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Test: 35 Year JEE Previous Year Questions: Differential Equations


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21 Questions MCQ Test Maths 35 Years JEE Main & Advanced Past year Papers | Test: 35 Year JEE Previous Year Questions: Differential Equations

Test: 35 Year JEE Previous Year Questions: Differential Equations for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The Test: 35 Year JEE Previous Year Questions: Differential Equations questions and answers have been prepared according to the JEE exam syllabus.The Test: 35 Year JEE Previous Year Questions: Differential Equations MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: 35 Year JEE Previous Year Questions: Differential Equations below.
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Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 1

Let a solution y = y(x) of the differential equation

STATEMENT-1 : 

STATEMENT-2 : 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 1

The given differential equation is



⇒ Statement 1 is true.

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 2

The order and degree of the differential equation 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 2

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 3

The solution of the equation  

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 3

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 4

The degree and order of the differential equation of the family of all parabolas whose axis is x - axis, are respectively.

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 4

y2 = 4a (x - h), 2 yy1 = 4a ⇒ yy1 = 2a Differentiating, ⇒ y12 + yy2 = 0
Degree  = 1,  order = 2.

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 5

The solution of the differential equation 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 5

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 6

The differential equation for the family of circle x2 + y2 - 2ay = 0, where a is anarbitrary constant is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 6


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 7

Solution of the differential equation ydx + (x + x2 y)dy = 0 is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 7

ydx + (x + x2y)dy = 0

It is Bernoullis form. Divide by x2


It is linear in t.

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 8

The differential equation representing the family of curves   is a parameter, is of order and degree as follows :

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 8

[On putting value of c from (ii) in (i)]
On simplifying, we get (y - 2 xy') 2 = 4 yy'3 ........ (iii)
Hence equation (iii) is of order 1 and degree 3.

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 9

then the solution of theequation is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 9



Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 10

The differential equation whose solution is Ax2 + By2 = 1 where A and B are arbitrary constants is of

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 10

 .........(1)

               ..........(2)
 ........(3)

From (2) and (3)

Dividing both sides by –B, we get

Which is a DE of order 2 and degree 1.

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 11

The differential equation of all circles passing through the origin and having their centres on the x-axis is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 11

General equation of circles passing through origin and having their centres on the x-axis is

x2 + y2 + 2gx = 0...(i)

On differentiating w.r.t x, we get

∴ equation (i) be


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 12

The soluton of the differential equation  satisfying the condition y(1) =1 is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 12


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 13

The differential equation which represents the family of curves are arbitrary constants, is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 13


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 14

Solution of the differential equation 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 14

cos x dy = y(sin x- y) dx

From equation (i)


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 15

then y (ln 2) is equal to :

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 15


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 16

Let I be the purchase value of an equipment and V (t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation  where k > 0 is a constant and T is thetotal life in years of the equipment. Then the scrap value V(T) of the equipment is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 16


Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 17

The population p (t) at time t of a certain mouse species satisfies the differential equation  If p (0) = 850, then the time at which the population becomes zero is :

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 17

Given differential equation is


Integrate both sides, we get





    ∴ t1 = 2ln 18

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 18

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by If thefirm employs 25 more workers, then the new level of production of items is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 18

By integrating

Given, when x = 0 then P = 2000

⇒ C = 2000
Now when x = 25 then
P = 100 × 25 – 8 × (25)3/2 + 2000
= 4500 – 1000
⇒ P = 3500

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 19

Let the population of rabbits surviving at time t be governed by the differential equation  If p(0) = 100, then p(t) equals:

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 19

Given differential equation is


By separating the variable, we get

Integrating on both the sides,


Using given condition p(t) = 400 – 300 et/2

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 20

Let y(x) be the solution of the differential equation  Then y (e) is equal to:

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 20

y logx = 2[x log x – x] + c
Put x = 1, y.0 = –2 + c  ⇒ c = 2
Put x = e
y loge = 2e(log e – 1)  + c  ⇒   y(e) = c = 2

Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 21

If a curve y = f(x) passes through the point (1, –1) and satisfies the differential equation, y(1 + xy) dx = x dy, then

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Differential Equations - Question 21

y (1 + xy)dx = xdy

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