\theta = (2\cos^2\theta - 1)\cos\theta - 2\sin\theta\cos\theta \cdot \sin\theta = 2\cos^3\theta - \cos\theta - 2\sin^2\theta\cos\theta = 2\cos^3\theta - \cos\theta - 2(1-\cos^2\theta)\cos\theta = 4\cos^3\theta - 3\cos\theta$. Companion: $\sin 3\theta = 3\sin\theta - 4\sin^3\theta$ (option C — common trap). Mnemonic: in both, the coefficients are 3 and 4, and the cubed term has the same trig function as the angle outside.

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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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More Mathematics topics

SequencesBinomial TheoremSequences and SeriesProbability & StatisticsGeometryPermutations and CombinationsVectors & 3D GeometryLimits and Continuity