MathsCBSE Class 12 · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2023-24: question 3

From the official CBSE sample question paper for 2023-24, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQDeterminants

If the area of the triangle with vertices $(- 3, 0)$ , $(3, 0)$ and $(0, k)$ is 9 sq units, then the value/s of $k$ will be

(A)9
(B) $\pm 3$
(C)-9
(D)6

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Use the determinant formula for the area of a triangle.

Hint 2

Remember that the area condition gives $\pm$ the value.

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.

Area $= \frac{1}{2} - 3 30 00 k 111$ . Expanding along $C_{2}$ gives the determinant $= - k (- 3 - 3) = 6 k$ , so Area $= \frac{1}{2} ∣6 k ∣ = 3∣ k ∣$ .
Setting $3∣ k ∣ = 9$ gives $k = \pm 3$ , which is option (B).
1 mark

Answer: $k = \pm 3$ , option (B)

Where the marks are

Uses the determinant area formula and solves $3∣ k ∣ = 9$ (1 mark)

Revise the chapter

Chapter: Determinants (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Determinants, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Mathematics sample paper 2023-24: question 3

Hints

Step-by-step solution

Revise the chapter

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