Start learning →

Indian Navy SSR Conic Sections — practice questions

Explore 48 free Conic Sections questions in Indian Navy SSR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Conic Sections with Quill →

Conic Sections questions and exercises with answers

Showing questions 1–30 of 48.

Difference of focal distances from any point on hyperbola x²/16 - y²/9 = 1:Read the answer and worked solution →The equation y² = 4ax represents a PARABOLA with: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 →Match each identity to its nameRead the answer and worked solution →

Worked practice questions

Difference of focal distances from any point on hyperbola x²/16 - y²/9 = 1:

  1. 18
  2. 8 (= 2a)
  3. sqrt(7)
  4. 10
Show answer and solution

Correct answer: B. 8 (= 2a)

**Definition of hyperbola:** |d_F1 - d_F2| = 2a. Here a² = 16, a = 4, 2a = 8. (Foci at (±5, 0) since c = sqrt(16+9) = 5.)

Open this question →

The equation y² = 4ax represents a PARABOLA with:

  1. Focus at (0, a) and directrix y = -a (vertical)
  2. Focus at (a, 0) and directrix x = -a
  3. Focus at the origin (0, 0) always
  4. Focus at (4a, 0) and directrix x = 0
Show answer and solution

Correct answer: B. Focus at (a, 0) and directrix x = -a

y² = 4ax: opens to the RIGHT. Focus at (a, 0), directrix x = -a (vertical line). Latus rectum length = 4a. For y² = -4ax (opens left), focus at (-a, 0).

Open this question →

Sort each inverse function into its domain

Read exercise and reference answers
Items
  1. Item
    sin⁻¹ x
    Category
    [−1, 1]
  2. Item
    cos⁻¹ x
    Category
    [−1, 1]
  3. Item
    cosec⁻¹ x
    Category
    R − (−1, 1)
  4. Item
    sec⁻¹ x
    Category
    R − (−1, 1)
  5. Item
    tan⁻¹ x
    Category
    R
  6. Item
    cot⁻¹ x
    Category
    R
Categories
  1. Item
    [−1, 1]
  2. Item
    R − (−1, 1)
  3. Item
    R
Only sin⁻¹ and cos⁻¹ accept every value from −1 to 1. cosec⁻¹ and sec⁻¹ need |x| ≥ 1, so the open middle is cut out. tan⁻¹ and cot⁻¹ accept any real number. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

How to practise

  1. Choose a Conic Sections 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 Mathematics topics

SequencesBinomial TheoremSequences and SeriesProbability & StatisticsGeometryPermutations and CombinationsLinear ProgrammingVectors & 3D Geometry