alleryStart learning →tan(45°) equals:
- ∞
- 0
- 1
- √3
Show answer and solution
Correct answer: C. 1
We have tan(45°) = sin(45°)/cos(45°).
That is tan(45°) = (1/√2)/(1/√2).
So tan(45°) = 1.
Indian Navy SSR (Sailor) Number Theory — practice questions
Explore 71 free Number Theory questions in Indian Navy SSR (Sailor) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Number Theory with Quill →Number Theory questions and exercises with answers
Showing questions 1–30 of 71.
tan(45°) equals:Read the answer and worked solution →For 3 sets A, B, C: n(A ∪ B ∪ C) =Read the answer and worked solution →The square of any odd integer, when divided by 8, leaves remainderRead the answer and worked solution →If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(a,b)}{\text{HCF}(a,b)}$ equalsRead 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 →Pop the prime numbers — skip the compositesRead 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 →
Worked practice questions
For 3 sets A, B, C: n(A ∪ B ∪ C) =
- Random
- Σn(individual) - Σn(pairs) + n(A ∩ B ∩ C)
- n(A) + n(B) + n(C)
- n(A) × n(B) × n(C)
Show answer and solution
Correct answer: B. Σn(individual) - Σn(pairs) + n(A ∩ B ∩ C)
**Inclusion-exclusion for 3 sets:** n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C).
Generalizes to n sets with alternating signs.
The square of any odd integer, when divided by 8, leaves remainder
- 3
- 5
- 0
- 1
Show answer and solution
Correct answer: D. 1
An odd integer is $2k+1$; its square is $4k(k+1)+1$.
Since $k(k+1)$ is even, $4k(k+1)$ is a multiple of 8, so the square is $\equiv 1 \pmod 8$.
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