CBSE Class 12 Mathematics Differentials Equation MCQs Set E

Question. The order of the differential equation whose solution is y = acosx + bsinx + ce^–x is
(a) 3
(b) 2
(c) 1
(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 ) − C₄e^{x + C5}
where C₁, C₂, C₃, C₄, C₅ are arbitrary constants, is
(a) 5
(b) 4
(c) 3
(d) 2

Answer: C

Question. The differential equation of all circles of radius a is of order
(a) 2
(b) 3
(c) 4
(d) none of these

Answer: A

Question. The differential equation of all parabolas whose axis of symmetry is along x-axis is of order
(a) 3
(b) 1
(c) 2
(d) none of these

Answer: C

Question. The degree of differential equation of all curves having normal of constant length c, is
(a) 1
(b) 3
(c) 4
(d) none of these

Answer: D

Question. The differential equation whose solution is y = Ae^3x + Be^–3x is given by
(a) y₂ – 3y₁ + 3y = 0
(b) xy₂ + 3y₁ – xy + x₂ + 3 = 0
(c) y₂ – 9y = 0
(d) (y₁)³ – 3y(xy₂ – 3y) = 0

Answer: C

Question. The differential equation satisfied by y = A/x + B is (A, B are parameters)
(a) x²y₁ = y
(b) xy₁ + 2y₂ = 0
(c) xy₂ + 2y₁ = 0
(d) none of these

Answer: C

Question. The differential equation which represent the family of curves y = ae^bx, where a and b are arbitrary constants, is
(a) y′ = y²
(b) y′′ = y y′
(c) y y′′ = y′
(d) y y′′ = (y′)²

Answer: D

Question. The differential equation having solution as y = 17e^x + ae^–x is
(a) y′′ – x = 0
(b) y′′ – y = 0
(c) y′ – y = 0
(d) y′ – x = 0.

Answer: B

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 order of the differential equation whose general solution is given by y = (A + B) cos (x + C) + De^x is
(a) 4
(b) 3
(c) 2
(d) 1

Answer: B

Question. The differential equation of all circles in the first quadrant which touch the coordinate axes is of order
(a) 1
(b) 2
(c) 3
(d) none of these

Answer: A

Question. The degree of the differential equation (d² y/dx²)^2/3 + 4 - 3 dy/dx = 0 is
(a) 2
(b) 1
(c) 3
(d) none of these

Answer: A

Question. The solution of the differential equation dy/dx = x² + y² + 1/2xy satisfying y(1) = 1, is
(a) a hyperbola
(b) a circle
(c) y² = x(1 + x) – 10
(d) (x – 2)² + (y – 3)² = 5xy

Answer: A

Question. Given the differential equation dy/dx = 6x²/2y + cos y ; y (1) = π Which of the following option is correct?
(a) Solution is y² – sin y = – 2x³ + C
(b) Solution is y² + sin y = 2x³ + C
(c) C = π + 2√2
(d) C = π² + 2

Answer: B

Question. For the differential equation x (dy/dx) + 2y  = xy (dy/dx)
(a) order is 1 and degree is 1
(b) solution is ln(yx²) = C – y
(c) order is 1 and degree is 2
(d) solution is ln(xy²) = C + y

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. If y′ = y + 1, y (0) = 1, then y (ln 2) =
(a) 1
(b) 2
(c) 3
(d) 4

Answer: C

Question. The general solution of the differential equation x(1 + y²) dx + y (1 + x²) dy = 0 is
(a) (1 + x²) (1 + y²) = 0
(b) (1 + x²) (1 + y²) = C
(c) (1 + x²) = C (1 + y²)
(d) (1 + y⁴) = C (1 + x²)

Answer: B

Question. If dy/dx = y sin 2x, y(0) = 1, then solution is
(a) y = e^sin2 x
(b) y = sin² x
(c) y = cos² x
(d) y = e^cos2 x

Answer: A

Question. The general solution of the differential equation dy/dx = x²/y² is
(a) x³ – y³ = c
(b) x³ + y³ = c
(c) x² + y² = c
(d) x² – y² = c

Answer: A

Question. The general solution of the differential equation dy/dx = y/x is
(a) y = k/x
(b) y = k log x
(c) y = k x
(d) log y = k x

Answer: C

Question. If dy/dx = x+y/x, y (1) = 1, then y =
(a) x + ln x
(b) x2 + x ln x
(c) xex – 1
(d) x + x ln x

Answer: D

Question. The order and degree respectively of the differential equation d²y/dx² + (dy/dx)^1/4 + x^1/5  0, are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3

Answer: A

Question. Integrating factor of xdy/dx − y = x⁴ − 3x is
(a) x
(b) log x
(c) 1x
(d) – x

Answer: C

Question. The number of solutions of dy/dx = y + 1/x - 1, when y(1) = 2 is
(a) none
(b) one
(c) two
(d) infinite

Answer: B

Question. 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

Question. Integrating factor of the differential equation dydx + y tan x − sec x = 0 is
(a) cos x
(b) sec x
(c) e^{cos x}
(d) e^{sec x}

Answer: B

Question. The solution of the differential equation dy/dx = 1 + y² / 1 + x² is
(a) y = tan^–1x
(b) y – x = k(1 + xy)
(c) x = tan^–1y
(d) tan (xy) = k

Answer: B

Question. The integrating factor of the differential equation dy/dx + y = 1 + y/x is
(a) x/e^x
(b) e^x/x
(c) xe^x
(d) e^x

Answer: B

Question. The solution of x (dy/dx) + y = e^x is
(a) y = e^x/x + k/x
(b) y = xe^x + cx
(c) y = xe^x + k
(d) x = e^y/y + k/y

Answer: A

Question. Differential equation having solution y = Ax + B³ is of order
(a) 3
(b) 2
(c) 1
(d) not defined

Answer: B

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

Answer: C

Question. Solution of dy/dx − 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

Question. Integrating factor of the differential equation (1− x²) dx/dx − xy = 1 is
(a) – x
(b) x/1+ x²
(c) √1 − x²
(d) 1/2 log(1− x²)

Answer: C