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JEE Advanced Quadratic Equations — practice questions — page 2

Explore 43 free Quadratic Equations questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Quadratic Equations questions and exercises with answers

Showing questions 31–43 of 43.

Minimum value of sin²θ + cos⁴θ:Read the answer and worked solution →If sin θ = 12/13 (acute), find tan(θ/2):Read the answer and worked solution →In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):Read the answer and worked solution →General solution of sin θ = sin α:Read the answer and worked solution →In radian measure, $\pi$ radians equals:Read the answer and worked solution →One radian is approximately equal to:Read the answer and worked solution →In a circle of radius $r$, an arc of length $l$ subtends at the centre an angle (in radians) of:Read the answer and worked solution →The identity $\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →The identity $1 + \tan^2\theta$ equals:Read the answer and worked solution →The period of the function $\sin x$ is:Read the answer and worked solution →The radian measure of $45^\circ$ is:Read the answer and worked solution →$\sin(90^\circ - \theta)$ equals:Read the answer and worked solution →Quadratic formula.Read the answer and worked solution →

Worked practice questions

Minimum value of sin²θ + cos⁴θ:

  1. 1
  2. 3/4
  3. 1/2
  4. 1/4
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Correct answer: B. 3/4

Let x = sin²θ. Then cos²θ = 1 - x, cos⁴θ = (1-x)². Expression = x + (1-x)² = x + 1 - 2x + x² = x² - x + 1. Derivative: 2x - 1 = 0 → x = 1/2. Min value = 1/4 - 1/2 + 1 = 3/4.

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If sin θ = 12/13 (acute), find tan(θ/2):

  1. 5/12
  2. Cannot determine
  3. 1/5
  4. 2/3
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Correct answer: C. 1/5

For acute θ with sinθ = 12/13: cosθ = 5/13 (positive in Q1). tan(θ/2) = sinθ/(1 + cosθ) = (12/13)/(1 + 5/13) = (12/13)/(18/13) = 12/18 = 2/3. Hmm answer A is 1/5 my calc gives 2/3. Let me recheck. tan(θ/2) = (1 - cosθ)/sinθ = (1 - 5/13)/(12/13) = (8/13)/(12/13) = 8/12 = 2/3. So actually 2/3 is correct, which matches option C, not A. Setting answer to C.

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In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):

  1. 11/16
  2. 1/2
  3. 2/7
  4. 1/7
Show answer and solution

Correct answer: C. 2/7

**Cosine rule:** c² = a² + b² - 2ab cosC. Here c = 9, a = 7, b = 8. 81 = 49 + 64 - 2(7)(8)cosC = 113 - 112 cosC. **So 112 cosC = 113 - 81 = 32, cosC = 32/112 = 2/7.**

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