CBSE Class 12 Mathematics sample paper 2025-26: question 10
From the official CBSE sample question paper for 2025-26, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q10 · 1 mark · MCQDifferential Equations
The solution of the differential equation represents a family of
- (A)straight lines
- (B)parabolas
- (C)Circles
- (D)Ellipses
Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.
Hints
Open one hint at a time and try again before the next.
Hint 1
The variables are already separated; integrate each side.
Hint 2
What curve does constant represent?
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.
Integrating, .
- 1 mark
So , which is a family of circles centred at the origin. Option (C).
Answer: Circles, option (C)
Where the marks are
- Separates the variables, integrates to and identifies circles (1 mark)
Revise the chapter
- Chapter: Differential Equations (notes, formulas, where marks are lost and every past question)
More questions from Differential Equations
- Sample paper 2025-26, Q34(A) · 5 marksSolve the differential equation: y+d/dx(xy)=x( x+x)
- Sample paper 2025-26, Q34(B) · 5 marksFind the particular solution of the differential equation: 2y e^x/ydx+(y-2x e^x/y)dy=0 given that y(0)=1
- 2025 board paper, set 65/1/1, Q12 · 1 markThe integrating factor of differential equation (x+2y³)dy/dx=2y is
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