MCQ Chapter 9 Differential Equations Class 12 Mathematics

MCQ Questions Class 12

Please refer to Differential Equations MCQ Questions Class 12 Mathematics below. These MCQ questions for Class 12 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Differential Equations will help you to prepare for the exams and get more marks.

Differential Equations MCQ Questions Class 12 Mathematics

Please see solved MCQ Questions for Differential Equations in Class 12 Mathematics. All questions and answers have been prepared by expert faculty of standard 12 based on the latest examination guidelines.

MCQ Questions Class 12 Mathematics Differential Equations

Question. The differential equation representing the family of curves y2 = 2c ( x+√c) , where c > 0, is a parameter, is of order and degree as follows :
(a) order 1, degree 2
(b) order 1, degree 1
(c) order 1, degree 3
(d) order 2, degree 2

Answer

C

Question. The general solution of differential equation

Answer

A

Question. Solution of the differential equation

Answer

C

Question. Solution of the differential equation

Answer

B

Question. Solution of the differential equation

Answer

D

Question. Solution of the differential equation

Answer

C

Question. The general solution of the differential equation

Answer

C

Question. Solution of the differential equation

Answer

B

Question. Solution of the differential equation

Answer

C

Question. Solution of the differential equation

Answer

B

Question. The general solution of

Answer

C

Question. Solution of the differential equation

Answer

A

Question. The differential equation y dy/dx+x=c  represents family of 
(a) hyperbolas
(b) parabolas
(c) ellipses
(d) circles

Answer

D

Question. Solution of the differential equation

Answer

B

Question. The solution of the equation dy/dx=x(2log x+1)/sin y +y cos y is 

Answer

A

Question. The solution of dy/dx + = xy= xy2 is

Answer

B

Question. The solution of differential equation

Answer

C

Question. The general solution of dy/dx=2xex2-y is

Answer

C

Question. The solution of x dy- y dx+ x2 ex dx=0 is

Answer

A

Question. The solution of the differential equation

Answer

A

Question. The solution of differential equation

Answer

C

Question. The general solution of the differential equation

Answer

B

Question.

Answer

B

Question. The solution of differential equation

Answer

A

Question. The solution of ydx- xdy =xydx – = is
(a) y= Cxe -x
(b) 2y= Cxe -x
(c) y= 3Cxe -x
(d) y2 =Cxe -x 

Answer

A

Question. Consider the differential equation

MCQ Chapter 9 Differential Equations Class 12 Mathematics
Answer

C

Question. The equation of the curve through the point (1, 2) and whose slope is y-1/x2+x , is
(a) (y – 1)(x +1) – 2x = 0
(b) 2x(y – 1) + x +1 = 0
(c) x(y -1)(x +1) + 2 = 0
(d) None of these

Answer

A

Question. The order and degree of the differential equation

(a) 2, 2
(b) 2, 3
(c) 2, 1
(d) None of these

Answer

A

Question. The differential equation of all non-horizontal lines in a plane is
(a) d2y/dx2
(b) d2x/dy2 = 0
(c) dy/dx = 0
(d) dx/dy = 0

Answer

B

Question. If y(t) is a solution of(1+t)dy/dt – ty = 1 and y(0) = –1, then the value of y (1) is
(a) 1/2
(b) -1/2
(c) 2
(d) 1

Answer

B

Question. The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants, will be
(a) 2
(b) 4
(c) 6
(d) None of these

Answer

B

Question. Consider the following statements
I. The order of the differential equation dy/dx = ex is 1.
II. The order of the differential equation d2y/dx2 + y = 0 is 2.
III. The order of the differential equation (d3y/dx3) + x2 (d2y/dx2)3 = 0 is 3.
Choose correct option.
(a) I and II are true
(b) II and III are true
(c) I and III are true
(d) All are true

Answer

D

Question. The differential equation (1+ y2 )x dx – (1+ x2 )ydy = 0 represents a family of :
(a) ellipses of constant eccentricity
(b) ellipses of variable eccentricity
(c) hyperbolas of constant eccentricity
(d) hyperbolas of variable eccentricity

Answer

D

Question. For the function y = Bx2 to be the solution of differential equation (dy/dx)3 – 15x2 dy/dx – 2xy = 0, the value of B is __________, given that B ≠ 0.
(a) 2
(b) 4
(c) 6
(d) 8

Answer

A

Question.

MCQ Chapter 9 Differential Equations Class 12 Mathematics

Codes
A B C D E F
(a) 2 1 4 3 6 5
(b) 2 1 4 6 5 3
(c) 5 6 1 4 3 2
(d) 3 5 1 6 4 2

Answer

D

Question. Solution of the differential equation xdy – ydx = √x2+y2 dx is
(a) y = cx2
(b) y = cx2 + √x2 + y2
(c) y + √x2 + y2 = cx2
(d) y – √x2 – y2 = c

Answer

C

Question. The particular solution of log dy/dx = 3x + 4y, y(0) = 0 is
(a) e3x + 3e–4y = 4
(b) 4e3x – 3–4y = 3
(c) 3e3x + 4e4y = 7
(d) 4e3x + 3e–4y = 7 

Answer

D

Question. General solution of the differential equation dy/dx + y g’ (x) = g(x). g’ (x), where g(x) is a function of x is
(a) g(x) – log[1- y – g(x)] = C
(b) g(x) – log[1+ y – g(x)] = C
(c) g(x) +[1+ y – logg(x)] = C
(d) g(x) + log[1+ y – g(x)] = C

Answer

D

Question. The equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx (x ≠ 0) is
(a) x2 = y + log |x|
(b) y = x2 + log |x|
(c) y2 = x + log |x|
(d) y = x + log |x|

Answer

B

Question. The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis is
(a) y2y” – 2xy’ = 0
(b) y2 – 2xyy” = 0
(c) y2 – 2xyy’ = 0
(d) None of these

Answer

C

Question. The order and degree of the differential equation y = x dy/dx + √a2(dy/dx)2 + b2 is
(a) order = 1, degree = 2
(b) order = 2, degree = 1
(c) order = 2, degree = 2
(d) None of these

Answer

A

Question. The order of the differential equation whose general solution is given by
y = (C1 + C2) cos (x +C3) – C4ex+C5 where C1, C2, C3, C4, C5 are arbitrary constant, is
(a) 5
(b) 4
(c) 3
(d) 2

Answer

C

Question. If dx +dy = (x + y) (dx – dy), then log (x + y) is equal to
(a) x + y + C
(b) x + 2y + C
(c) x – y + C
(d) 2x + y + C

Answer

C

Question. A homogeneous differential equation of the dx/dy = h (x/y) can be solved by making the substitution
(a) y = vx
(b) v = yx
(c) x = vy
(d) x = v

Answer

C

Question. The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is
(a) d2y/dx2 + y = 0
(b) d2y/dx2 – y = 0
(c) d2y/dx2 = dy/dx + y
(d) dy/dx + y = 0

Answer

A

Question. The differential equation dy/dx = √1-y2/y 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

C

Question. The solution of differential equation

MCQ Chapter 9 Differential Equations Class 12 Mathematics

(a) ye2√x =2 √x + C
(b) ye √x = √x + C
(c) ye2√x =√y + C
(d) ye2√x =2√x + C

Answer

A

Question. The order and degree of the differential equation d4y/dx4 + sin (y”) = 0 are respectively
(a) 4 and 1
(b) 1 and 2
(c) 4 and 4
(d) 4 and not defined

Answer

D

Question. The differential equation which represent the family of curves y = aebx, where a and b are arbitrary constants.
(a) y’ = y2
(b) y” = y y’
(c) y y” = y’
(d) y y” = (y’)2

Answer

D

Question. The order of the differential equation of all tangent lines to the parabola y = x2, is
(a) 1
(b) 2
(c) 3
(d) 4

Answer

A

Question. The differential equations of all conics whose axes coincide with the co-ordinate axis is

MCQ Chapter 9 Differential Equations Class 12 Mathematics
Answer

C

Question. The solution of the equation dy/dx = 3x-4y- 2/3x-4y- 3 is
(a) (x – y2) + c = log (3x – 4y + 1)
(b) x – y + c = log (3x – 4y + 4)
(c) (x – y + c) = log (3x – 4y – 3)
(d) x – y + c = log (3x – 4y + 1)

Answer

D

Question. A differential equation of the form dy/dx = F(x, y) is said to be homogeneous, if F(x, y) is a homogeneous function of degree,
(a) 0
(b) 1
(c) 2
(d) 3

Answer

A

Question. If the I.F. of the differential equation dy/dx + 5y = cos x is ∫ eAdx , then A =
(a) 0
(b) 1
(c) 3
(d) 5

Answer

D

Question. If (1+ex/y) dx + (1-x/y)ex/y dy = 0 , then
(a) x – yex/y = c
(b) y – xex/y = c
(c) x + yex/y = c
(d) y + xex/y = c

Answer

C

Question. Solution of differential equation xdy – ydx = 0 represents:
(a) rectangular hyperbola.
(b) parabola whose vertex is at origin.
(c) circle whose centre is at origin.
(d) straight line passing through origin.

Answer

D

Question. Family y = Ax + A3 of curves will correspond to a differential equation of order
(a) 3
(b) 2
(c) 1
(d) not infinite

Answer

B

Question. The order and degree of the differential equation d2y/dx2 + (dy/dx)1/3 + x1/4 – 0 is
(a) order = 3, degree = 2
(b) order = 2, degree = 3
(c) order = 2, degree = 2
(d) order = 3, degree = 3

Answer

B

Question. If y = ex (sin x + cos x), then the value of d2y/dx2 – 2 dy/dx + 2y , is
(a) 0
(b) 1
(c) 2
(d) 3

Answer

A

Question. General solution of dy/dx + 2xy/1+x2 = 1/(1+x2)2 is
(a) y(1 + x2) = c + tan–1 x
(b) y/1+x2 + c tan-1 x
(c) y log (1 + x2) = c + tan–1 x
(d) y (1 + x2) = c + sin–1 x

Answer

A

Question. The solution of the differential equation dy/dx = ex–y + x2e–y is
(a) ex = y3/3 = ey + c
(b) ey = x2/3 + ex + c
(c) ey = x3/3 + ex + c
(d) None of these

Answer

C

Question. The solution of the differential equation

MCQ Chapter 9 Differential Equations Class 12 Mathematics

(a) y/4 + 1/x2 + y2 = c
(b) y/x – 1/x2+y2 = c
(c) x/y – 1/x2+y2 = c
(d) None of these

Answer

B

Question. In the particular solution of differential equation dy/dx = 1/x(3y2 – 1) , the value of constant term is ________, given that y = 2 when x = 1.
(a) 2
(b) 4
(c) 6
(d) 8

Answer

C

Question. The expression satisfying the differential equation (x2-1)dy/dx + 2xy = 1 is
(a) x2y – xy2 = c
(b) (y2 -1)x = y + c
(c) (x2 -1) y = x + c
(d) None of these

Answer

C

Question. Which of the following differential equation has y = x as one of its particular solution ?

MCQ Chapter 9 Differential Equations Class 12 Mathematics
Answer

C

Assertion and Reason type Questions :

(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.

Question. Assertion: The degree of the differential equation d2y/dx2 + 3(dy/dx)2 = x2 log (d2y/dx2) is not defined.
Reason : If the differential equation is a polynomial in terms of its derivatives, then its degree is defined.

Answer

A

Question. Assertion : The number of arbitrary constants in the solution of differential equation d2y/dx2 = 0 are 2.
Reason: The solution of a differential equation contains as many arbitrary constants as is the order of differential equation.

Answer

A

Question. Assertion : The degree of the differential equation d3y/dx3 + 2(d2y/dx2)3/2 + 2y = 0 is zero
Reason: The degree of a differential equation is not defined if it is not a polynomial eq in its derivatives.

Answer

D