Differential Equations  MCQs

MCQs of Differential Equations

Showing 41 to 50 out of 145 Questions
41.
The equation of curve passing through (2, 1) and slope of tangent at (x, y) is x2+y22xy is
(a) 2x2-y2=3x
(b) 2x2-y2=6y
(c) xx2-y2=6
(d) xx2+y2=10
Answer:

Option (a)

42.
The solution of the equation d2ydx2=e-2x
(a) e-2x4
(b) e-2x4+cx+d
(c) 12e-2x+cx2+d
(d) 14e-4x+cx+d
Answer:

Option (b)

43.
The solution of the differential equation 1+y2+x-etan-1ydydx=0 is
(a) xe2tan-1y=etan-1y+k
(b) x-2=ke2tan-1y
(c) 2xetan-1y=e2tan-1y+k
(d) xetan-1y=etan-1y+k
Answer:

Option (c)

44.
If t+1dydx-ty=1 and y(0) = -1 then y(1) = _____
(a) loge2+12
(b) -12
(c) 54
(d) e-12
Answer:

Option (b)

45.
The differential equation representing the family of curves y2=2cx + c where c > 0, is a parameter, is of order and degree is follows :
(a) 1, 1
(b) 1, 2
(c) 2, 2
(d) 1, 3
Answer:

Option (d)

46.
The solution of the differential equation dydx=x+yx satisfying the condition y(1) = 1 is
(a) y=xlogx + x
(b) y=logx + x
(c) y=logx + x2
(d) y= xex-1
Answer:

Option (a)

47.
The differential equation of the family of circles with fixed radius 5 unit and centre on the line y = 2 is
(a) x-22dydx2=25-y-22
(b) x-22dydx2=25-y+22
(c) y-2dydx2=25-y-22
(d) y-22dydx2=25-y-22
Answer:

Option (d)

48.
The differential equation which represent the family of curves y=c1ec2xwhere c1 and c2 are arbitrary constants is
(a) y'=y2
(b) y''=y'y
(c) yy''=y'
(d) yy''=y'2
Answer:

Option (d)

49.
If a curve passes through the point 2, 72 and has slope 1-1x2 at any point (x, y) on it, then the ordinate of the point on the curve whose abscissa is -2 is :
(a) -32
(b) 32
(c) 52
(d) -52
Answer:

Option (a)

50.
The equation of the curve passing through the origin and satisfying the differential equation 1+x2dydx+2xy=4x2 is :
(a) 1+x2y=x3
(b) 31+x2y=2x3
(c) 1+x2y=3x3
(d) 31+x2y=4x3
Answer:

Option (d)

Showing 41 to 50 out of 145 Questions