alleryStart learning →Empty set has cardinality:
- 1
- -1
- ∞
- 0
Show answer and solution
Correct answer: D. 0
Empty set ∅ or {}: no elements, n(∅) = 0. Subset of every set. Unique.
Indian Navy 10+2 B.Tech Cadet Relations and Functions — practice questions
Explore 37 free Relations and Functions questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Relations and Functions with Quill →Relations and Functions questions and exercises with answers
Showing questions 1–30 of 37.
Empty set has cardinality:Read the answer and worked solution →100 students; 50 like math, 60 like physics, 30 like both. Find students who like neither:Read the answer and worked solution →|A| = 5, |B| = 3. Number of relations from A to B:Read the answer and worked solution →Distributive law: A ∩ (B ∪ C) =Read the answer and worked solution →Number of equivalence relations on set {a, b, c}:Read the answer and worked solution →The range of the function $f(x)=x^2,\; x\in\mathbb{R}$ is:Read the answer and worked solution →The domain of $f(x)=\sqrt{4-x^2}$ is:Read the answer and worked solution →Which of the following sets of ordered pairs represents a function?Read the answer and worked solution →For finite sets, $n(A\times B)$ equals: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 →
Worked practice questions
100 students; 50 like math, 60 like physics, 30 like both. Find students who like neither:
- 30
- 40
- 0
- 20 (= 100 - n(M ∪ P) = 100 - (50+60-30) = 100-80 = 20)
Show answer and solution
Correct answer: D. 20 (= 100 - n(M ∪ P) = 100 - (50+60-30) = 100-80 = 20)
n(M ∪ P) = 50 + 60 - 30 = 80 like at least one.
Neither = 100 - 80 = 20.
|A| = 5, |B| = 3. Number of relations from A to B:
- 125
- 2^15 = 32768
- 8
- 15
Show answer and solution
Correct answer: B. 2^15 = 32768
2^(|A| × |B|) = 2^15 = 32768. Versus number of functions: 3^5 = 243. So relations vastly more than functions.
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