MCQs Differential Equations for ISC Class 12 Maths Questions with Answers

MCQs Differential Equations for ISC Class 12 Maths Questions with Answers. These MCQs / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming Sem-2 exam of council. Visit official website CISCE for detail information about ISC Class-12 Maths.

ISC Class 12 MCQs Differential Equations Questions with Answers

Board	ISC
Class	12th (XII)
Subject	Maths
Chapter	Differential Equations
Syllabus	on bifurcated syllabus (after reduction)
Session	2021-22
Bifurcated	Sem-2
Topic	MCQs / Objective Type Question

MCQs Differential Equations for ISC Class 12 Maths Questions with Answers

Question 1: Family y = Ax + A³ of curves will correspond to a differential equation of order

(a) 3
(b) 2
(c) 1
(d) not finite

Answer: (b) 2

Question 2: The general solution of 𝑑𝑦/𝑑𝑥 = 2x e^x2-y is

(a) e^x2-y = c
(b) e^-y + e^x2 = c
(c) e^y = e^x2 + c
(d) e^x2+y = c

Answer: (c) e^y = e^x2 + c

Question 3: 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: (c) straight line passing through origin

Question 4: 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: (d) rectangular hyperbola

Question 5:  The differential equation of all circles which pass through the origin and whose centre lies on y-axis is

Answer: (a)

Question 6:  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 7: The number of arbitrary constants in the general solution of a differential equation of fourth order is:

(a) 0
(b) 2
(c) 3
(d) 4

Answer: (d) 4

Question 8: 10 The number of arbitrary constants in the particular solution of a differential equation of third order is:

(a) 3
(b) 2
(c) 1
(d) 0

Answer: (d) 0

Question 9: The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

(a) (x – 2)² y’² = 25 – (y – 2)²
(b) (x – 2) y’² = 25 – (y – 2)²
(c) (y – 2) y’² =25 – (y – 2)²
(d) (y – 2)² y’² = 25 – (y – 2)²

Answer: (d) (y – 2)² y’² = 25 – (y – 2)²

Question 10: The degree of the differential equation

(a) 1
(b) 2
(c) 3
(d) not defined

Answer: (d) not defined

Question 11:  Integrating factor of the differential equation 𝑑𝑦/𝑑𝑥 + y tanx – sec x = 0 is

(a) cos x
(b) sec x
(c) e^{cos x}
(d) e^{sec x}

Answer: (b) sec x

Question 12:   If (x + y)² 𝑑𝑦/𝑑𝑥 = a², y = 0 when x = 0, then y = a if 𝑥/𝑎 =

(a) 1
(b) tan 1
(c) tan 1 + 1
(d) tan 1 – 1

Answer: (d) tan 1 – 1

Question 13: Family r = Ax + A³ of curves is represented by the differential equation of degree

(a) 1
(b) 2
(c) 3
(d) 4

Answer: (b) 2

Question 14: 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: (b) y’y” + y = sin x

Question 15: The order and degree of a differential equation d2y/dx2+(dy/dx)1/4 +x1/5=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 16:  If sinx 𝑑𝑦𝑑𝑥 + 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 17:  Given the differential equation 𝑑𝑦/𝑑𝑥 = 6𝑥²/(2𝑦+cos𝑦); 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 18: The solution of differential equation (e^y + 1) cosx dx + e^y sinx dy = 0 is

(a) (e^y + 1) sinx = c
(b) e^x sinx = c
(c) (e^x + 1) cosx = c
(d) none of these

Answer: (a) (e^y + 1) sinx = c

Question 19: 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 20:  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 = c
(d) cos x cos y = c

Answer: (b) sin x sin y = c

Question 21: 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 22: 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: (b) 0.8 π cm/s

Question 23: The differential equation which represents the family of curves y = e^c₂x, where c₁ and c₂ are arbitrary constants, is:

(a) y” = y’y
(b) yy” = y’
(c) yy” = (y’)²
(d) y’ = y²

Answer: (d) y’ = y²

Question 24: 

Answer: (d) 2/e

Question 25: If y = e–x (A cos x + Bsinx) , then it is a solution of

(a) d²y/dx² +2dy/dx =0
(b) d²y/dx² – 2d²y/dx² + 2y = 0
(c) d²y/dx² +2dy/dx + 2y = 0
(d) d²y/dx²+2y=0

Answer: (c) d²y/dx² +2dy/dx + 2y = 0

Question 26: 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 = c
(d) cos x cos y = c

Answer: (b) sin x sin y = c

Question 27: The differential equation whose solution is (x – h)² + (y – k)² = a² is (a is a constant)

Answer: (b)

Question 28: The differential equation satisfied by y = 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 29: Which of the following is a homogeneous differential equation?

(a) (4x + 6y + 5)dy – (3y + 2x + 4)dx = 0
(b) xy dx – (x³ + y²)dy = Q
(c) (x³ + 2y²) dx + 2xy dy = 0
(d) y² dx + (x² – xy – y²)dy = 0

Answer: (d) y² dx + (x² – xy – y²)dy = 0

Question 30: The degree of the differential equation representing the family of curves (x – a)² + y² = 16 is

(a) 0
(b) 2
(c) 3
(d) 1

Answer: (d) 1

Question 31: The solution of the differential equation 𝑑𝑦/𝑑𝑥 = (1+𝑦²)/(1+𝑥²) 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 32: Which of the following is the general solution of 𝑑²𝑦/𝑑𝑥² – 2(𝑑𝑦/𝑑𝑥) + y = 0

(a) y = (Ax + B)e^x
(b) y = (Ax + B)e^-x
(c) y = Ae^x + Be^-x
(d) y = A cos x + B sin x

Answer: (a) y = (Ax + B)e^x

Question 33: 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: (d) x² – y² – 2xy + c = 0

Question 34: 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 35: 

Answer: (d) 6

Question 36: Differential equation which has solution of the form y = Acosax + Bsinax , where A and B are arbitrary constants is

(a) d²y/dx² -α2y = 0
(b) d²y/dx² + α2y = 0
(c) d²y/dx² + αy = 0
(d) d²y/dx² – αy = 0

Answer: (b) d²y/dx² + α2y = 0

Question 37: 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: (d) y = 2ex – 1

Question 38: Integrating factor of the differential equation (1- x2)dy/dx – xy = 1 is

(a) –x
(b) x/1 +x²
(c) √(1 -x2)
(d)1/2 log(1-x²)

Answer: (c) √(1 -x2)

–: End of MCQs Differential Equations for ISC Class 12  :–