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Indian Navy INET Number Theory — practice questions

Explore 48 free Number Theory questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Number Theory questions and exercises with answers

Showing questions 1–30 of 48.

If $\text{HCF}(a, b) = 12$ and $\text{LCM}(a, b) = 180$, then the number of possible ordered pairs $(a, b)$ isRead the answer and worked solution →The unit digit of $7^{2026}$ isRead the answer and worked solution →If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equalsRead 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 →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 slopeRead the answer and worked solution →

Worked practice questions

If $\text{HCF}(a, b) = 12$ and $\text{LCM}(a, b) = 180$, then the number of possible ordered pairs $(a, b)$ is

  1. 2
  2. 6
  3. 1
  4. 4
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Correct answer: D. 4

Write $a = 12m$, $b = 12n$ with $\gcd(m,n)=1$ and $mn = 180/12 = 15$. **Coprime factor pairs of 15:** $(1,15),(15,1),(3,5),(5,3)$ — 4 ordered pairs.

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The unit digit of $7^{2026}$ is

  1. 1
  2. 7
  3. 3
  4. 9
Show answer and solution

Correct answer: D. 9

Unit digits of powers of 7 cycle with period 4: $7,9,3,1$. Since $2026 \equiv 2 \pmod 4$, the unit digit matches $7^2 = 49$, i.e. 9.

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If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equals

  1. $\dfrac{1}{x} + \dfrac{1}{y}$
  2. $x + y$
  3. $\dfrac{1}{x} - \dfrac{1}{y}$
  4. $xy$
Show answer and solution

Correct answer: A. $\dfrac{1}{x} + \dfrac{1}{y}$

Let $3^x=4^y=12^z=k$. Then $3=k^{1/x}$, $4=k^{1/y}$, $12=k^{1/z}$. Since $12 = 3\cdot4$: $k^{1/z}=k^{1/x}\cdot k^{1/y}=k^{1/x+1/y}$, so $\dfrac1z=\dfrac1x+\dfrac1y$.

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More Mathematics topics

Probability & StatisticsSequences and SeriesBinomial TheoremGeometrySequencesVectors & 3D GeometryPermutations and CombinationsLinear Programming