Check the below NCERT MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Differential Equations Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.
Differential Equations Class 12 MCQs Questions with Answers
MCQ On Differential Equations Class 12 Chapter 9 Question 1.
Integration factor of differential equation \(\frac{dy}{dx}\) + py = Q, where P and IQ are functions of x is
(a) ∫epdx
(b) \(_{e}\)∫pdx
(c) \(_{e}\)-∫pdx
(d) None of these
Answer
Answer: (d) None of these
Differential Equations Class 12 MCQ Chapter 9 Question 2.
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
Answer: (b) 0.8 π cm/s
Differential Equations MCQ Class 12 Chapter 9 Question 3.
The solution of \(\frac{dy}{dx}\) = 1 + x + y + xy is
(a) x – y = k(1 + xy)
(b) log (1 + y) = x + \(\frac{x^2}{2}\) + k
(c) log (1 + x) + y + \(\frac{y^2}{2}\) = k
(d) None of these
Answer
Answer: (b) log (1 + y) = x + \(\frac{x^2}{2}\) + k
MCQ On Differential Equations Class 12 Chapter 9 Question 4.
The degree of the differential equation
(\(\frac{d^2y}{dx}\))² + (\(\frac{dy}{dx}\))² = x sin \(\frac{dy}{dx}\) is
(a) 1
(b) 2
(c) 3
(d) not defined
Answer
Answer: (d) not defined
Differential Equations MCQ Questions And Answers Class 12 Chapter 9 Question 5.
The degree of differential equation
[1 + (\(\frac{dy}{dx}\))²]\(\frac{3}{2}\) = \(\frac{d^2y}{dx^2}\) is
(a) 4
(b) \(\frac{3}{2}\)
(c) 2
(d) not defined
Answer
Answer: (c) 2
Differential Equation MCQ Class 12 Chapter 9 Question 6.
The order and degree of the differential equation
\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))\(\frac{1}{4}\) + x\(\frac{1}{3}\) = 0 respectvely, are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3
Answer
Answer: (a) 2 and not defined
Differential Equations MCQ With Answers Class 12 Chapter 9 Question 7.
If y = e-x (A cos x + B sin x), then y is a solution of
(a) \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) = 0
(b) \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + 2y = 0
(c) \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0
(d) \(\frac{d^2y}{dx^2}\) + 2y = 0
Answer
Answer: (c) \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0
Differential Equations MCQ Questions Class 12 Chapter 9 Question 8.
The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is
(a) \(\frac{d^2y}{dx^2}\) – α²y = 0
(b) \(\frac{d^2y}{dx^2}\) + α²y = 0
(c) \(\frac{d^2y}{dx^2}\) + αy = 0
(d) \(\frac{d^2y}{dx^2}\) – αy = 0
Answer
Answer: (b) \(\frac{d^2y}{dx^2}\) + α²y = 0
MCQ Differential Equations Class 12 Chapter 9 Question 9.
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
Answer: (c) straight line passing through origin
Integrating Factor MCQ Class 12 Chapter 9 Question 10.
Integrating factor of the differential equation cos x \(\frac{dy}{dx}\) + y sin x = 1 is
(a) cos x
(b) tan x
(c) sec x
(d) sin x
Answer
Answer: (c) sec x
Differential Equations MCQ With Solution Pdf Class 12 Chapter 9 Question 11.
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) \(\frac{tan x}{tan y}\) = k
(d) tan x.tan y = k
Answer
Answer: (d) tan x.tan y = k
Differential Equation MCQs Class 12 Chapter 9 Question 12.
Family r = Ax + A³ of curves is represented by the differential equation of degree
(a) 1
(b) 2
(c) 3
(d) 4
Answer
Answer: (b) 2
MCQ Of Differential Equation Class 12 Chapter 9 Question 13.
Integrating factor of \(\frac{xdy}{dx}\) – y = x4 – 3x is
(a) x
(b) log x
(c) \(\frac{1}{2}\)
(d) -x
Answer
Answer: (c) \(\frac{1}{2}\)
Linear Differential Equations MCQs With Answers Class 12 Chapter 9 Question 14.
Solution of \(\frac{dy}{dx}\) – y = 1 y(0) = 1 is given by
(a) xy = -ex
(b) xy = -e-x
(c) xy = -1
(d) y = 2ex – 1
Answer
Answer: (d) y = 2ex – 1
MCQs On Differential Equations Class 12 Chapter 9 Question 15.
The number of solutions of \(\frac{dy}{dx}\) = \(\frac{y+1}{x-1}\) when y(1) = 2 is
(a) none
(b) one
(c) two
(d) infinite
Answer
Answer: (b) one
Differential Equations MCQs Class 12 Chapter 9 Question 16.
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
Answer: (b) y’y” + y = sin x
MCQ Questions On Differential Equations Class 12 Chapter 9 Question 17.
Integrating factor of the differential equation
(1 – x²) \(\frac{dy}{dx}\) – xy = 1 is
(a) -x
(b) \(\frac{x}{1+x^2}\)
(c) \(\sqrt{1-x^2}\)
(d) \(\frac{1}{2}\) log(1 – x²)
Answer
Answer: (c) \(\sqrt{1-x^2}\)
MCQ On Differential Calculus Class 12 Chapter 9 Question 18.
tan-1 x + tan-1 y = c is the general solution of the differential equation
(a) \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
(b) \(\frac{dy}{dx}\) = \(\frac{1+x^2}{1+y^2}\)
(c) (1 + x²)dy + (1 + y²)dx = 0
(d) (1 +x²2)dx+(1 + y²)dy = 0
Answer
Answer: (c) (1 + x²)dy + (1 + y²)dx = 0
Maths MCQ Questions Class 12 Chapter 9 Question 19.
The differential equation y \(\frac{dy}{dx}\) + x = c represents
(a) Family of hyperbolas
(b) Family of parabolas
(c) Family of ellipses
(d) Family of circles
Answer
Answer: (d) Family of circles
MCQ Questions For Class 12 Maths With Answers Chapter 9 Question 20.
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
Answer: (a) ex cos y = k
Question 21.
The degree of the differential equation
\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))³ + 6y5 = 0 is
(a) 1
(b) 2
(c) 3
(d) 5
Answer
Answer: (a) 1
Question 22.
The solution of \(\frac{dy}{dx}\) + 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
Answer: (b) y = xe-x
Question 23.
Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is
(a) cos x
(b) sec x
(c) ecos x
(d) esec x
Answer
Answer: (b) sec x
Question 24.
The solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
(a) y = tan-1 x
(b) y – x = k(1 + xy)
(c) x = tan-1 y
(d) tan (xy) = k
Answer
Answer: (b) y – x = k(1 + xy)
Question 25.
The integrating factor of the differential equation \(\frac{dy}{dx}\) + y = \(\frac{1+y}{x}\) is
(a) \(\frac{x}{e^x}\)
(b) \(\frac{e^x}{x}\)
(c) xex
(d) ex
Answer
Answer: (b) \(\frac{e^x}{x}\)
Question 26.
y = aemx + be-mx satisfies which of the following differential equation?
(a) \(\frac{dy}{dx}\) + my = 0
(b) \(\frac{dy}{dx}\) – my = 0
(c) \(\frac{d^2y}{dx^2}\) – m²y = 0
(d) \(\frac{d^2y}{dx^2}\) +m²y = 0
Answer
Answer: (c) \(\frac{d^2y}{dx^2}\) – m²y = 0
Question 27.
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 = z
(d) cos x cos y = c
Answer
Answer: (b) sin x sin y = c
Question 28.
The solution of x \(\frac{dy}{dx}\) + y = ex is
(a) y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)
(b) y = xex + cx
(c) y = xex + k
(d) x = \(\frac{e^vy}{y}\) + \(\frac{k}{y}\)
Answer
Answer: (a) y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)
Question 29.
The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is
(a) (x² – y²)\(\frac{dy}{dx}\) = 2xy
(b) 2 (x² + y²)\(\frac{dy}{dx}\) = xy
(c) 2(x² – y²)\(\frac{dy}{dx}\) = xy
(d) (x² + y²) \(\frac{dy}{dx}\) = 2xy
Answer
Answer: (a) (x² – y²)\(\frac{dy}{dx}\) = 2xy
Question 30.
Family y = Ax + A³ of curves will correspond to a differential equation of order
(a) 3
(b) 2
(c) 1
(d) not finite
Answer
Answer: (b) 2
Question 31.
The general solution of \(\frac{dy}{dx}\) = 2x ex2-y is
(a) ex2-y = c
(b) e-y + ex2 = c
(c) ey = ex2 + c
(d) ex2+y = c
Answer
Answer: (c) ey = ex2 + c
Question 32.
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
Answer: (d) rectangular hyperbola
Question 33.
The general solution of the differential equation \(\frac{dy}{dx}\) = e\(\frac{x^2}{2}\) + xy is
(a) y = ce\(\frac{-x^2}{2}\)
(b) y = ce\(\frac{x^2}{2}\)
(c) y = (x + c)e\(\frac{x^2}{2}\)
(d) y = (c – x)e\(\frac{x^2}{2}\)
Answer
Answer: (c) y = (x + c)e\(\frac{x^2}{2}\)
Question 34.
The solution of the equation (2y – 1) dx-(2x + 3)dy = 0 is
(a) \(\frac{2x-1}{2y+3}\) = k
(b) \(\frac{2y+1}{2x-3}\) = k
(c) \(\frac{2x+3}{2y-1}\) = k
(d) \(\frac{2x-1}{2y-1}\) = k
Answer
Answer: (c) \(\frac{2x+3}{2y-1}\) = k
Question 35.
The differential equation for which y = a cos x + b sin x is a solution is
(a) \(\frac{d^2y}{dx^2}\) + y = 0
(b) \(\frac{d^2y}{dx^2}\) – y = 0
(c) \(\frac{d^2y}{dx^2}\) + (a + b)y = 0
(d) \(\frac{d^2y}{dx^2}\) + (a – b)y = 0
Answer
Answer: (a) \(\frac{d^2y}{dx^2}\) + y = 0
Question 36.
The solution of \(\frac{dy}{dx}\) + 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
Answer: (d) y = xe-x
Question 37.
The order and degree of the differential equation
(\(\frac{d^2y}{dx^3}\))² – 3\(\frac{d^2y}{dx^2}\) + 2(\(\frac{dy}{dx}\))4 = y4 are
(a) 1, 4
(b) 3, 4
(c) 2, 4
(d) 3, 2
Answer
Answer: (d) 3, 2
Question 38.
The order and degree of the differential equation
[1 + (\(\frac{dy}{dx}\))²] = \(\frac{d^2y}{dx^2}\) are
(a) 1, \(\frac{3}{2}\)
(b) 2, 3
(c) 2, 1
(d) 3, 4
Answer
Answer: (c) 2, 1
Question 39.
The differential equation of the family of curves y² = 4a (x + a) is
(a) y² = 4\(\frac{dy}{dx}\) (x + \(\frac{dy}{dx}\))
(b) 2y\(\frac{dy}{dx}\) = 4a
(c) y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
(d) 2x\(\frac{dy}{dx}\) + y(\(\frac{dy}{dx}\))² – y
Answer
Answer: (c) y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
Question 40.
Which of the following is the general solution of \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + y = 0
(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
Answer: (a) y = (Ax + B)ex
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