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Indian Navy SSR (Sailor) Conic Sections — practice questions

Explore 49 free Conic Sections questions in Indian Navy SSR (Sailor) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Conic Sections questions and exercises with answers

Showing questions 1–30 of 49.

Find the length of the latus rectum of the parabola $y^2 = 8x$.Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →The Cassegrain telescope design uses the reflective property of a:Read the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead 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 →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →True or false: the historical noteRead the answer and worked solution →Complete the arc length relationRead the answer and worked solution →

Worked practice questions

Find the length of the latus rectum of the parabola $y^2 = 8x$.

  1. $2$
  2. $4$
  3. $8$
  4. $16$
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Correct answer: C. $8$

Compare $y^2 = 8x$ with the standard form $y^2 = 4ax$: $4a = 8 \Rightarrow a = 2$. Latus rectum length = $4a = \mathbf{8}$. **Geometric meaning.** The latus rectum is the chord through the focus, perpendicular to the axis. For $y^2 = 4ax$ the focus is $(a, 0)$ plugging $x = a$ gives $y^2 = 4a^2$ ⇒ $y = \pm 2a$ ⇒ chord length $4a$.

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tan(45°) equals:

  1. ∞
  2. 0
  3. 1
  4. √3
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Correct answer: C. 1

We have tan(45°) = sin(45°)/cos(45°). That is tan(45°) = (1/√2)/(1/√2). So tan(45°) = 1.

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The Cassegrain telescope design uses the reflective property of a:

  1. Parabola (rays through focus to source)
  2. Hyperbola (ray to one focus reflects to other)
  3. Ellipse (light from one focus reflects to other)
  4. Circle (perpendicular reflection)
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Correct answer: B. Hyperbola (ray to one focus reflects to other)

Cassegrain telescope uses a parabolic primary mirror + HYPERBOLIC secondary mirror. **The hyperbola's reflective property:** ray aimed at one focus reflects to the other focus, which is useful for the eyepiece location.

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