The order and degree of the differential equation [1+ (dy/dx )² ]³ = (d²y)/(dx²) respectively are : (A) 1, 2 (B) 2, 3 (C) 2, 1 (D) 2, 6

MathsCBSE Class 12 · Board exam 2024, set 65/1/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2024: question 14

Set in the CBSE Class 12 board exam of 2024, paper 65/1/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQDifferential Equations

The order and degree of the differential equation $[1 + (\frac{d y}{d x})^{2}]^{3} = \frac{d ^{2} y}{d x ^{2}}$ respectively are :

(A)1, 2
(B)2, 3
(C)2, 1
(D)2, 6

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/1/1.

Hints

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

Hint 1

Order is the highest derivative that appears.

Hint 2

Degree is the power of that highest-order derivative.

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.

The highest-order derivative is $\frac{d ^{2} y}{d x ^{2}}$ , so the order is 2.
½ mark
The equation is polynomial in its derivatives and $\frac{d ^{2} y}{d x ^{2}}$ appears to power 1, so the degree is 1.
½ mark

Answer: (C) 2, 1

Where the marks are

Order 2 and degree 1 (1 mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Differential Equations, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Mathematics 2024: question 14

Hints

Step-by-step solution

Revise the chapter

More questions from Differential Equations