CBSE Class 12 Mathematics sample paper 2026-27: question 23(A)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Direction ratios of the line through $(2,6,5)$ and $(3,p,7)$: $⟨1,p-6,2⟩$. Direction ratios of the line through $(-4,3,4)$ and $(-1,0,q)$: $⟨3,-3,q-4⟩$. Parallel lines have proportional direction ratios: $\frac{1}{3}=\frac{p-6}{-3}=\frac{2}{q-4}$.

   1 mark

2. From $\frac{p-6}{-3}=\frac{1}{3}$: $p-6=-1$, so $p=5$. From $\frac{2}{q-4}=\frac{1}{3}$: $q-4=6$, so $q=10$.

   ½ mark

3. $\frac{q}{p}=\frac{10}{5}=2$

   ½ mark

Answer: $\frac{q}{p}=2$ (with $p=5,q=10$)

Revise the chapter

• Chapter: Three Dimensional Geometry (notes, formulas, where marks are lost and every past question)