The solution of xdydx = y + ey

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

71.

The differential equation of the family of parabolas with vertex at (0, - 1) and having axis along the Y-axis is

  • yy' + 2xy + 1 = 0

  • xy' + y + 1 = 0

  • xy' - 2y - 2

  • xy' - y - 1 = 0


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72.

The solution of xdydx = y + eyx with y1 = 0 is

  • 1 = logx + e yx

  • logx = e - yx

  • 1 = 2logx + e - yx

  • logx + e - yx = 1


D.

logx + e - yx = 1

Given differential eq isxdydx = y + xeyxdydx = yx + eyxIt is a homogeneous differential equation Put y = vx  dydx = v +xdvdx v +xdvdx = vxx + evxx v +xdvdx = v + evxdvdx = ev e - vdv = 1xdxOn integrating both sides, we get- e - v = logx +c- e - yx = logx +cGiven, y1 = 0  e - 01 = log1 +c- 1 = 0 +c  c = - 1  - e - yx = logx - 11 = logx + e - yx


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73.

The solution of cos(y) + (xsin(y) - 1)dy/dx = 0 is, 

  • xsecy = tany + C

  • tany - secy = Cx

  • tany + secy = Cx

  • xsecy + tany = C


74.

Three non-zero non-collinear vectors a^, b^ and c^ are such that a^ + 3b^ is collinear with c^, while c^ is 3b^ + 2c^ collinear with a. Then a^ + 3b^ + 2c^ equals

  • 0

  • 2a^

  • 3b^

  • 4c^


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75.

If a^, b^ and c^ are non-coplanar vectors and if d^ is such that d^ = 1xa^ + b^ + c^ and d^ = 1yb^ + c^ + d^ where x and y are non-zero real numbers, then 1xya^ + b^ + c^ + d^ equals to

  • 3c

  • - a

  • 0

  • 2a


76.

The angle between the lines r^ = 2i^ - 3j^ + k^ + λi^ + 4j^ + 3k^ and r^ = i^ - j^ + 2k^ + μi^ + 2j^ - 3k^ is

  • π2

  • cos-1991

  • cos-1784

  • π3


77.

If a, b and c are vectors with magnitudes 2, 3 and 4 respectively, then the best upper bound of a^ - b^2 + b^ - c^2 + c^ - a^2 among the given values is

  • 93

  • 97

  • 87

  • 90


78.

If x, y and z are non-zero real numbers and a^ = xi^ + 2j^b^ = yj^ + 3k^ and c^ = xi^ + yj^ + zk^ are such that a^ × b^ = zi^ - 3j^ + k^, then a^ b^ c^ equals to

  • 3

  • 10

  • 9

  • 6


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79.

If x is real, then the minimum value of y = x2 - x + 1x2 + x + 1 is

  • 3

  • 13

  • 12

  • 2


80.

The locus of the centroid of the triangle with vertices at (acos(θ), asin(θ)), (bsin(θ), - bcos(θ)) and (1, 0) is (here, θ is a parameter)

  • 3x + 12 + 9y2 = a2 + b2

  • 3x - 12 + 9y2 = a2 - b2

  • 3x - 12 + 9y2 = a2 + b2

  • 3x + 12 + 9y2 = a2 - b2


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