NCERT Exemplar MCQ

Question 1 of 10

NCERT Exemplar

The solution of the differential equation \(2 x \cdot \frac{d y}{d x}-y=3\) represents a family of

A straight lines B circles C parabolas D ellipses

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Question 2 of 10

NCERT Exemplar

A solution of the differential equation \(\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}+y=0\) is

A \(y=2\) B \(y=2 x\) C \(y=2 x-4\) D \(y=2 x^2-4\)

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Question 3 of 10

NCERT Exemplar

Solution of \(\frac{d y}{d x}-y=1, y(0)=1\) is given by

A \(x y=-e^x\) B \(x y=-e^{-x}\) C \(x y=-1\) D \(y=2 e^x-1\)

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Question 4 of 10

NCERT Exemplar

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

A \(y=e^{x-y}-x^2 e^{-y}+c\) B \(e^y-e^x=\frac{x^3}{3}+c\) C \(e^x+e^y=\frac{x^3}{3}+c\) D \(e^x-e^y=\frac{x^3}{3}+c\)

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Question 5 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 6 of 10

NCERT Exemplar

The general solution of \(\frac{d y}{d x}=2 x e^{x^2-y}\) is :

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

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Question 7 of 10

NCERT Exemplar

Family \(y=\mathrm{A} x+\mathrm{A}^3\) of curves is represented by the differential equation of degree :

A 1 B 2 C 3 D 4

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Question 8 of 10

NCERT Exemplar

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

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

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Question 9 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 10 of 10

NCERT Exemplar

The integrating factor of the differential equation \(\frac{d y}{d x}+y=\frac{1+y}{x}\) is:

A \(\frac{x}{e^x}\) B \(\frac{e^x}{x}\) C \(x e^x\) D \(e^x\)

Select one option. Answers are shown after the test.

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