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UPCET / UPSEE Limits and Continuity — practice questions — page 5

Explore 131 free Limits and Continuity questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Limits and Continuity questions and exercises with answers

Showing questions 121–131 of 131.

Assertion and reasonRead 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 →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 →Radians and degreesRead the answer and worked solution →True or false: reading the identitiesRead the answer and worked solution →Match each limit ideaRead the answer and worked solution →Tap what is true of a limitRead the answer and worked solution →

Worked practice questions

Assertion and reason

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Questions
  1. Reason
    sec²x equals 1 + tan²x, and a square is never negative.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    sec²x is never less than 1.
  2. Reason
    sine is odd and cosine is even.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    sin and cos behave differently under a sign change of x.
  3. Reason
    sin(−x) = −sin x.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    cos(−x) = −cos x.
  4. Reason
    π radians corresponds to 180 degrees.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Angles can be measured in radians instead of degrees.
The reason must genuinely explain the assertion. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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Two are true, one is not

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Questions
  1. False statement
    1 + tan²x = cosec²x
    Statements
    1. cos²x + sin²x = 1
    2. 1 + tan²x = sec²x
    3. 1 + tan²x = cosec²x
  2. False statement
    cosine is odd
    Statements
    1. cosine is odd
    2. sine is odd
    3. cosine is even
  3. False statement
    cos(x+y) uses a plus
    Statements
    1. cos(x+y) uses a minus
    2. cos(x+y) uses a plus
    3. sin(x+y) uses a plus
The false line swaps an identity or a sign. Source: syllabus Maths, Ch 3 Trigonometric Functions.

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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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