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Indian Navy MR Algebra — practice questions

Explore 49 free Algebra questions in Indian Navy MR 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 49.

$\sin(180° - \theta)$ equals:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read 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 →True or false: orders and shapesRead the answer and worked solution →Complete the arc length relationRead the answer and worked solution →

Worked practice questions

$\sin(180° - \theta)$ equals:

  1. $-\cos\theta$
  2. $-\sin\theta$
  3. $\sin\theta$
  4. $\cos\theta$
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Correct answer: C. $\sin\theta$

Supplementary-angle identity: $\sin(180° - \theta) = \sin\theta$. Reason: sine is positive in the second quadrant (where $180° - \theta$ lies for $0° < \theta < 180°$), and the reference angle is $\theta$. Companion identities: - $\cos(180° - \theta) = -\cos\theta$ - $\tan(180° - \theta) = -\tan\theta$

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sin(A + B) equals:

  1. cosA cosB - sinA sinB
  2. sinA cosB - cosA sinB
  3. sinA cosB + cosA sinB
  4. sinA + sinB
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Correct answer: C. sinA cosB + cosA sinB

**Compound angle formula:** sin(A + B) = sinA cosB + cosA sinB. (And sin(A - B) = sinA cosB - cosA sinB.)

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If tan θ = 1/2 (acute), find sin 2θ:

  1. 1/5
  2. 3/5
  3. 4/5
  4. 2/5
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Correct answer: C. 4/5

sin 2θ = 2 sinθ cosθ. From tan = 1/2, draw right triangle: opp=1, adj=2, hyp=√5. sinθ = 1/√5, cosθ = 2/√5. So sin 2θ = 2(1/√5)(2/√5) = 4/5.

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