MathsCBSE Class 12 · Sample paper, session 2024-25 · 3 marks · Short answer

CBSE Class 12 Mathematics sample paper 2024-25: question 26

From the official CBSE sample question paper for 2024-25, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerCompetency-basedApplication of Derivatives

A kite is flying at a height of 3 metres and 5 metres of string is out. If the kite is moving away horizontally at the rate of 200 cm/s, find the rate at which the string is being released.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Draw the right triangle formed by the height, the horizontal distance and the string.

Hint 2

Differentiate the Pythagoras relation with respect to time; find $x$ when the string is 5 m.

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.

Figure: right triangle with vertical side 3 m (height of kite), horizontal side $x$ m and hypotenuse $y$ m (string).
½ mark
By Pythagoras, $x^{2} + 3^{2} = y^{2}$ .
½ mark
When $y = 5$ , $x = 25 - 9 = 4$ . Differentiating w.r.t. $t$ : $2 x \frac{d x}{d t} = 2 y \frac{d y}{d t}$ .
1 mark
With $\frac{d x}{d t} = 200$ cm/s: $4 (200) = 5 \frac{d y}{d t} \Rightarrow \frac{d y}{d t} = 160$ cm/s. The string is released at 160 cm/s.
1 mark

Answer: 160 cm/s

Where the marks are

Correct figure (½ mark)
Relation $x^{2} + 9 = y^{2}$ (½ mark)
Finds $x = 4$ and differentiates (1 mark)
$\frac{d y}{d t} = 160$ cm/s (1 mark)

Revise the chapter

Chapter: Application of Derivatives (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Application of Derivatives, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25: every question, by section.

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CBSE Class 12 Mathematics sample paper 2024-25: question 26

Hints

Step-by-step solution

Revise the chapter

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