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Test: Differential Equations- Assertion & Reason Type Questions - JEE MCQ


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6 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Differential Equations- Assertion & Reason Type Questions

Test: Differential Equations- Assertion & Reason Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Differential Equations- Assertion & Reason Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Differential Equations- Assertion & Reason Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Differential Equations- Assertion & Reason Type Questions below.
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Test: Differential Equations- Assertion & Reason Type Questions - Question 1

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The differential equation formed by eliminating a and b from

Reason (R):y = aex + be-x ….(i)Differentiating w. r. t. 'x'

Differentiating again w .r .t .'x'

Subtracting eqn. (i) from eqn. (ii)

= 0

Test: Differential Equations- Assertion & Reason Type Questions - Question 2

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The solution of differential equation

Reason (R): we can clearly see that it is an homogeneous equation substituting

y = vx

separating the variables and integrating we get

is the solution where, C is constant.

Test: Differential Equations- Assertion & Reason Type Questions - Question 3

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The degree of the differential equation given by

Reason (R): The degree of a differential equation is the degree of the highest order derivative when differential coefficients are free from radicals and fraction.

The given differential equation has first order derivative which is free from radical and fraction with power = 1, thus it has a degree of 1.

Test: Differential Equations- Assertion & Reason Type Questions - Question 4

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The order and degree of the differential equation are 2 and 1

respectively

Reason (R): The differential equation

is of order 1 and degree 3.

Detailed Solution for Test: Differential Equations- Assertion & Reason Type Questions - Question 4
Squaring both sides of the given differential equation,

The highest order is 2 and its power is 1

∴ Order is 2, degree is 1

Hence, Assertion (A) is true.

The equation given in reason (R) is,

Highest order is 1 and its power is 3

∴ Order is 1 and degree is 3.

Hence, reason (R) is also true.

Test: Differential Equations- Assertion & Reason Type Questions - Question 5

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): Solution of the differential equation

Reason (R):

separating the variables

Test: Differential Equations- Assertion & Reason Type Questions - Question 6

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The order of the differential equation given by

Reason (R): Since the order of a differential equation is defined as the order of the highest derivative occurring in the differential equation, i.e., for nth derivative dny/dxn if n = 1. then it’s order = 1.

Given differential equation contains only dy/dx derivative with variables and constants.

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