Maths MCQs for Class 12 with Answers Chapter 9 Differential Equations
Differential Equations Class 12 Maths MCQs Pdf
1. Order of differential equation correspon- ding to family of curves y = Ae2x + Be2x is ______ .
Answer/Explanation
Answer:
Explaination: 2, as there are two arbitrary constants and we have to differentiate twice.
2. The order of the differential equation corresponding to the family of curves y = c(x – c)², c is constant is ______ .
Answer/Explanation
Answer:
Explaination: One, as there is one arbitrary constant.
3. The degree of differential equation
is not defined. State true or false.
Answer/Explanation
Answer:
Explaination: Three, as equation cannot be represented as polynomial of derivatives.
4. If p and q are the degree and order of the differential equation
then the value of 2p – 3q is
(a) 7
(b) -7
(c) 3
(d) -3
Answer/Explanation
Answer: b
Explaination:
(b), as degree p = 1 and order q = 3
∴ 2p – 3q = 2 – 9 = -7
5. The degree of the differential equation
(a) 1
(b) 2
(c) 3
(d) 4
Answer/Explanation
Answer: c
Explaination:
(c), as differential equation is
Exponent of highest order derivative is 3.
6. The degree of the differential equation
(a) 1
(b) 2
(c) 3
(d) not defined
Answer/Explanation
Answer: d
Explaination:
(d), as equation cannot be represented as a polynomial of derivatives.
7. The order of the differential equation of all the circles of given radius 4 is
(a) 1
(b)2
(c) 3
(d) 4
Answer/Explanation
Answer: b
Explaination:
(b), as centre is arbitrary (h, k), two arbitrary constants so we have to differentiate twice to eliminate h, k
∴ order is 2.
8. Degree of the differential equation
is not defined. State true or false.
Answer/Explanation
Answer:
Explaination:
False, as equation can be written as
Further it can be written as a polynomial of derivatives. 9.
9. Write the degree of the differential equation
Answer/Explanation
Answer:
Explaination: Degree 1
10. Write the degree of the differential equation
Answer/Explanation
Answer:
Explaination: Degree 3.
11. Find the value of m and n, where m and n are order and degree of differential equation
Answer/Explanation
Answer:
Explaination:
Order of differential equation (m) = 3
Degree of differential equation (n) = 2
12. Write the order and degree of the differential equation \(\frac{d y}{d x}+\sin \left(\frac{d y}{d x}\right)\) = 0. [HOTS] Answer:Answer/Explanation
Explaination:
Highest order derivative is \(\frac{dy}{dx}\). Hence, order of differential equation is 1. Equation cannot be written as a polynomial’ in derivatives. Hence, degree is not defined.
13. The differential equation of the family of lines passing through ongrn is
(a) y = mx
(b) \(\frac{dy}{dx}\) = m
(c) x dy – y dx = 0
(d) \(\frac{dy}{dx}\) = 0
Answer/Explanation
Answer: c
Explaination:
(c), as general equation of line through origin is
y = mx
⇒ \(\frac{dy}{dx}\) = m
Substituting in (i), we get dy
y = \(\frac{dy}{dx}\).x
⇒ x dy – y dx = 0
14. Find the differential equation representing the family of curves y = aebx + 5, where a and b are arbitrary constants. [CBSE 2018] Answer:Answer/Explanation
Explaination:
Consider y = aebx + 5
.On differentiating both sides, w.r.t, x
\(\frac{dy}{dx}\) = abebx + 5 = by …..(i)
Again differentiating w.r.t. x, we get
\(\frac{d^{2} y}{d x^{2}}=b \cdot \frac{d y}{d x}\) …..(ii)
From (i) and (ii), eliminating b, we get
\(y \cdot \frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}\) as required equation.
15. Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of the x-axis. [NCERT; DoE] Answer:Answer/Explanation
Explaination:
General equation of parabola is y² = 4ax …..(i)
Differentiating, we get 2yy’ = 4a
⇒ yy’ = 2a.
Substituting in (i), we gety2 = 2xyy’.
16. Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y-axis. [Delhi 2011] Answer:Answer/Explanation
Explaination:
x² = 4 ay
⇒ 2x = 4 ay’
⇒ \(\frac{x^{2}}{2 x}=\frac{4 a y}{4 a y^{\prime}}\)
⇒ xy’ – 2y = 0 is the required equation.
17. General solution of the differential equation log\(\frac{dy}{dx}\) = 2x +y is _______ .
Answer/Explanation
Answer:
Explaination:
18. Solve the differential equation \(\frac{dy}{dx}\) = ex – y + x3e-y.
Answer/Explanation
Answer:
Explaination:
19. Find the particular solution of the differential equation \(\frac{dy}{dx}\) =y tanx, given that y= 1 when x = 0.
Answer/Explanation
Answer:
Explaination:
∫ \(\frac{dy}{y}\) = ∫tan x dx
⇒ log |y| = log|sec x| + log C
⇒ y = C sec x ….(i)
Given y = 1, x = 0
⇒ 1 = C sec 0
⇒ C = 1
∴ solution is y = sec x [from (i)]
20. Find the general solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{x+1}{2-y}\), (y ≠ 2). [NCERT] Answer:Answer/Explanation
Explaination:
