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Indian Navy SSR Algebra — practice questions

Explore 67 free Algebra questions in Indian Navy SSR 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 67.

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:Read the answer and worked solution →$\cos 3\theta$ equals: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 →The angle 90° in radians is: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 →

Worked practice questions

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:

  1. $\dfrac{1}{2}$
  2. $1$
  3. $0$
  4. $-1$
Show answer and solution

Correct answer: C. $0$

Square both sides of $\sin\theta + \cos\theta = 1$: $(\sin\theta + \cos\theta)^2 = 1^2$ $\sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta = 1$ Using $\sin^2 + \cos^2 = 1$: $1 + 2\sin\theta\cos\theta = 1$ $\sin\theta \cos\theta = 0$. Verify: the original equation holds only when $\theta = 0°$ (so $\sin = 0$, $\cos = 1$) or $\theta = 90°$ (so $\sin = 1$, $\cos = 0$). In both cases the product is 0. ✓

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$\cos 3\theta$ equals:

  1. $3\sin\theta - 4\sin^3\theta$
  2. $3\cos\theta - 4\cos^3\theta$
  3. $4\sin^3\theta - 3\sin\theta$
  4. $4\cos^3\theta - 3\cos\theta$
Show answer and solution

Correct answer: D. $4\cos^3\theta - 3\cos\theta$

Triple-angle for cosine: $\cos 3\theta = 4\cos^3\theta - 3\cos\theta$. Derivation: $\cos 3\theta = \cos(2\theta + \theta) = \cos 2\theta \cos\theta - \sin 2\theta \sin\theta = (2\cos^2\theta - 1)\cos\theta - 2\sin\theta\cos\theta \cdot \sin\theta = 2\cos^3\theta - \cos\theta - 2\sin^2\theta\cos\theta = 2\cos^3\theta - \cos\theta - 2(1-\cos^2\theta)\cos\theta = 4\cos^3\theta - 3\cos\theta$. Companion: $\sin 3\theta = 3\sin\theta - 4\sin^3\theta$ (option C — common trap). Mnemonic: in both, the coefficients are 3 and 4, and the cubed term has the same trig function as the angle outside.

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The distance between the points $(1,2)$ and $(1,5)$ is:

  1. 6
  2. 3
  3. 5
  4. 4
Show answer and solution

Correct answer: B. 3

Same x, so distance = |5−2| = 3.

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