Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 9 Differential Equations. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Differential Equations MCQs Pdf with Answers to know their preparation level.

Differential Equations Class 12 Maths MCQs Pdf

Question 1.

Answer:
(c) \(\frac{x}{y}-y^{2}=c\)

Question 2.


Answer:
(b) \(y=\frac{\sqrt{1+x^{2}}}{x}+\frac{c}{x}\)

Question 3.

Answer:
(c) \(y e^{-3 x}=-e^{-3 x} \frac{(2 \cos 2 x+3 \sin 2 x)}{13}+c\)

Question 4.
The solution of the differential equation,

Answer:
(a) \(y=\sin \frac{1}{x}-\cos \frac{1}{x}\)

Question 5.
The degree of the differential equation

(a) 1
(b) 2
(c) 3
(d) not defined
Answer:
(d) not defined

Question 6.
The order and degree of the differential equation \(\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{\frac{1}{4}}+x^{\frac{1}{5}}=0\) respectively are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3
Answer:
(a) 2 and not defined

Question 7.
Integrating factor of the differential equation

Answer:
(c) \(\sqrt{1-x^{2}}\)

Question 8.
Integrating factor of the differential equation \(\frac{d y}{d x}\) + y tanx – sec x = 0 is
(a) cos x
(b) sec x
(c) e^{cos x}
(d) e^{sec x}
Answer:
(b) sec x

Question 9.
If (x + y)² \(\frac{d y}{d x}\) = a², y = 0 when x = 0, then y = a if \(\frac{x}{a}\) =
(a) 1
(b) tan 1
(c) tan 1 + 1
(d) tan 1 – 1
Answer:
(d) tan 1 – 1

Question 10.

Answer:
(a) e^x – 1

Question 11.
If sinx \(\frac{d y}{d x}\) + y cosx = x sinx, then (y – 1) sinx =
(a) c – x sinx
(b) c + xcosx
(c) c – x cos x
(d) c + x sin x
Answer:
(c) c – x cos x

Question 12.
The solution of differential equation (e^y + 1) cosx dx + e^y sinx dy = 0 is
(a) (e^y + 1) sinx = c
(b) e^x sinx = c
(c) (e^x + 1) cosx = c
(d) none of these
Answer:
(a) (e^y + 1) sinx = c

Question 13.
The solution of the differential equation \(\frac{d y}{d x}=\frac{x}{1+x^{2}}\) is

Answer:
(c) \(y=\log (\sqrt{1+x^{2}})+c\)

Question 14.

Answer:
(c) \(\frac{e^{6}+9}{2}\)

Question 15.

Answer:
(a) y = e sin²x

Question 16.
The differential equation of all ‘Simple Harmonic Motions’ of given period \(\frac{2 \pi}{n}\) is

Answer:
(b) \(\frac{d^{2} x}{d t^{2}}+n^{2} x=0\)

Question 17.
The differential equation of all parabolas whose axes are parallel to y-axis is

Answer:
(a) \(\frac{d y}{d x}=-\frac{c^{2}}{x^{2}}\)

Question 18.
The Solution of cos(x + y) dy = dx is

Answer:
(a) \(y=\tan \left(\frac{x+y}{2}\right)+C\)

Question 19.

Answer:
(d) x + x ln x

Question 20.

Answer:
(c) √3e

Question 21.

Answer:
(d) \(\frac{\pi}{12}\)

Question 22.

Answer:
(d) \(\sec \frac{y}{x}=c x y\)

Question 23.

Answer:
(c) \(-2 \sqrt{\frac{x}{y}}=\ln c y\)

Question 24.

Answer:
(c) \(x+y e^{x / y}=c\)

Question 25.

Answer:
(c) Circle

Question 26.
The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

Answer:
(a) \(\left(x^{2}-y^{2}\right) \frac{d y}{d x}-2 x y=0\)

Question 27.
The differential equation of the family of circles touching the x-axis at origin is given by

Answer:
(b) \(y^{\prime}=\frac{2 x y}{x^{2}-y^{2}}\)

Question 28.
The differential equation representing the family of ellipses with centre at origin and foci on x-axis is given as
(a) xy’ + y = 0
(b) x²y²(y”)² + yy’= 0
(c) xyy” + x(y’)² – yy’ = 0
(d) None of these
Answer:
(b) x²y²(y”)² + yy’= 0

Question 29.
The differential equation of all parabolas whose axes are along x-axis is
(a) \(y_{2}^{2}+y_{1}=0\)
(b) \(y_{1}^{2}+y_{2}=0\)
(c) \(y_{1}^{2}+y_{1} y_{2}=0\)
(d) \(y_{1}^{2}+y y_{2}=0\)
Answer:
(d) \(y_{1}^{2}+y y_{2}=0\)

Question 30.
The equation of family of curves for which the length of the normal is equal to the radius vector is
(a) \(y^{2} \mp x^{2}=k^{2}\)
(b) \(y \pm x=k\)
(c) y² = kx
(d) none of these
Answer:
(a) \(y^{2} \mp x^{2}=k^{2}\)

Question 31.
Given the differential equation \(\frac{d y}{d x}=\frac{6 x^{2}}{2 y+\cos y}\); y(1) = π
Mark out the correct statement.
(a) solution is y² – sin y = -2x³ + C
(b) solution is y² + sin y = 2x³ + C
(c) C = π²+ 2√2
(d) C = π² + 2
Answer:
(b) solution is y² + sin y = 2x³ + C

Question 32.
The differential equation of all parabolas whose axis of symmetry is along the axis of the x-axis is of order
(a) 3
(b) 1
(c) 2
(d) none of these
Answer:
(c) 2

Question 33.
The degree of the equation satisfying the relation \(\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=\lambda(\sqrt{1+y^{2}}-y \sqrt{1+x^{2}})\) is
(a) 1
(b) 2
(c) 3
(d) none of these
Answer:
(a) 1

Question 34.
The degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2 / 3}+4-\frac{3 d y}{d x}=0\) is
(a) 2
(b) 1
(c) 3
(d) none of these
Answer:
(a) 2

Question 35.
The differential equation whose solution is (x – h)² + (y – k)² = a² is (a is a constant)

Answer:
(b) \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=a^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2}\)

Question 36.
The differential equation satisfied by y = \(\frac{A}{x}\) + B is (A, B are parameters)
(a) x² y₁ = y
(b) xy₁ + 2y₂ = 0
(c) xy₂ + 2y₁ = 0
(d) none of these
Answer:
(c) xy₂ + 2y₁ = 0

Question 37.
The solution of a differential equation is y = c₁e^4x + c₂e^3x, the differential equation is given by

Answer:
(c) \(\frac{d^{2} y}{d x^{2}}-7 \frac{d y}{d x}+12 y=0\)

Question 38.
The differential equation satisfied by

Answer:
(b) \(\frac{d y}{d x}=\frac{1+y^{2}}{1+x^{2}}\)

Question 39.
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 + xy)
(c) x = tan^-1 y
(d) tan(xy) = k
Answer:
(b) y – x = k(1 + xy)

Question 40.
The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
(a) \(\frac{\sin x}{\sin y}=c\)
(b) sin x sin y = c
(c) sin x + sin y = c
(d) cos x cos y = c
Answer:
(b) sin x sin y = c

Question 41.
Which of the following is the general solution of

Answer:
(a) y = (Ax + B) e^x

Question 42.

Answer:
(a) \(y\left(1+x^{2}\right)=c+\tan ^{-1} x\)

Question 43.

Answer:
(c) \(\sqrt{x^{2}+y^{2}}+y=c x^{2}\)

Question 44.
The solution of the differential equation (x² + y²) dx – 2xy dy = 0 is

Answer:
(d) \(\frac{x^{2}-y^{2}}{x}=c\)

Question 45.
The solution of the differential equation x dy + (x + y) dx = 0 is

Answer:
(b) \(c=x y+\frac{x^{2}}{2}\)

Question 46.
The solution of differential equation \(\frac{d y}{d x}=\frac{x-y}{x+y}\) is
(a) x² – y² + 2xy + c = 0
(b) x² – y² – xy + c = 0
(c) x² – y² + xy + c = 0
(d) x² – y² – 2xy + c = 0
Answer:
(d) x² – y² – 2xy + c = 0

Question 47.
The particular solution In(\(\frac{d y}{d x}\)) = 3x + 4y, y(0) = 0 is
(a) e^3x + 3e^-4y = 4
(b) 4e^3x – 3e^-4y = 3
(c) 3e^3x + 4e^4y = 7
(d) 4e^3x + 3e^-4y = 7
Answer:
(d) 4e^3x + 3e^-4y = 7

Question 48.
The solution of the differential equation

Answer:
(c) y = x tan(C – x)

Question 49.
The solution of the differential equation

Answer:
(d) None of these

Question 50.
The solution of the differential equation

Answer:
(c) \(y=x \tan \left(\frac{C-x^{2}-y^{2}}{2}\right)\)

Question 51.

Answer:
(b) \(c e^{y / 2}\)

Question 52.
The differential equation \(\frac{d y}{d x}=\sqrt{\frac{1-y^{2}}{y}}\) determines a family of circle with
(a) variable radii and fixed centre (0, 1)
(b) variable radii and fixed centre (0, -1)
(c) fixed radius 1 and variable centre on x-axis
(d) fixed radius 1 and variable centre on y-axis
Answer:
(c) fixed radius 1 and variable centre on x-axis

Question 53.
If y dx + y² dy = x dy, x ∈ R, y > 0 and y(1) = 1, then y(-3) =
(a) 3
(b) 2
(c) 1
(d) 5
Answer:
(a) 3

Question 54.
The solution of y dx + (x + x²y) dy = 0 is

Answer:
(b) \(-\frac{1}{x y}+\ln y=c\)

Question 55.

Answer:
(c) \(\frac{e^{2}+1}{4}\)

Question 56.

Answer:
(d) 6

Question 57.

Answer:
(d) \(\frac{5}{2}\)

Question 58.

Answer:
(d) \(\frac{2}{e}\)

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