JEE Main Differential Equations Practice Questions With Solutions

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JEE Main Differential Equations Practice Questions with Solutions

Differential Equations are a challenging part of the Trigonometry section of Mathematics. Mastering the topics of trigonometry requires some extra effort, as this part is tricky. The JEE Main Differential Equations Practice Questions with Solutions have questions from all the important topics of differential equations. The important topics from the Differential Equations chapter are Basics and Definitions of Differential Equations, Solving Differential Equations, Formation of Differential Equations, General and Particular Solutions, Second-Order Differential Equations, and Applications of Differential Equations. The JEE Main Differential Equations practice questions with solutions have a variety of questions from this chapter. The practise test also contains the solutions to each question as well as their detailed explanation. Students can look into these explanations in case they are not able to understand any questions. These practice tests consist of about 15 to 20 questions for candidates to practise and improve their knowledge of the duality of particles. Solving these practice tests will help candidates become aware of the structure of the questions asked and will enable them to solve these questions with ease.

You may expect about 2 to 3 questions in the JEE Main exam to be generally asked from the Differential Equations chapter in the JEE Main entrance examination. The questions from this chapter will be in the form of multiple choice and integer type questions. Practising the JEE Main Differential Equations Practice Questions with Solutions is important to perform well in the JEE Main entrance exam. It is recommended for candidates to solve at least 10 to 15 questions from the Differential Equations chapter every week in order to improve accuracy and time management skills. The JEE Main Differential Equations Practice Test consists of a variety of questions from this chapter. Solving these practice tests regularly will help the students improve their problem-solving skills and gain confidence while answering challenging questions from the differential equation chapter in the Mathematics section of the JEE Main entrance exam.

JEE Main Mathematics Differential Equations Practice Questions

Chemistry Physics

Question 1.

Let $\int_{0}^{x} \sqrt{1 - {(y^{'} (t))}^{2}} d t = \int_{0}^{x} y (t) d t, 0 \leq x \leq 3, y \geq 0, y (0) = 0$ . Then at $x = 2, y^{''} + y + 1$ is equal to

\sqrt{2}

1/2

Question 2.

The solution of the differential equation $(x^{2} + y^{2}) d x - 5 x y d y = 0, y (1) = 0$ , is :

{| x^{2} - 4 y^{2} |}^{5} = x^{2}

{| x^{2} - 2 y^{2} |}^{6} = x

{| x^{2} - 2 y^{2} |}^{5} = x^{2}

{| x^{2} - 4 y^{2} |}^{6} = x

Question 3.

The solution curve, of the differential equation $2 y \frac{d y}{d x} + 3 = 5 \frac{d y}{d x}$ , passing through the point $(0, 1)$ is a conic, whose vertex lies on the line :

2 x + 3 y = - 9

2 x + 3 y = - 6

2 x + 3 y = 9

2 x + 3 y = 6

Question 4.

Let $y = y (x)$ be the solution curve of the differential equation $\sec y \frac{d y}{d x} + 2 x \sin y = x^{3} \cos y, y (1) = 0$ . Then $y (\sqrt{3})$ is equal to:

\frac{π}{6}

\frac{π}{12}

\frac{π}{3}

\frac{π}{4}

Question 5.

Let $f (x)$ be a positive function such that the area bounded by $y = f (x), y = 0$ from $x = 0$ to $x = a > 0$ is $e^{- a} + 4 a^{2} + a - 1$ . Then the differential equation, whose general solution is $y = c_{1} f (x) + c_{2}$ , where $c_{1}$ and $c_{2}$ are arbitrary constants, is

(8 e^{x} + 1) \frac{d^{2} y}{d x^{2}} - \frac{d y}{d x} = 0

(8 e^{x} + 1) \frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} = 0

(8 e^{x} - 1) \frac{d^{2} y}{d x^{2}} - \frac{d y}{d x} = 0

(8 e^{x} - 1) \frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} = 0

Question 6.

Let $y = y (x)$ be the solution of the differential equation $(1 + y^{2}) e^{\tan x} d x + \cos^{2} x (1 + e^{2 \tan x}) d y = 0, y (0) = 1$ . Then $y (\frac{π}{4})$ is equal to

\frac{1}{e^{2}}

\frac{2}{e^{2}}

\frac{2}{e}

\frac{1}{e}

Question 7.

Suppose the solution of the differential equation $\frac{d y}{d x} = \frac{(2 + α) x - β y + 2}{β x - 2 α y - (β γ - 4 α)}$ represents a circle passing through origin. Then the radius of this circle is :

\sqrt{17}

\frac{\sqrt{17}}{2}

\frac{1}{2}

Question 8.

Let $y = y (x)$ be the solution of the differential equation $(2 x \log_{e} x) \frac{d y}{d x} + 2 y = \frac{3}{x} \log_{e} x, x > 0$ and $y (e^{- 1}) = 0$ . Then, $y (e)$ is equal to

- \frac{3}{e}

- \frac{3}{2 e}

- \frac{2}{3 e}

- \frac{2}{e}

Question 9.

Let $y = y (x)$ be the solution of the differential equation $(1 + x^{2}) \frac{d y}{d x} + y = e^{\tan^{- 1} x}$ , $y (1) = 0$ . Then $y (0)$ is

\frac{1}{4} (e^{π / 2} - 1)

\frac{1}{2} (1 - e^{π / 2})

\frac{1}{4} (1 - e^{π / 2})

\frac{1}{2} (e^{π / 2} - 1)

Question 10.

The differential equation of the family of circles passing through the origin and having centre at the line $y = x$ is :

(x^{2} - y^{2} + 2 x y) d x = (x^{2} - y^{2} + 2 x y) d y

(x^{2} + y^{2} - 2 x y) d x = (x^{2} + y^{2} + 2 x y) d y

(x^{2} + y^{2} + 2 x y) d x = (x^{2} + y^{2} - 2 x y) d y

(x^{2} - y^{2} + 2 x y) d x = (x^{2} - y^{2} - 2 x y) d y

Question 1.

If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} + 2 y = \sin (2 x), y (0) = \frac{3}{4}$ , then $y (\frac{π}{8})$ is equal to :

e^{- π / 8}

e^{π / 4}

e^{- π / 4}

e^{π / 8}

Question 2.

Let $y = y (x)$ be the solution of the differential equation $(x^{2} + 4)^{2} d y + (2 x^{3} y + 8 x y - 2) d x = 0$ . If $y (0) = 0$ , then $y (2)$ is equal to

2 π

\frac{π}{8}

\frac{π}{16}

\frac{π}{32}

Question 3.

If the solution $y = y (x)$ of the differential equation $(x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 2) d y - (2 x^{2} + 2 x + 3) d x = 0$ satisfies $y (- 1) = - \frac{π}{4}$ , then $y (0)$ is equal to :

- \frac{π}{12}

\frac{π}{2}

\frac{π}{4}

Question 4.

Let

α

be a non-zero real number. Suppose

f : R \to R

is a differentiable function such that

f (0) = 2

and

lim_{x \to - \infty} f (x) = 1

. If

f^{'} (x) = α f (x) + 3

, for all

x \in R

, then

f (- \log_{e} 2)

is equal to :

Question 5.

Let

y = y (x)

be the solution of the differential equation

\frac{d y}{d x} = 2 x (x + y)^{3} - x (x + y) - 1, y (0) = 1

.

Then,

{(\frac{1}{\sqrt{2}} + y (\frac{1}{\sqrt{2}}))}^{2}

equals :

\frac{4}{4 + \sqrt{e}}

\frac{3}{3 - \sqrt{e}}

\frac{2}{1 + \sqrt{e}}

\frac{1}{2 - \sqrt{e}}

Question 6.

The temperature $T (t)$ of a body at time $t = 0$ is $160^{\circ} F$ and it decreases continuously as per the differential equation $\frac{d T}{d t} = - K (T - 80)$ , where $K$ is a positive constant. If $T (15) = 120^{\circ} F$ , then $T (45)$ is equal to

^{\circ}

^{\circ}

^{\circ}

^{\circ}

Question 7.

Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = \frac{(\tan x) + y}{\sin x (\sec x - \sin x \tan x)}, x \in (0, \frac{π}{2})$ satisfying the condition $y (\frac{π}{4}) = 2$ . Then, $y (\frac{π}{3})$ is

\sqrt{3} (2 + \log_{e} 3)

\sqrt{3} (1 + 2 \log_{e} 3)

\sqrt{3} (2 + \log_{e} \sqrt{3})

\frac{\sqrt{3}}{2} (2 + \log_{e} 3)

Question 8.

The solution curve of the differential equation $y \frac{d x}{d y} = x (\log_{e} x - \log_{e} y + 1), x > 0, y > 0$ passing through the point $(e, 1)$ is

| \log_{e} \frac{y}{x} | = y^{2}

| \log_{e} \frac{y}{x} | = x

| \log_{e} \frac{x}{y} | = y

2 | \log_{e} \frac{x}{y} | = y + 1

Question 9.

Let $y = y (x)$ be the solution of the differential equation $\sec x d y + {2 (1 - x) \tan x + x (2 - x)} d x = 0$ such that $y (0) = 2$ . Then $y (2)$ is equal to:

2 {\sin (2) + 1}

2 {1 - \sin (2)}

Question 10.

If $\sin (\frac{y}{x}) = \log_{e} | x | + \frac{α}{2}$ is the solution of the differential equation $x \cos (\frac{y}{x}) \frac{d y}{d x} = y \cos (\frac{y}{x}) + x$ and $y (1) = \frac{π}{3}$ , then $α^{2}$ is equal to

JEE Main Differential Equations Practice Questions With Solutions

JEE Main Differential Equations Practice Questions with Solutions

JEE Main Mathematics Differential Equations Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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