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NCERT Solutions for class 12 Maths | Chapter 9 - Differential Equations

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Free download in PDF Class 12 Maths Chapter 9 Differential Equations Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

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(1) The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is
[A] an ellipse
[B] parabola
[C] circle
[D] rectangular hyperbola
Answer: rectangular hyperbola
(2) Family y = Ax + A³ of curves will correspond to a differential equation of order
[A] 3
[B] 2
[C] 1
[D] not finite
Answer: 2

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(3) The solution of the differential equation
[A] y = tan-1 x
[B] y – x = k(1 + xy)
[C] x = tan-1 y
[D] tan (xy) = k
Answer: y – x = k(1 + xy)
(4) Integrating factor of the differential equation dy/dx + y tan x – sec x = 0 is
[A] cos x
[B] sec x
[C] ecos x
[D] esec x
Answer: sec x
(5) The degree of the differential equation

[A] 1
[B] 2
[C] 3
[D] 5
Answer: 1
(6) The general solution of the differential equation
[A]
[B]
[C]
[D]
Answer:
(7) The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
[A] sinx/siny = c
[B] sin x sin y = c
[C] sin x + sin y = z
[D] cos x cos y = c
Answer: sin x sin y = c
(8) The general solution of ex cos y dx – ex sin y dy = 0 is
[A] ex cos y = k
[B] ex sin y = k
[C] ex = k cos y
[D] ex = k sin y
Answer: ex cos y = k
(9) The differential equation represents
[A] Family of hyperbolas
[B] Family of parabolas
[C] Family of ellipses
[D] Family of circles
Answer: Family of circles
(10) Which of the following is a second order differential equation?
[A] (y’)² + x = y²
[B] y’y” + y = sin x
[C] y” + (y”)² + y = 0
[D] y’ = y²
Answer: y’y” + y = sin x
(11) The number of solutions of when y(1) = 2 is
[A] none
[B] one
[C] two
[D] infinite
Answer: one
(12) Family r = Ax + A³ of curves is represented by the differential equation of degree
[A] 1
[B] 2
[C] 3
[D] 4
Answer: 2
(13) Integrating factor of the differential equation cos x dy/dx + y sin x = 1 is
[A] cos x
[B] tan x
[C] sec x
[D] sin x
Answer: sec x
(14) Solution of differential equation xdy – ydx = Q represents
[A] a rectangular hyperbola
[B] parabola whose vertex is at origin
[C] straight line passing through origin
[D] a circle whose centre is at origin
Answer: straight line passing through origin
(15) The order and degree of the differential equation

= 0 respectvely, are

[A] 2 and not defined
[B] 2 and 2
[C] 2 and 3
[D] 3 and 3
Answer: 2 and not defined
(16) The degree of differential equation

[A] 4
[B] 3/2
[C] 2
[D] not defined
Answer: 2
(17) The degree of the differential equation

[A] 1
[B] 2
[C] 3
[D] not defined
Answer: not defined
(18) The solution of dy/dx = 1 + x + y + xy is
[A] x – y = k(1 + xy)
[B] log (1 + y) = x + x22 + k
[C] log (1 + x) + y + y22 = k
[D] None of these
Answer: log (1 + y) = x + x22 + k
(19) The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is
[A] 0.4 π cm/s
[B] 0.8 π cm/s
[C] 0.8 cm/s
[D] None of these
Answer: 0.8 π cm/s
(20) Integration factor of differential equation dy/dx + py = Q, where P and IQ are functions of x is
[A] ∫epdx
[B] e∫pdx
[C] e-∫pdx
[D] None of these
Answer: None of these

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