Bihar Board Class 12 (Arts) Relations, Functions & Inverse Trigonometry — practice questions — page 3

Explore 65 free Relations, Functions & Inverse Trigonometry questions in Bihar Board Class 12 (Arts) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Relations, Functions & Inverse Trigonometry questions and exercises with answers

Showing questions 61–65 of 65.

True or false: reading the tableRead the answer and worked solution →In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:Read the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →

Worked practice questions

True or false: reading the table

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Questions

Statement is true
Yes
Statement
The principal range of cos⁻¹ is [0, π].
Statement is true
No
Statement
The principal range of tan⁻¹ is a closed interval.
Statement is true
Yes
Statement
cot⁻¹ has domain R and principal range (0, π).
Statement is true
Yes
Statement
sec⁻¹ has π/2 removed from its principal range.
Statement is true
No
Statement
cosec⁻¹ has π/2 removed from its principal range.
Statement is true
Yes
Statement
cosec⁻¹ and sec⁻¹ share the domain R − (−1, 1).

Each statement is a row of the summary table, stated straight or bent. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:

$1/2$
$60/1024$
$210/1024$
$120/1024$

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Correct answer: C. $210/1024$

P(X=6) = C(10,6) × (0.5)⁶ × (0.5)⁴ = 210 × (1/2)¹⁰ = 210/1024 ≈ 0.205. C(10,6) = 210.

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Match each inverse function to its principal value branch

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Matching pairs

Left
sin⁻¹ x
Right
[−π/2, π/2]
Left
cos⁻¹ x
Right
[0, π]
Left
cosec⁻¹ x
Right
[−π/2, π/2] − {0}

The principal branch is the one interval on which the function is made one-one so the inverse is single valued. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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