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Indian Navy AA (Artificer Apprentice) Algebra — practice questions

Explore 44 free Algebra questions in Indian Navy AA (Artificer Apprentice) 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 44.

$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →The midpoint of the segment joining $(2,3)$ and $(4,7)$ 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 →Complete the definition of slopeRead the answer and worked solution →True or false: slopeRead the answer and worked solution →Zero slope, undefined slope, or neither?Read the answer and worked solution →

Worked practice questions

$\sin^2\theta + \cos^2\theta$ equals:

  1. $2$
  2. $0$
  3. $\tan\theta$
  4. $1$
Show answer and solution

Correct answer: D. $1$

The **Pythagorean identity** $\sin^2\theta + \cos^2\theta = 1$ holds for every real $\theta$. It comes from Pythagoras applied to the unit circle: any point on it has coordinates $(\cos\theta, \sin\theta)$ with distance 1 from origin so the sum of squared coordinates is 1. Companion identities: - Dividing by $\cos^2\theta$: $1 + \tan^2\theta = \sec^2\theta$. - Dividing by $\sin^2\theta$: $\cot^2\theta + 1 = \csc^2\theta$.

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The midpoint of the segment joining $(2,3)$ and $(4,7)$ is:

  1. (6, 10)
  2. (1, 2)
  3. (2, 4)
  4. (3, 5)
Show answer and solution

Correct answer: D. (3, 5)

((2+4)/2, (3+7)/2) = (3,5).

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Match each kind of matrix to its condition

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Matching pairs
  1. Left
    Row matrix
    Right
    exactly one row
  2. Left
    Column matrix
    Right
    exactly one column
  3. Left
    Square matrix
    Right
    as many rows as columns
  4. Left
    Diagonal matrix
    Right
    every off-diagonal entry is 0
  5. Left
    Identity matrix
    Right
    1s on the diagonal, 0s elsewhere
  6. Left
    Zero matrix
    Right
    every entry is 0
The chapter's taxonomy, straight from the summary. Source: syllabus Maths Part I, Ch 3 Matrices.

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