NCERT MCQ CLASS-12 CHAPTER-9 | MATH NCERT MCQ | DIFFERENTIAL EQUATIONS | EDUGROWN

In This Post we are  providing Chapter-9 Differential Equations NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON DIFFERENTIAL EQUATIONS

Question 1.
Integration factor of differential equation dydx + py = Q, where P and IQ are functions of x is
(a) ∫e^pdx
(b) e∫pdx
(c) e-∫pdx
(d) None of these

Answer: (d) None of these

Question 2.
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 3.
The solution of dydx = 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: (b) log (1 + y) = x + x22 + k

Question 4.
The degree of the differential equation
(d2ydx)² + (dydx)² = x sin dydx is
(a) 1
(b) 2
(c) 3
(d) not defined

Answer: (d) not defined

Question 5.
The degree of differential equation
[1 + (dydx)²]³² = d2ydx2 is
(a) 4
(b) 32
(c) 2
(d) not defined

Answer: (c) 2

Question 6.
The order and degree of the differential equation
d2ydx2 + (dydx)¹⁴ + x¹³ = 0 respectively, are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3Answer

Answer: (a) 2 and not defined

Question 7.
If y = e^-x (A cos x + B sin x), then y is a solution of
(a) d2ydx2 + 2dydx = 0
(b) d2ydx2 – 2dydx + 2y = 0
(c) d2ydx2 + 2dydx + 2y = 0
(d) d2ydx2 + 2y = 0

Answer: (c) d2ydx2 + 2dydx + 2y = 0

Question 8.
The differential equation for y = A cos αx + B sin αx where A and B are arbitrary constants is
(a) d2ydx2 – α²y = 0
(b) d2ydx2 + α²y = 0
(c) d2ydx2 + αy = 0
(d) d2ydx2 – αy = 0

Answer: (b) d2ydx2 + α²y = 0

Question 9.
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 center is at origin

Answer: (c) straight line passing through origin

Question 10.
Integrating factor of the differential equation cos x dydx + y sin x = 1 is
(a) cos x
(b) tan x
(c) sec x
(d) sin x

Answer: (c) sec x

Question 11.
Solution of the differential equation tan y sec² x dx + tan x sec² y dy + 0 is .
(a) tan x + tan y = k
(b) tan x – tan y = k
(c) tan x*tan y = k
(d) tan x.tan y = k

Answer: (d) tan x.tan y = k

Question 12.
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 13.
Integrating factor of xdydx – y = x⁴ – 3x is
(a) x
(b) log x
(c) 12
(d) -x

Answer: (c) 12

Question 14.
Solution of dydx – y = 1 y(0) = 1 is given by
(a) xy = -e^x
(b) xy = -e^-x
(c) xy = -1
(d) y = 2e^x – 1

Answer: (d) y = 2e^x – 1

Question 15.
The number of solutions of dydx = y+1x−1 when y(1) = 2 is
(a) none
(b) one
(c) two
(d) infinite

Answer: (b) one