CBSE Class 12 Mathematics Set 3- (65/2/3) Question Paper 2026 with Solution PDF

CBSE CLASS XII Questions

• 1.

  Evaluate: \[ \int_0^\pi \frac{dx}{a^2 \cos^2 x + b^2 \sin^2 x}. \]

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• 2.

  If \( \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = 0 \), \( |\overrightarrow{a}| = \sqrt{37} \), \( |\overrightarrow{b}| = 3 \), and \( |\overrightarrow{c}| = 4 \), then the angle between \( \overrightarrow{b} \) and \( \overrightarrow{c} \) is:

  • \( \frac{\pi}{6} \)
  • \( \frac{\pi}{4} \)
  • \( \frac{\pi}{3} \)
  • \( \frac{\pi}{2} \)
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• 3.

  Find the probability distribution of the number of boys in families having three children, assuming equal probability for a boy and a girl.

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• 4.

  Let \( R \) be a relation defined by the teacher to plan the seating arrangement of students in pairs, where \( R = \{(x, y) : x, y \text{ are Roll Numbers of students such that } y = 3x \} \). List the elements of \( R \). Is the relation \( R \) reflexive, symmetric, and transitive? Justify your answer.

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• 5.

  The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate is its area increasing when the side of the triangle is 15 cm?

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• 6.

  Find: \[ \int \frac{2x}{(x^2 + 3)(x^2 - 5)} \, dx \]

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