NCERT Class 12 Math Differential Equation Chapter 9 MCQ Question Answer for Preparation of Exams. Here we Provide Class 12 Math Question Answer, Important Questions, MCQ for Various State Boards Students like CBSE, Haryana, uttar pradesh, mp and other state students.

**Also Read : – Class 12 Math NCERT Solution**

NCERT Class 12 Math Chapter 9 Differential Equation MCQ Question Answer Solution.

**Differential Equation Class 12 Math Chapter 9 MCQ Question Answer**

**Multiple Choice Questions and Answer for Easy to Understand the Chapter.**

**1. Which of the following differential equation has y = c _{1}e^{x} + c_{2}e^{-x }as the general solution ?**

(A) (d

^{2}y/dx

^{2})+y = 0

(B) (d

^{2}y/dx

^{2}) – y = 0

(C)(d

^{2}y/dx

^{2}) + 1 = 0

(D) (d

^{2}y/dx

^{2}) – 1 = 0

**Answer**

**Ans. (B) (d ^{2}y/dx^{2}) – y = 0**

**2. Which of the following differential equations has y = x as one of its particular solution?**

(A) (d^{2}y/dx^{2}) – x^{2}(dy/dx) + xy = x

(B) (d^{2}y/dx^{2}) + x(dy/dx) + xy = x

(C) (d^{2}y/dx^{2}) – x^{2}(dy/dx) + xy = 0

(D) (d^{2}y/dx^{2}) + x^{2}(dy/dx) + xy = 0

**Answer**

**Ans. (C) (d ^{2}y/dx^{2}) – x^{2}(dy/dx) + xy = 0**

**3. The general solution of the differential equation (dy/dx) = e ^{x+y} is**

(A) e

^{x }+e

^{-y}= C

(B) e

^{x }+e

^{y}= C

(C) e

^{–}

^{x }+e

^{y}= C

(D) e

^{–}

^{x }+e

^{-y}= C

**Answer**

**Ans. (A) e ^{x }+e^{-y} = C**

**4. A homogenous differential equation of the from (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**

**Ans. (C) x = vy**

**5. Which of the following is a homogeneous differential equation ?**

(A) (4x + 6y + 5)dy – (3y + 2x + 4)dx = 0

(B) (xy)dx – (x^{3} + y^{3})dy = 0

(C) (x^{3 }+ 2y^{2})dx + 2xydy = 0

(D) y^{2}dx + (x^{2} -xy -y^{2})dy = 0

**Answer**

**Ans. (D) y ^{2}dx + (x^{2} -xy -y^{2})dy = 0**

**6. The integrating factor of the differential equation x(dy/dx) – y = 2x ^{2 }is**

(A) e

^{–}

^{x }

(B) e

^{-y}

(C) 1/x

(D) x

**Answer**

**Ans. (C) 1/x**

**7. The Integrating factor of the differential equation (1 – y ^{2})dx/dy + yx = ay where (-1<y<1) is**

(A) 1/(y

^{2 }– 1)

(B) 1/√(y

^{2}– 1)

(C) 1/(1 – y

^{2})

(D) 1/√(1 – y

^{2})

**Answer**

**Ans. (D) 1/√(1 – y ^{2})**

**8. The number of arbitrary constants in the general solution of a differential equation of fourth order are:**

(A) 0

(B) 2

(C) 3

(D) 4

**Answer**

**Ans. (D) 4**

**9. The number of arbitrary in the particular solution of a differential equation of third order are:**

(A) 3

(B) 2

(C) 1

(D) 0

**Answer**

**Ans. (D) 0**

**10. The degree of the differential equation (d ^{2}y/dx^{2})^{3 }+ (dy/dx)^{2} + sin(dy/dx) + 1 = 0**

(A) 3

(B) 2

(C) 1

(D) not defined

**Answer**

**Ans. (D) not defined**

**11. The order of the differential equation 2x ^{2}(d^{2}y/dx^{2}) – 3(dy/dx) + y = 0**

(A) 2

(B) 1

(C) 0

(D) not defined

**Answer**

**Ans. (A) 2**

**12. The general solution of the differential equation e ^{x}dy + (ye^{x} + 2x)dx = 0 is**

(A) xe

^{y}+ x

^{2}= C

(B) xe

^{y }+ y

^{2 }= C

(C) ye

^{x}+ x

^{2}= C

(D) ye

^{y}+ x

^{2}= C

**Answer**

**Ans. (C) ye ^{x} + x^{2} = C**