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Indian Navy Pilot Algebra — practice questions

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

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Algebra questions and exercises with answers

Showing questions 1–30 of 48.

The diagonal entries of any skew-symmetric matrix are:Read the answer and worked solution →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 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 →Match the trig identity to its resultRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Symmetric or skew symmetric?Read the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →Complete the equality conditionRead the answer and worked solution →Order the steps: is AB defined, and what order is it?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Special square matricesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →

Worked practice questions

The diagonal entries of any skew-symmetric matrix are:

  1. Always $1$
  2. Always $0$
  3. Equal to each other but not necessarily $0$
  4. Always negative
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Correct answer: B. Always $0$

A skew-symmetric matrix satisfies $a_{ij} = -a_{ji}$ for all $i, j$. Setting $i = j$ gives $a_{ii} = -a_{ii}$, hence $2a_{ii} = 0$, so $a_{ii} = 0$. Every diagonal entry of a skew-symmetric matrix is therefore zero.

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sin(2θ) equals:

  1. 2 sin θ cos θ
  2. sin²θ - cos²θ
  3. sin θ + cos θ
  4. 2 sin θ
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Correct answer: A. 2 sin θ cos θ

**Double-angle formula:** sin(2θ) = 2 sinθ cosθ. (Derived from sin(θ + θ).)

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In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:

  1. a/sinA = b/sinB = c/sinC
  2. a + b + c = 0
  3. sinA = sinB
  4. a²+b² = c²
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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.

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