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

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Questions
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 class 12 maths chapter 9 differential equations
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

class 12 maths chapter 9 differential equations

A 1
B 2
C 3
D 5

Answer:1
6 The general solution of the differential equation class 12 maths chapter 9 differential equations
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 class 12 maths chapter 9 differential equations 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

class 12 maths chapter 9 differential equations = 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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