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JEE Main Algebra: Simultaneous Linear Equations & Quadratics — practice questions

Explore 12 free Algebra: Simultaneous Linear Equations & Quadratics questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: Simultaneous Linear Equations & Quadratics questions and exercises with answers

Showing questions 1–12 of 12.

$\sin(180° - \theta)$ equals:Read the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Which test applies?Read the answer and worked solution →Flip and pair: condition with conclusionRead the answer and worked solution →Tap every statement true of slopeRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Complete the angle between two linesRead the answer and worked solution →True or false: using coordinatesRead the answer and worked solution →A cylindrical tube with a rounded end is a cylinder with a:Read the answer and worked solution →A cylindrical tube with a rounded end is a cylinder with a:Read the answer and worked solution →$\sin(180° - \theta)$ equals:Read 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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Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about slope are false.
    Choices
    1. Item
      A vertical line has undefined slope
      Correct
      Yes
    2. Explanation
      Zero slope belongs to HORIZONTAL lines.
      Item
      A vertical line has slope zero
    3. Explanation
      Its slope is zero, not undefined.
      Item
      A horizontal line has undefined slope
    4. Explanation
      Their slopes multiply to −1.
      Item
      Perpendicular lines share a slope
Each trap inverts one of the tests. Source: syllabus Maths, Ch 9 Straight Lines.

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Which test applies?

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Items
  1. Item
    Are these two lines never going to meet?
    Category
    Parallel test
  2. Item
    Compare the two slopes for equality
    Category
    Parallel test
  3. Item
    Do these lines meet at a right angle?
    Category
    Perpendicular test
  4. Item
    Multiply the slopes and look for −1
    Category
    Perpendicular test
  5. Item
    Do these three points lie on one line?
    Category
    Collinearity test
  6. Item
    Compare slope AB with slope BC
    Category
    Collinearity test
Categories
  1. Item
    Parallel test
  2. Item
    Perpendicular test
  3. Item
    Collinearity test
Choosing the right condition for the question asked. Source: syllabus Maths, Ch 9 Straight Lines.

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