CBSE Class 12 Maths Set 1 Question Paper 2026 Available- Download PDF with Solutions

CBSE CLASS XII Questions

• 1.

  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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• 2.

  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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• 3.

  Find the point on the line \( \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} \) at a distance of \( \sqrt{2} \) units from the point \( (-1, -1, 2) \).

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• 4.

  Find the values of \( a \) for which \( f(x) = \sqrt{3} \sin x - \cos x - 2ax + b \) is decreasing on \( \mathbb{R} \).

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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.

  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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