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Questions › CUET-PG › CUET-PG 2023 Shift 1 › Q50
4 marks, −1Mathematics › Difference and differential equations › Stability and phase diagramsModerateabout 1 min

CUET-PG 2023 Shift 1 Question 50: Difference and differential equations

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): Assertion (A): For a differential equation x˙+ax=b\dot{x} + ax = bx˙+ax=b for a≠0a \neq 0a=0, F(x)=x˙=b−axF(x) = \dot{x} = b - axF(x)=x˙=b−ax and the equilibrium is at x=bax = \frac{b}{a}x=ab​. This equilibrium is stable for a>0a > 0a>0. Reason (R): The equilibrium is obtained for x˙=b−ax=0\dot{x} = b - ax = 0x˙=b−ax=0 or x=bax = \frac{b}{a}x=ab​. Stability is obtained when F′(x)F'(x)F′(x) is < 0. Here F′(x)=−aF'(x) = -aF′(x)=−a and so the equilibrium is stable if a>0a > 0a>0. In the light of the above statements, choose the correct answer from the options given below:

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Plain-text version

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): Assertion (A): For a differential equation ẋ + ax = b for a ≠ 0, F(x) = ẋ = b - ax and the equilibrium is at x = b/a. This equilibrium is stable for a > 0. Reason (R): The equilibrium is obtained for ẋ = b - ax = 0 or x = b/a. Stability is obtained when F′(x) is < 0. Here F′(x) = -a and so the equilibrium is stable if a > 0. In the light of the above statements, choose the correct answer from the options given below: (A) Both (A) and (R) are true and (R) is the correct explanation of (A) (B) Both (A) and (R) are true but (R) is not the correct explanation of (A) (C) (A) is true but (R) is false (D) (A) is false but (R) is true

Also written as: Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): Assertion (A): For a differential equation x_dot + ax = b for a != 0, F(x) = x_dot = b - ax and the equilibrium is at x = b/a. This equilibrium is stable for a > 0. Reason (R): The equilibrium is obtained for x_dot = b - ax = 0 or x = b/a. Stability is obtained when F'(x) is < 0. Here F'(x) = -a and so the equilibrium is stable if a > 0. In the light of the above statements, choose the correct answer from the options given below:

Difference and differential equations has come up 20 times in 5 exams since 2014.

What this question tests

This question is on Stability and phase diagrams, part of Difference and differential equations in Mathematics.

Whether solutions settle to an equilibrium and how to read the phase line.

TestStop has 8 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Stability and phase diagrams

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