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JEE Advanced Straight Lines and Conic Sections — practice questions — page 3

Explore 79 free Straight Lines and Conic Sections questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Straight Lines and Conic Sections questions and exercises with answers

Showing questions 61–79 of 79.

Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →Which section does the plane cutRead the answer and worked solution →Proper or degenerateRead the answer and worked solution →Sum, difference or equalRead the answer and worked solution →Type the conic termRead the answer and worked solution →Pop the conic sectionsRead the answer and worked solution →One word is wrongRead the answer and worked solution →Order by the tilt of the planeRead the answer and worked solution →Ellipse and hyperbolaRead the answer and worked solution →Which one does not belongRead the answer and worked solution →Sum or differenceRead the answer and worked solution →Spot the false statementRead the answer and worked solution →Which ones belongRead the answer and worked solution →Knock out the true statementsRead the answer and worked solution →Conic sections bingoRead the answer and worked solution →

Worked practice questions

Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these identities are false.
    Choices
    1. Item
      1 + cot²x = cosec²x
      Correct
      Yes
    2. Explanation
      sec goes with tan, not cot.
      Item
      1 + cot²x = sec²x
    3. Explanation
      The identity is a SUM, not a difference.
      Item
      cos²x − sin²x = 1
    4. Explanation
      Cosine is even, so the sign does not flip.
      Item
      cos(−x) = −cos x
Each trap swaps a Pythagorean identity or a parity. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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Order the steps: convert degrees to radians

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Steps
  1. Start from the angle in degrees
  2. Multiply by π
  3. Divide by 180
  4. The result is the angle in radians
One conversion factor, applied once. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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Flip and pair: identity with its value

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Matching pairs
  1. A
    cos²x + sin²x
    B
    1
  2. A
    1 + tan²x
    B
    sec²x
  3. A
    1 + cot²x
    B
    cosec²x
  4. A
    sin(−x)
    B
    −sin x
  5. A
    cos(−x)
    B
    cos x
The core identities by sight. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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