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Quantitative Aptitude Practice Calculus Study Material

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Differential Equations

The equation of parabola having the vertex at origin and the axis along the positive y-axis is:

a) X^2 = 4ay
b) X^2 = 4ay^2
c) Y^2 = 4ax
d) Y^2 = 4ax^2

✔Answer

Correct Answer Is : X^2 = 4ay

Solution Is :

True or false:the differential equation has y=x as one of its partial solution (d^2y/dx^2 -x^2 dy/dx + xy =x).

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : FALSE

Solution Is :

Evaluate : dy/dx = (1 - cos x)/(1 + cos x)

a) Y = 2tan (x/2)
b) Y = 2tan (x/2) - x
c) Y = 2tan (x/2) + x
d) Y = 2tan (x/2) - x + c

✔Answer

Correct Answer Is : Y = 2tan (x/2) - x + c

Solution Is :

Evaluate: dy/dx = (1 + x^2)(1 + y^2)

a) Tan ^-1 y = x + c
b) Tan ^-1 y = x + (x/y)+ c
c) Tan ^-1 y = (x^3/3)+ c
d) Tan ^-1 y = x + (x^3/3)+ c

✔Answer

Correct Answer Is : Tan ^-1 y = x + (x^3/3)+ c

Solution Is :

Evaluate : ylog y dx - xdy = 0

a) Y = e
b) Y = e^x
c) Y = e^cx
d) None of these

✔Answer

Correct Answer Is : Y = e^cx

Solution Is :

Evaluate: cos(dy/dx) = a(a Є R); y = 1 when x = 0.

a) Cos(y - 1) = a
b) Cos(y - 1/x) = a
c) Cos(y + 1/x) = a
d) Cos(y + 1) = a

✔Answer

Correct Answer Is : Cos(y - 1/x) = a

Solution Is :

Find the equation of a curve passing through the point (0 , 0) and whose differential equation is y` = e^ sin x.

a) 2y - 1 = e^x (sin x - cos x)
b) 2y - 1 = e^x (sin x + cos x)
c) 2y - 1 = e^x
d) 2y + 1 = e^x (sin x - cos x)

✔Answer

Correct Answer Is : 2y - 1 = e^x (sin x - cos x)

Solution Is :

The slope of a tangent to the curve in the coordinate axis is given by the relation:

a) Xy
b) Dy/dx
c) Dy*dx
d) X/y

✔Answer

Correct Answer Is : Dy/dx

Solution Is :

Evaluate: y` = (x + y/x)

a) Y = xlog x
b) Y = xlog x + Cx
c) Y = log x + Cx
d) Y = x + Cx

✔Answer

Correct Answer Is : Y = xlog x + Cx

Solution Is :

True or false: the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin xyy" + x(y`)^2 - yy` = 0.

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : TRUE

Solution Is :

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Quantitative Aptitude Practice Calculus Study Material

Differential Equations

The equation of parabola having the vertex at origin and the axis along the positive y-axis is:

Correct Answer Is : X^2 = 4ay

Solution Is :

True or false:the differential equation has y=x as one of its partial solution (d^2y/dx^2 -x^2 dy/dx + xy =x).

Correct Answer Is : FALSE

Solution Is :

Evaluate : dy/dx = (1 - cos x)/(1 + cos x)

Correct Answer Is : Y = 2tan (x/2) - x + c

Solution Is :

Evaluate: dy/dx = (1 + x^2)(1 + y^2)

Correct Answer Is : Tan ^-1 y = x + (x^3/3)+ c

Solution Is :

Evaluate : ylog y dx - xdy = 0

Correct Answer Is : Y = e^cx

Solution Is :

Evaluate: cos(dy/dx) = a(a Є R); y = 1 when x = 0.

Correct Answer Is : Cos(y - 1/x) = a

Solution Is :

Find the equation of a curve passing through the point (0 , 0) and whose differential equation is y` = e^ sin x.

Correct Answer Is : 2y - 1 = e^x (sin x - cos x)

Solution Is :

The slope of a tangent to the curve in the coordinate axis is given by the relation:

Correct Answer Is : Dy/dx

Solution Is :

Evaluate: y` = (x + y/x)

Correct Answer Is : Y = xlog x + Cx

Solution Is :

True or false: the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin xyy" + x(y`)^2 - yy` = 0.

Correct Answer Is : TRUE

Solution Is :

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