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UPCET / UPSEE Geometry — practice questions — page 3

Explore 134 free Geometry questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry questions and exercises with answers

Showing questions 61–90 of 134.

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 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 →

Worked practice questions

Spot the one that does not belong

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Questions
  1. Items
    1. sin⁻¹ x
    2. cos⁻¹ x
    3. tan⁻¹ x
    Odd item
    tan⁻¹ x
  2. Items
    1. sec⁻¹ x
    2. tan⁻¹ x
    3. cot⁻¹ x
    Odd item
    sec⁻¹ x
  3. Items
    1. [−π/2, π/2]
    2. [0, π]
    3. (−π/2, π/2)
    Odd item
    [0, π]
  4. Items
    1. cosec⁻¹ x
    2. sec⁻¹ x
    3. cos⁻¹ x
    Odd item
    cos⁻¹ x
  5. Items
    1. (0, π)
    2. [−1, 1]
    3. R − (−1, 1)
    Odd item
    (0, π)
Each group is built on a single row or column of the summary table. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Two are true, one is not

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Questions
  1. False statement
    tan⁻¹ has domain [−1, 1]
    Statements
    1. tan⁻¹ has domain [−1, 1]
    2. sin⁻¹ has domain [−1, 1]
    3. cos⁻¹ has principal range [0, π]
  2. False statement
    sec⁻¹ removes 0 from its range
    Statements
    1. cot⁻¹ has principal range (0, π)
    2. sec⁻¹ removes 0 from its range
    3. cosec⁻¹ has domain R − (−1, 1)
  3. False statement
    Every trigonometric function is one-one on its natural domain
    Statements
    1. The principal value of an inverse lies in its principal branch
    2. sin (sin⁻¹ x) = x for x in [−1, 1]
    3. Every trigonometric function is one-one on its natural domain
The false statement in each round is a range or domain swapped for a neighbouring one. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Assertion and reason

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Questions
  1. Reason
    The sine function never takes a value outside [−1, 1].
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    sin⁻¹ is defined only on [−1, 1].
  2. Reason
    The tangent function takes every real value on (−π/2, π/2).
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    tan⁻¹ is defined for every real number.
  3. Reason
    cosec x is undefined at integral multiples of π, and 0 is one of them.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    The principal range of cosec⁻¹ has 0 removed.
  4. Reason
    The superscript −1 always denotes a reciprocal.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    sin⁻¹ x is the same as 1/sin x.
The classic exam format for this chapter, testing whether the reason really explains the assertion. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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