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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 solution of is
[A]
[B] xex + cx
[C] y = xex + k
[D]
Answer:
(2) The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is
[A] (x² – y²)dy/dx = 2xy
[B] 2 (x² + y²)dy/dx = xy
[C] 2(x² – y²)dy/dx = xy
[D] (x² + y²) dy/dx = 2xy
Answer: (x² – y²)dy/dx = 2xy

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(3) The solution of dy/dx + y = e-x, y (0) = 0 is
[A] y = e-x (x – 1)
[B] y = xex
[C] y = xe-x + 1
[D] y = xe-x
Answer: y = xe-x
(4) The order and degree of the differential equation

[A] 1, 3/2
[B] 2, 3
[C] 2, 1
[D] 3, 4
Answer: 2, 1
(5) Which of the following is the general solution of
[A] y = (Ax + B)ex
[B] y = (Ax + B)e-x
[C] y = Aex + Be-x
[D] y = A cos x + B sin x
Answer: y = (Ax + B)ex
(6) The integrating factor of the differential equation is
[A] xe/x
[B] ex/x
[C] xex
[D] ex
Answer: ex/x
(7) Solution of dy/dx – y = 1 y(0) = 1 is given by
[A] xy = -ex
[B] xy = -e-x
[C] xy = -1
[D] y = 2ex – 1
Answer: y = 2ex – 1
(8) Solution of the differential equation tan y sec² x dx + tan x sec² y dy + 0 is .
[A] tan x + tan y = k
[B] tan x – tan y = k
[C] tanx/tany = k
[D] tan x.tan y = k
Answer: tan x.tan y = k
(9) The order and degree of the differential equation

[A] 1, 4
[B] 3, 4
[C] 2, 4
[D] 3, 2
Answer: 3, 2
(10) The general solution of dy/dx = 2x ex2-y is
[A] ex2-y = c
[B] e-y + ex2  = c
[C] ey = ex2  + c
[D] ex2+y = c
Answer: ey = ex2  + c
(11) y = aemx + be-mx satisfies which of the following differential equation?
[A] dy/dx + my = 0
[B] dy/dx – my = 0
[C] d2y/dx2 – m²y = 0
[D] d2y/dx2 +m²y = 0
Answer: d2y/dx2 – m²y = 0
(12) The solution of the equation (2y – 1) dx-(2x + 3)dy = 0 is
[A]
[B]
[C]
[D]
Answer:
(13) Integrating factor of xdy/dx – y = x4 – 3x is
[A] x
[B] log x
[C] 1/2
[D] -x
Answer: 1/2
(14) The differential equation for which y = a cos x + b sin x is a solution is
[A]
[B]
[C]
[D]
Answer:
(15) The solution of dy/dx + y = e-x, y (0) = 0 is
[A] y = ex(x – 1)
[B] y = xe-x
[C] y = xe-x + 1
[D] y = (x + 1 )e-x
Answer: y = xe-x
(16) 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: 3
(17) The differential equation 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: fixed radius 1 and variable centre on x-axis
(18) The particular solution In(dy/dx) = 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: 4e3x + 3e-4y = 7
(19) The solution of differential equation dy/dx=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: x2 – y2 – 2xy + c = 0
(20) The solution of the differential equation x dy + (x + y) dx = 0 is
[A]
[B]
[C]
[D] None of these
Answer:

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