NCERT Exemplar MCQ

Question 1 of 10

NCERT Exemplar

The solution of \(\frac{d y}{d x}+y=e^{-x}, y(0)=0\) is:

A \(y=e^{-x}(x-1)\) B \(y=x e^x\) C \(y=x e^{-x}+1\) D \(y=x e^{-x}\)

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Question 2 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 3 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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Question 4 of 10

NCERT Exemplar

The solution of the differential equation \(x \frac{d y}{d x}+2 y=x^2\) is

A \(y=\frac{x^2+c}{4 x^2}\) B \(y=\frac{x^2}{4}+c\) C \(y=\frac{x^4+c}{x^2}\) D \(y=\frac{x^4+c}{4 x^2}\)

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Question 5 of 10

NCERT Exemplar

Solution of the differential equation \(\frac{d x}{x}+\frac{d y}{y}=0\) is

A \(\frac{1}{x}+\frac{1}{y}=c\) B \(\log x \cdot \log y=c\) C \(x y=c\) D \(x+y=c\)

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Question 6 of 10

NCERT Exemplar

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

A \(y\left(1+x^2\right)=c+\tan ^{-1} x\) B \(\frac{y}{1+x^2}=c+\tan ^{-1} x\) C \(y \log \left(1+x^2\right)=c+\tan ^{-1} x\) D \(y\left(1+x^2\right)=c+\sin ^{-1} x\)

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Question 7 of 10

NCERT Exemplar

The differential equation \(y \frac{d y}{d x}+x=c\) represents :

A Family of hyperbolas B Family of parabolas C Family of ellipses D Family of circles

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Question 8 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 9 of 10

NCERT Exemplar

The solution of the differential equation \(\frac{d y}{d x}=\frac{1+y^2}{1+x^2}\) is:

A \(y=\tan ^{-1} x\) B \(y-x=k(1+x y)\) C \(x=\tan ^{-1} y\) D \(\tan (x y)=k\)

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Question 10 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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