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.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q61
Answer:
(c) \(\frac{x}{y}-y^{2}=c\)

Question 2.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q62
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q62.1
Answer:
(b) \(y=\frac{\sqrt{1+x^{2}}}{x}+\frac{c}{x}\)

Question 3.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q63
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,
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q65
Answer:
(a) \(y=\sin \frac{1}{x}-\cos \frac{1}{x}\)

Question 5.
The degree of the differential equation
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q66
(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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q69
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) ecos x
(d) esec 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.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q32
Answer:
(a) ex – 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 (ey + 1) cosx dx + ey sinx dy = 0 is
(a) (ey + 1) sinx = c
(b) ex sinx = c
(c) (ex + 1) cosx = c
(d) none of these
Answer:
(a) (ey + 1) sinx = c

Question 13.
The solution of the differential equation \(\frac{d y}{d x}=\frac{x}{1+x^{2}}\) is
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q37
Answer:
(c) \(y=\log (\sqrt{1+x^{2}})+c\)

Question 14.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q38
Answer:
(c) \(\frac{e^{6}+9}{2}\)

Question 15.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q39
Answer:
(a) y = e sin2x

Question 16.
The differential equation of all ‘Simple Harmonic Motions’ of given period \(\frac{2 \pi}{n}\) is
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q11
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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q12
Answer:
(a) \(\frac{d y}{d x}=-\frac{c^{2}}{x^{2}}\)

Question 18.
The Solution of cos(x + y) dy = dx is
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q41
Answer:
(a) \(y=\tan \left(\frac{x+y}{2}\right)+C\)

Question 19.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q42
Answer:
(d) x + x ln x

Question 20.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q43
Answer:
(c) √3e

Question 21.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q45
Answer:
(d) \(\frac{\pi}{12}\)

Question 22.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q46
Answer:
(d) \(\sec \frac{y}{x}=c x y\)

Question 23.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q47
Answer:
(c) \(-2 \sqrt{\frac{x}{y}}=\ln c y\)

Question 24.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q48
Answer:
(c) \(x+y e^{x / y}=c\)

Question 25.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q50
Answer:
(c) Circle

Question 26.
The differential equation of all circles which pass through the origin and whose centre lies on y-axis is
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q14
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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q15
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)
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q5
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 = c1e4x + c2e3x, the differential equation is given by
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q9
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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q10
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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q74
Answer:
(a) y = (Ax + B) ex

Question 42.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q75
Answer:
(a) \(y\left(1+x^{2}\right)=c+\tan ^{-1} x\)

Question 43.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q51
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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q52
Answer:
(d) \(\frac{x^{2}-y^{2}}{x}=c\)

Question 45.
The solution of the differential equation x dy + (x + y) dx = 0 is
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q53
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) e3x + 3e-4y = 4
(b) 4e3x – 3e-4y = 3
(c) 3e3x + 4e4y = 7
(d) 4e3x + 3e-4y = 7
Answer:
(d) 4e3x + 3e-4y = 7

Question 48.
The solution of the differential equation
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q23
Answer:
(c) y = x tan(C – x)

Question 49.
The solution of the differential equation
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q24
Answer:
(d) None of these

Question 50.
The solution of the differential equation
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q25
Answer:
(c) \(y=x \tan \left(\frac{C-x^{2}-y^{2}}{2}\right)\)

Question 51.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q26
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
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q30
Answer:
(b) \(-\frac{1}{x y}+\ln y=c\)

Question 55.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q56
Answer:
(c) \(\frac{e^{2}+1}{4}\)

Question 56.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q57
Answer:
(d) 6

Question 57.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q58
Answer:
(d) \(\frac{5}{2}\)

Question 58.
Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations Q59
Answer:
(d) \(\frac{2}{e}\)

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