10 Question MCQ (including Assertion)

Question 1 of 10

NCERT Exemplar

General solution of $\frac{d y}{d x}+y \tan x=\sec x$ is:

A $y \sec x=\tan x+c$ B $y \tan x=\sec x+c$ C $\tan x=y \tan x+c$ D $x \sec x=\tan y+c$

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Question 2 of 10

NCERT Exemplar

The order and degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]=\frac{d^2 y}{d x^2}$ are :

A $2, \frac{3}{2}$ B 2, 3 C 2, 1 D 3, 4

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Question 3 of 10

Which of the following is the general solution of $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+y=0$ ?

A $y=(\mathrm{A} x+\mathrm{B}) \mathrm{e}^x$ B $y=(\mathrm{A} x+\mathrm{B}) e^{-x}$ C $y=\mathrm{A} e^x+\mathrm{B} e^{-x}$ D $y=\mathrm{A} \cos x+\mathrm{B} \sin x$

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Question 4 of 10

NCERT Exemplar

Family $y=\mathrm{A} x+\mathrm{A}^3$ of curves will correspond to a differential equation of order

A 3 B 2 C 1 D not defined

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Question 5 of 10

NCERT Exemplar

The degree of the differential equation $\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2$ is

A 1 B 2 C 3 D 4

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Question 6 of 10

NCERT Exemplar

The solution of $x \frac{d y}{d x}+y=e^x$ is:

A $y=\frac{e^x}{x}+\frac{k}{x}$ B $y=x e^x+c x$ C $y=x e^x+k$ D $x=\frac{e^y}{y}+\frac{k}{y}$

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Question 7 of 10

NCERT Exemplar

The differential equation for which $y=a \cos x+b \sin x$ is a solution, is :

A $\frac{d^2 y}{d x^2}+y=0$ B $\frac{d^2 y}{d x^2}-y=0$ C $\frac{d^2 y}{d x^2}+(a+b) y=0$ D $\frac{d^2 y}{d x^2}+(a-b) y=0$

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Question 8 of 10

NCERT Exemplar

The order and degree of the differential equation
$$ \left(\frac{d^3 y}{d x^3}\right)^2-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4 \text { are : } $$

A 1, 4 B 3, 4 C 2, 4 D 3, 2

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Question 9 of 10

NCERT Exemplar

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^2=x \sin \left(\frac{d y}{d x}\right)$ is:

A 1 B 2 C 3 D not defined

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Question 10 of 10

NCERT Exemplar

The general solution of the differential equation $\left(e^x+1\right) y d y=(y+1) e^x d x$ is:

A $(y+1)=k\left(e^x+1\right)$ B $y+1=e^x+1+k$ C $y=\log \left\{k(y+1)\left(e^x+1\right)\right\}$ D $y=\log \left\{\frac{e^x+1}{y+1}\right\}+k$

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10 Question MCQ (including Assertion)