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

CBSE CLASS XII Questions

• 1.

  A man needs to hang two lanterns on a straight wire whose end points have coordinates A (4, 1, -2) and B (6, 2, -3). Find the coordinates of the points where he hangs the lanterns such that these points trisect the wire AB.

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• 2.

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

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• 3.

  The values of $\lambda$ so that $f(x) = \sin x - \cos x - \lambda x + C$ decreases for all real values of $x$ are :

  • $1<\lambda<\sqrt{2}$
  • $\lambda \geq 1$
  • $\lambda \geq \sqrt{2}$
  • $\lambda<1$
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• 4.

  If $A$ and $B$ are two square matrices each of order 3 with $|A| = 3$ and $|B| = 5$, then $|2AB|$ is:

  • 30
    
  • 120
    
  • 15
    
  • 225
    
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• 5.

  Find the foot of the perpendicular drawn from the point \( (1, 1, 4) \) on the line \( \frac{x+2}{5} = \frac{y+1}{2} = \frac{z-4}{-3} \).

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• 6.

  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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