alleryStart learning →sin(2θ) equals:
- 2 sin θ cos θ
- sin²θ - cos²θ
- sin θ + cos θ
- 2 sin θ
Show answer and solution
Correct answer: A. 2 sin θ cos θ
**Double-angle formula:** sin(2θ) = 2 sinθ cosθ.
(Derived from sin(θ + θ).)
Indian Navy Pilot Permutations and Combinations — practice questions
Explore 58 free Permutations and Combinations questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Permutations and Combinations with Quill →Permutations and Combinations questions and exercises with answers
Showing questions 1–30 of 58.
sin(2θ) equals:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →The probability of getting an even number on a single throw of a die is:Read the answer and worked solution →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →Find the midpoint of A(2, −3) and B(8, 5).Read the answer and worked solution →Two dice are rolled. The probability of getting AT LEAST ONE SIX is: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 →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
In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:
- a/sinA = b/sinB = c/sinC
- a + b + c = 0
- sinA = sinB
- a²+b² = c²
Show answer and solution
Correct answer: A. a/sinA = b/sinB = c/sinC
**Sine rule:** a/sinA = b/sinB = c/sinC = 2R (where R is circumradius).
Useful for solving triangles when you know any side + opposite angle + one more piece.
The probability of getting an even number on a single throw of a die is:
- $\tfrac23$
- $\tfrac12$
- $\tfrac16$
- $\tfrac13$
Show answer and solution
Correct answer: B. $\tfrac12$
Even numbers on a die are {2,4,6}: 3 of 6 outcomes ⟹ 3/6 = 1/2.
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