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JEE Questions for Maths Differential Equations Quiz 2 - MCQExams.com
JEE
Maths
Differential Equations
Quiz 2
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parabola
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hyperbola
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circle
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ellipse
The general solution of the differential equation (1 + y
2
)d
x
+ (1 +
x
2
) dy = 0 is
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x - y = C (1 - xy)
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x - y = C (1 + xy)
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x + y = C (1 - xy)
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x + y = C (1 + xy)
The solution of the differential equation (1 + y
2
) tan
-1
x
d
x
+ y (1 +
x
2
)dy = 0 is
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log (1 + y+ (tan-1 x)2 = C
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log(1 + x+ log (tan-1 y) + C
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(tan-1 x) (1 + y+ C = 0
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2)
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Which of the following is correct solution of
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x + yex/y = C
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y + xex/y = C
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x + y = Ce-x/y
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y = x + Cex/y
The solution of the differential equation
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2)
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x
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1/x
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logx
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ex
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2)
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Which of the following is a correct solution of
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y x sec y = C + tan x
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yx cos y = C + tan x
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yx secx = C + tan x
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None of these
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- (1/2)
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e + 1/2
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e - 1/2
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1/2
The solution of the differential equation
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2)
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The integrating factor of
x
dy/d
x
+ (1 +
x
) y =
x
is
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x
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2x
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ex log x
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x ex
Solution of the equation
x
2
y -
x
3
dy/d
x
= y
4
cos
x
, when y(= 1 is
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y3 = 3x3 sin x
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x3 = 3y3 sin x
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x3 = y3 sin x
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x3 = y3 cos x
The integrating factor of the differential equation (y log y)d
x
= (log y -
x
) dy is
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1/log y
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log (log y)
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1 + log y
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1/log (log y)
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log y
The integrating factor of the differential equation
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ex
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log x
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log (logx)
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x
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The solution of the differential equation
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2)
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If the integrating factor of the differential equation
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x
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x2/2
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1/x
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1/x2
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1/2x
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2)
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None of the above
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2)
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If y ' ' - 3 y ' + 2y = 0 where y(= 1, y '(= 0, then the value of y at
x
= log 2 is
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1
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-1
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2
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0
The equation of the curve whose subnormal is equal to constant a is
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y = ax + b
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y2 = 2ax + b
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ay2 - x3 = a
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None of these
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2)
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If
x
dy = y (d
x
+ y dy), y(= and y(
x
) > 0, then y(-is equal to
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3
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2
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1
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0
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None of these
The solution of the differential equation y d
x
(
x
+
x
2
y)dy = 0
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2)
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0%
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2)
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The solution of
x
dy - y d
x
+
x
2
e
x
d
x
= 0 is
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2)
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The curve y = (cos
x
+ y)
1/2
satisfies the differential equation
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2)
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The differential equation of the family of parabolas with vertex at (0, -and having axis along Y - axis is
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yy' + 2xy + 1 = 0
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xy' + y + 1 = 0
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xy' - 2y - 2 = 0
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xy' - y - 1 = 0
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2)
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0%
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3, 1
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1, 3
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1, 1
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3, 3
The family of curves y = e
a sin
x
, where a is an arbitrary constant, is represented by the differential equation
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2)
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If
x
2
+ y
2
= 1, then
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yy' ' - (2y ')2 + 1 = 0
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yy' ' + (y ')2 + 1 = 0
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yy' ' - ( y ')2 - 1 = 0
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yy' ' + ( 2y ')2 + 1 = 0
The differential equation of the family y = ae
x
+ b
x
e
x
+ c
x
2
e
x
of curves, where a, b, c are arbitrary constants, is
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y ' ' ' + 3 y ' ' + 3y ' + y = 0
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y ' ' ' + 3 y ' ' - 3y ' - y = 0
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y ' ' ' - 3 y ' ' - 3y ' + y = 0
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y ' ' ' - 3 y ' ' + 3y ' - y = 0
The order of the differential equation of all tangent lines to the parabola y =
x
2
is
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1
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2
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3
0%
4
The differential equation of the family of circles with fixed radius 5 units and center on the line y = 2 is
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(x - 2)2 y '2 = 25 - (y - 2)2
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(x -y'2 = 25 - (y - 2)2
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(y -y '2 = 25 - (y - 2)2
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(y - 2)2 y '2 = 25 - (y - 2)2
The differential equation of all straight lines touching the circle
x
2
+ y
2
= a
2
is
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2)
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The order of the differential equation whose general solution is given by y = (c
1
+ c
2
) cos (
x
+c
3
) - c
4
e
x
+c
5
, where c
1
, c
2
, c
3
, c
4
, c
5
are arbitrary constants, is
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4
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3
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2
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5
The differential equation representing the family of curves y =
x
e
c
x
(c is constant) is
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2)
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The order and degree of the differential equation
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3, 2
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3, 10
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2, 3
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3, 5
The differential equation of all circles which passes through the origin and whose centre lies on Y - axis, is
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2)
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y = 2e
2
x
- e
-
x
is a solution of the differential equation
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y2 + y1 + 2y = 0
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y2 - y1 + 2y = 0
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y2 + y1 = 0
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y2 - y1 - 2y = 0
The equation of family of a curve is y
2
= 4a(
x
+ a), then differential equation of the family is
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y = y ' ' + x
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y = y ' + x
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y = 2 y ' x + y y'2
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y ' ' + y ' + y2 = 0
The differential equation of the family of straight lines whose slope is equal to y - intercept, is
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2)
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The differential equation obtained by eliminating the arbitrary constants a and b from
x
y = ae
x
+ be
-
x
is
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2)
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The differential equation whose solution A
x
2
+ By
2
= 1, where A and B are arbitrary constant is of
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first order and second degree
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first order and first degree
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second order and first degree
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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
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2)
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The order and degree of the differential equation
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(1, 2)
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(2, 2)
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(1, 1)
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(2, 1)
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(0, 1)
The differential equation of system of concentric circles with centre (1,is
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2)
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The differential equation satisfied by the family of curves y = a
x
cos(1/
x
+ b), where a, b parameters is
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x2 y2 + y = 0
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x4 y2 + y = 0
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xy2 - y = 0
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x4 y2 - y = 0
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