JEE Questions for Maths Differential Equations Quiz 2 - MCQExams.com


Maths-Differential Equations-22648.png
  • parabola
  • hyperbola
  • circle
  • ellipse
The general solution of the differential equation (1 + y2)dx + (1 + x2) dy = 0 is
  • x - y = C (1 - xy)
  • x - y = C (1 + xy)
  • x + y = C (1 - xy)
  • x + y = C (1 + xy)
The solution of the differential equation (1 + y2) tan-1 x dx + y (1 + x2)dy = 0 is

  • Maths-Differential Equations-22651.png
  • log (1 + y+ (tan-1 x)2 = C
  • log(1 + x+ log (tan-1 y) + C
  • (tan-1 x) (1 + y+ C = 0

Maths-Differential Equations-22652.png

  • Maths-Differential Equations-22653.png
  • 2)
    Maths-Differential Equations-22654.png

  • Maths-Differential Equations-22655.png

  • Maths-Differential Equations-22656.png
Which of the following is correct solution of
Maths-Differential Equations-22657.png
  • x + yex/y = C
  • y + xex/y = C
  • x + y = Ce-x/y
  • y = x + Cex/y
The solution of the differential equation
Maths-Differential Equations-22658.png

  • Maths-Differential Equations-22659.png
  • 2)
    Maths-Differential Equations-22660.png

  • Maths-Differential Equations-22661.png

  • Maths-Differential Equations-22662.png

Maths-Differential Equations-22663.png
  • x
  • 1/x
  • logx
  • ex

Maths-Differential Equations-22664.png

  • Maths-Differential Equations-22665.png
  • 2)
    Maths-Differential Equations-22666.png

  • Maths-Differential Equations-22667.png

  • Maths-Differential Equations-22668.png
Which of the following is a correct solution of
Maths-Differential Equations-22670.png
  • y x sec y = C + tan x
  • yx cos y = C + tan x
  • yx secx = C + tan x
  • None of these

Maths-Differential Equations-22671.png
  • - (1/2)
  • e + 1/2
  • e - 1/2
  • 1/2
The solution of the differential equation
Maths-Differential Equations-22672.png

  • Maths-Differential Equations-22673.png
  • 2)
    Maths-Differential Equations-22674.png

  • Maths-Differential Equations-22675.png

  • Maths-Differential Equations-22676.png
The integrating factor of x dy/dx + (1 + x) y = x is
  • x
  • 2x
  • ex log x
  • x ex
Solution of the equation x2y - x3 dy/dx = y4 cos x, when y(= 1 is
  • y3 = 3x3 sin x
  • x3 = 3y3 sin x
  • x3 = y3 sin x
  • x3 = y3 cos x
The integrating factor of the differential equation (y log y)dx = (log y - x) dy is
  • 1/log y
  • log (log y)
  • 1 + log y
  • 1/log (log y)
  • log y
The integrating factor of the differential equation
Maths-Differential Equations-22677.png
  • ex
  • log x
  • log (logx)
  • x

Maths-Differential Equations-22678.png

  • Maths-Differential Equations-22679.png
  • 2)
    Maths-Differential Equations-22680.png

  • Maths-Differential Equations-22681.png

  • Maths-Differential Equations-22682.png
The solution of the differential equation
Maths-Differential Equations-22683.png

  • Maths-Differential Equations-22684.png
  • 2)
    Maths-Differential Equations-22685.png

  • Maths-Differential Equations-22686.png

  • Maths-Differential Equations-22687.png
If the integrating factor of the differential equation
Maths-Differential Equations-22688.png
  • x
  • x2/2
  • 1/x
  • 1/x2
  • 1/2x

Maths-Differential Equations-22689.png

  • Maths-Differential Equations-22690.png
  • 2)
    Maths-Differential Equations-22691.png

  • Maths-Differential Equations-22692.png
  • None of the above

Maths-Differential Equations-22693.png

  • Maths-Differential Equations-22694.png
  • 2)
    Maths-Differential Equations-22695.png

  • Maths-Differential Equations-22696.png

  • Maths-Differential Equations-22697.png
If y ' ' - 3 y ' + 2y = 0 where y(= 1, y '(= 0, then the value of y at x = log 2 is
  • 1
  • -1
  • 2
  • 0
The equation of the curve whose subnormal is equal to constant a is
  • y = ax + b
  • y2 = 2ax + b
  • ay2 - x3 = a
  • None of these

Maths-Differential Equations-22698.png

  • Maths-Differential Equations-22699.png
  • 2)
    Maths-Differential Equations-22700.png

  • Maths-Differential Equations-22701.png

  • Maths-Differential Equations-22702.png
If x dy = y (dx + y dy), y(= and y(x) > 0, then y(-is equal to
  • 3
  • 2
  • 1
  • 0
  • None of these
The solution of the differential equation y dx (x + x2y)dy = 0

  • Maths-Differential Equations-22703.png
  • 2)
    Maths-Differential Equations-22704.png

  • Maths-Differential Equations-22705.png

  • Maths-Differential Equations-22706.png

Maths-Differential Equations-22707.png

  • Maths-Differential Equations-22708.png
  • 2)
    Maths-Differential Equations-22709.png

  • Maths-Differential Equations-22710.png

  • Maths-Differential Equations-22711.png
The solution of x dy - y dx + x2 ex dx = 0 is

  • Maths-Differential Equations-22712.png
  • 2)
    Maths-Differential Equations-22713.png

  • Maths-Differential Equations-22714.png

  • Maths-Differential Equations-22715.png
The curve y = (cos x + y)1/2 satisfies the differential equation

  • Maths-Differential Equations-22716.png
  • 2)
    Maths-Differential Equations-22717.png

  • Maths-Differential Equations-22718.png

  • Maths-Differential Equations-22719.png
The differential equation of the family of parabolas with vertex at (0, -and having axis along Y - axis is
  • yy' + 2xy + 1 = 0
  • xy' + y + 1 = 0
  • xy' - 2y - 2 = 0
  • xy' - y - 1 = 0

Maths-Differential Equations-22722.png

  • Maths-Differential Equations-22723.png
  • 2)
    Maths-Differential Equations-22724.png

  • Maths-Differential Equations-22725.png

  • Maths-Differential Equations-22726.png

Maths-Differential Equations-22727.png
  • 3, 1
  • 1, 3
  • 1, 1
  • 3, 3
The family of curves y = ea sin x, where a is an arbitrary constant, is represented by the differential equation

  • Maths-Differential Equations-22729.png
  • 2)
    Maths-Differential Equations-22730.png

  • Maths-Differential Equations-22731.png

  • Maths-Differential Equations-22732.png

  • Maths-Differential Equations-22733.png
If x2 + y2 = 1, then
  • yy' ' - (2y ')2 + 1 = 0
  • yy' ' + (y ')2 + 1 = 0
  • yy' ' - ( y ')2 - 1 = 0
  • yy' ' + ( 2y ')2 + 1 = 0
The differential equation of the family y = aex + bxex + cx2 ex of curves, where a, b, c are arbitrary constants, is
  • y ' ' ' + 3 y ' ' + 3y ' + y = 0
  • y ' ' ' + 3 y ' ' - 3y ' - y = 0
  • y ' ' ' - 3 y ' ' - 3y ' + y = 0
  • y ' ' ' - 3 y ' ' + 3y ' - y = 0
The order of the differential equation of all tangent lines to the parabola y = x2 is
  • 1
  • 2
  • 3
  • 4
The differential equation of the family of circles with fixed radius 5 units and center on the line y = 2 is
  • (x - 2)2 y '2 = 25 - (y - 2)2
  • (x -y'2 = 25 - (y - 2)2
  • (y -y '2 = 25 - (y - 2)2
  • (y - 2)2 y '2 = 25 - (y - 2)2
The differential equation of all straight lines touching the circle x2 + y2 = a2 is

  • Maths-Differential Equations-22737.png
  • 2)
    Maths-Differential Equations-22738.png

  • Maths-Differential Equations-22739.png

  • Maths-Differential Equations-22740.png
The order of the differential equation whose general solution is given by y = (c1 + c2) cos (x +c3) - c4 ex+c5, where c1, c2, c3, c4, c5 are arbitrary constants, is
  • 4
  • 3
  • 2
  • 5
The differential equation representing the family of curves y = xecx (c is constant) is

  • Maths-Differential Equations-22741.png
  • 2)
    Maths-Differential Equations-22742.png

  • Maths-Differential Equations-22743.png

  • Maths-Differential Equations-22744.png

  • Maths-Differential Equations-22745.png
The order and degree of the differential equation
Maths-Differential Equations-22746.png
  • 3, 2
  • 3, 10
  • 2, 3
  • 3, 5
The differential equation of all circles which passes through the origin and whose centre lies on Y - axis, is

  • Maths-Differential Equations-22747.png
  • 2)
    Maths-Differential Equations-22748.png

  • Maths-Differential Equations-22749.png

  • Maths-Differential Equations-22750.png
y = 2e2x - e-x is a solution of the differential equation
  • y2 + y1 + 2y = 0
  • y2 - y1 + 2y = 0
  • y2 + y1 = 0
  • y2 - y1 - 2y = 0
The equation of family of a curve is y2 = 4a(x + a), then differential equation of the family is
  • y = y ' ' + x
  • y = y ' + x
  • y = 2 y ' x + y y'2
  • y ' ' + y ' + y2 = 0
The differential equation of the family of straight lines whose slope is equal to y - intercept, is

  • Maths-Differential Equations-22751.png
  • 2)
    Maths-Differential Equations-22752.png

  • Maths-Differential Equations-22753.png

  • Maths-Differential Equations-22754.png
The differential equation obtained by eliminating the arbitrary constants a and b from xy = aex + be-x is

  • Maths-Differential Equations-22756.png
  • 2)
    Maths-Differential Equations-22757.png

  • Maths-Differential Equations-22758.png

  • Maths-Differential Equations-22759.png
The differential equation whose solution Ax2 + By2 = 1, where A and B are arbitrary constant is of
  • first order and second degree
  • first order and first degree
  • second order and first degree
  • second order and second degree
The differential equation of the family of parabolas with focus as the origin and the axis as X - axis, is

  • Maths-Differential Equations-22760.png
  • 2)
    Maths-Differential Equations-22761.png

  • Maths-Differential Equations-22762.png

  • Maths-Differential Equations-22763.png
The order and degree of the differential equation
Maths-Differential Equations-22764.png
  • (1, 2)
  • (2, 2)
  • (1, 1)
  • (2, 1)
  • (0, 1)
The differential equation of system of concentric circles with centre (1,is

  • Maths-Differential Equations-22765.png
  • 2)
    Maths-Differential Equations-22766.png

  • Maths-Differential Equations-22767.png

  • Maths-Differential Equations-22768.png
The differential equation satisfied by the family of curves y = a x cos(1/x + b), where a, b parameters is
  • x2 y2 + y = 0
  • x4 y2 + y = 0
  • xy2 - y = 0
  • x4 y2 - y = 0
0:0:1


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