JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

Let

\frac{dy}{dx} = \frac{ax - by + a}{bx + cy + a}

, a, b,

c \in \mathbf{R}

, represents a circle with center

(\alpha, \beta)

. Then,

\alpha + 2\beta

is equal to :

(1) $-1$
(2) $0$
(3) $1$ Official answer
(4) $2$

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Direct Integration

Same idea in other shifts

Asked 3× in all

2 Apr 2026, Shift 1 · Q17If the curve $y=f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy=y(2+\log_e x)\,dx$ , $x>0$ , then $f(e)$ …EasySingle correct
31 Aug 2021, Shift 2 · Q70If $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y}\log_e 2}$ , $y(0) = 0$ , then for $y = 1$ , the value of $x$ …HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.