The solution of the differential equation 1 + y2&n

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

71.

If x3e5xdx = e5x54fx + C,then fx = ?

  • x35 - 3x252 + 6x53 - 654

  • 5x3 - 52x2 + 53x - 6

  • 53x3 - 15x2 + 30x - 6

  • 53x3 - 75x2 + 30x - 6


72.

xx2 + 2x + 22dx = ?

  • x2 + 2x2 +2x + 2 - 12tan-1x - 1 + C

  • x2 - 24x2 + 2x +2 - 12tan-1x +1 +C

  • x2 + 22x2 + 2x +2 - 12tan-1x +1 +C

  • 2x - 1x2 +2x +2 + 12tan-1x +1 +C


73.

If loga2 + x2dx = hx + C, then hx = ?

  • xloga2 +x2 + 2tan-1xa

  • x2loga2 +x2 +x +atan-1xa

  • xloga2 + x2 - 2x + 2atan-1xa

  • x2loga2 +x2 + 2x - a2tan-1xa


74.

For x > 0, if logx5dx = ?xAlogx5 + Blogx4+Clogx3 + Dlogx2 +Elogx + F + Constant, thenA +B +C +D+E+ F = ?

  • - 44

  • - 42

  • - 40

  • - 36


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75.

By the definition of the definite integral, the value of limn1n2 - 1 + 1n2 - 22 + ... 1n2 - n - 12 is equal to

  • π

  • π2

  • π4

  • π6


76.

π4π4x + π42 - cos2xdx is equal to

  • 8π35

  • 2π39

  • 4π239

  • π263


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77.

The solution of the differential equation 1 + y2 + x - etan-1ydydx = 0, is

  • xetan-1y = tan-1y + C

  • xe2tan-1y = tan-1y + C

  • 2xetan-1y = e2tan-1y + C

  • x2etan-1y = 4e2tan-1y + C


C.

2xetan-1y = e2tan-1y + C

We have,1 + y2 + x - etan-1ydydx = 0dydx + x1 + y2 = etan-1y1 + y2This equation is form of linear differential equationdxdy  Px = Qwhere, P = 11 + y2, Q = etan-1y1 + y2Now, IF = ePdy = e11 + y2dy = etan-1y Solution of differential equation isx . IF = Q . IFdy + C  xetan-1y = etan-1y1 + y2dy + C  xetan-1y = e2tan-1y2 + C     xetan-1y = e2tan-1y2 + C   2xetan-1y = e2tan-1y + C


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78.

The solution of the differential equation 2x - 4y + 3dydx + x - 2y + 1 = 0 is

  • log2x - 4y + 3 = x - 2y + C

  • log22x - 4y + 3 = 2x - 2y+ C

  • log2x - 2y + 5 = 2x + y + C

  • log4x - 2y + 5 = 4x + 2y + C


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79.

The mid-point of the line segment joining the centroid and the orthocentre of the triangle whose vertices are (a, b),(a, c) and (d, c), is

  • 5a +d6, b + 5c6

  • `a + 5d6, 5b + c6

  • (a, 0)

  • (0, 0)


80.

The orthocentre of the triangle formed by the lines x + y = 1 and 2y2 - xy - 6x2 = 0

  • 43, 43

  • 23, 23

  • 23, - 23

  • 43,  - 43


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