If f(x), g(x) and h(x) are three polynomials of degree 2 and 

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81.

The solution of the differential equation

1 + y2 + x - etan-1ydydx = 0, is

  • x - 2 = Ketan-1y

  • 2xetan-1y = e2tan-1y + K

  • xetan-1y = tan-1y +K

  • xe2tan-1y = etan-1y + K


82.

The solution of the differential equation dydx = yf'(x) - y2fx is

  • f(x) = y + C

  • f(x) = y(x + C)

  • f(x) = x + C

  • None of the above


83.

The general solution of the differential equation (1 + y2) dx + (1 + x)dy = 0 is

  • x - y = C(1 - xy)

  • x - y = C(1 + xy)

  • x + y = C(1 - xy)

  • x + y = C(1 + xy)


84.

The order and degree of the differential equation ρ = 1 + dydx232d2ydx2 are, respectively

  • 2, 2

  • 2, 3

  • 2, 1

  • None of these


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85.

The solution of the differential equation

dydx + 2yx1 +x2 = 11 +x22 is

  • y1 + x2 = C + tan-1x

  • y1 +x2 = C + tan-1x

  • y log1 + x2 = C + tan-1x

  • y(1 + x2) = C + sin-1x


86.

The order and degree of the differential equation 1 + 4dydx23 = 4d2ydx2 are respectively

  • 1, 23

  • 3, 2

  • 2, 3

  • 2, 23


87.

The solution of the differential equation dydx = 4x + y + 12, is

  • (4x + y + 1) = tan (2x + C)

  • (4x + y + 1)2 = 2 tan (2x + C)

  • (4x + y + 1)3 = 3 tan (2x + C)

  • (4x + y + 1) = 2 tan (2x + C)


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88.

If f(x), g(x) and h(x) are three polynomials of degree 2 and x = fxgxhxf'xg'xh'xf''xg''xh''x, then x is a polynomials of degree

  • 2

  • 3

  • 0

  • atmost 3


C.

0

Now, x = fxgxhxf'xg'xh'xf''xg''xh''x 'x = f'xg'xh'xf'xg'xh'xf''xg''xh''x + fxfxhxf''xg''xh''xf''xg''xh''x + fxgxhxf'xg'xh'xf'''xg'''xh'''x '(x) = 0 + 0 + 0 = 0  x = constantThus, x is the polynomial of degree zeroSince, f(x), g(x)and h(x)are the polynomials of degree 2, therefore

f'''(x) = g'''(x) = h'''(x) = 0

 


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89.

The degree of the differential equation of all curves having normal of constant length c is

  • 1

  • 3

  • 4

  • None of these


90.

ddxatan-1x + blogx - 1x + 1 = 1x4 - 1  a - 2b is equal to

  • 1

  • - 1

  • 0

  • 2


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