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JEE Questions for Maths Differential Equations Quiz 1 - MCQExams.com
JEE
Maths
Differential Equations
Quiz 1
The solution of the differential equation dy/d
x
= sin (
x
+ y) tan (
x
+ y) - 1 is
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cosec (x + y) + tan (x + y) = x + C
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x + cosec (x + y) = C
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x + tan (x + y) = C
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x + sec (x + y) = C
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xsec y = tan y + C
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tan y - sec y = Cx
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tan y + sec y = Cx
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x sec y + tan y = C
The form of the differential equation of the central conics a
x
2
+ by
2
= 1 is
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0%
0%
2)
0%
0%
None of these
The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is
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0%
2)
0%
0%
The order and degree of the differential equation
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1, 2
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1, 3
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2, 1
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1, 1
The order and degree of differential equation
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2, 10
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3, 10
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3, 5
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3, 4
The differential equation of system of circles touching the Y - axis at origin is
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2)
0%
0%
0%
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2
0%
3
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1
0%
0
The degree of the differential equation satisfying
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1
0%
3
0%
2
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None of these
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4
0%
2
0%
3
0%
1
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r
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1/r
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1
0%
0
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0
0%
-1
0%
-2
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1
0%
2
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2y
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y2
0%
y3
0%
y4
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2
0%
3
0%
4
0%
5/2
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3
0%
2
0%
1
0%
not defined
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2, 3
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3, 2
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2, 4
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2, 2
From the differential equation of all family of lines y = m
x
+ 4/m by eliminating the arbitrary constant m.
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0%
2)
0%
0%
The order and degree of the differential equation
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(2, 4)
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(2, 3)
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(6, 4)
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(6, 9)
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(2, 12)
The differential equation representing the family of curves y
2
= 2c(
x
+ c
2/3
), where c is a positive parameter is of
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order 3, degree 3
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order 2, degree 4
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order 1, degree 5
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order 5, degree 1
The degree of the equation
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2
0%
0
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degree is not defined
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1
y = c
x
-
x
2
is the general solution of the differential equation
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(y ')2 - xy' + y = 0
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y ' ' = 0
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y ' = c
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(y ')2 + xy' + y = 0
The differential equation of all non - vertical lines in a plane is
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0%
0%
2)
0%
0%
The order and degree of the differential equation
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1 and 1/2
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2 and 1
0%
1 and 1
0%
1 and 2
The differential equation of coaxial parabola y
2
= 4a(
x
- b), where a and b are arbitrary constants, is
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0%
0%
2)
0%
0%
The differential equation of the family of circles passing through the fixed points (a,and (-a,is
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y1 (y2 - x+ 2xy + a2 = 0
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y1 y2 + xy + a2 x2 = 0
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y1 (y2 - x2 + a+ 2xy = 0
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y1(y2 + x- 2xy + a2 = 0
The differential equation of the family of curves y = e
2
x
(a cos
x
+ b sin
x
), where a and b are arbitrary constants, is given by
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y2 - 4y1 + 5y = 0
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2y2 - y1 + 5y = 0
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y2 + 4y1 - 5y = 0
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y2 - 2y1 + 5y = 0
The order and degree of the differential equation
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(2, 5)
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(3, 2)
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(1, 3)
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(2, 3)
The differential equation of all circles passing through the origin and having their centers on x - axis is
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0%
0%
2)
0%
0%
The differential equation of the systems of all circles of radius r in the XY - plane is
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0%
0%
2)
0%
0%
The order of the differential equation whose solution is y = a cos
x
+ b sin
x
+ ce
-
x
, is
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0%
3
0%
1
0%
2
0%
4
The differential equation representing the family of curves y
2
= 2c(
x
+ √c), where c > 0 is a parameter is of order and degree as follows,
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order 2, degree 2
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order 1, degree 3
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order 1, degree 1
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order 1, degree 2
If c
1
, c
2
, c
3
, c
4
, c
5
and c
6
are constants, then the order of the differential equation whose general solution is given by y = c
1
cos (
x
+c
2
) + c
3
sin (
x
+ c
4
) + c
5
e
x
+ c
6
is
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6
0%
5
0%
4
0%
3
0%
2
The differential equation of all parabolas whose axes are parallel to Y - axis, is
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0%
0%
2)
0%
0%
The differential equation of all straight lines passing through origin is
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0%
0%
2)
0%
0%
None of these
If
x
= sin t and y = cos pt, then
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(1 - x2)y2 + xy1 + p2 y = 0
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(1 - x2)y2 + xy1 - p2 y = 0
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(1 + x2)y2 - xy1 + p2 y = 0
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(1 - x2)y2 - xy1 + p2 y = 0
A normal is drawn at a point P(
x
, y) of a curve. It meets the X - axis at Q. if PQ is of constant length K, then the differential equation describing such a curve is
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0%
0%
2)
0%
0%
If y = a sin (5
x
+ c), then
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0%
2)
0%
0%
The differential equation for which sin
-1
x
+ sin
-1
y = c is given by
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0%
0%
2)
0%
0%
The differential equation of the family of curves y = a cos(
x
+ b) is
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0%
0%
2)
0%
0%
None of these
The solution of the differential equation
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2ye2x = Ce2x + 1
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2ye2x = Ce2x - 1
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ye2x = Ce2x + 2
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None of these
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0%
2)
0%
0%
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hyperbola
0%
circle
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ellipse
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parabola
Which one of the following is correct solution of
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sec x = C - 2 sec y
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sec y = C + 2 cos y
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sec y = C - 2 cos x
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sec x = C - 2 cos y
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0%
2)
0%
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The general solution of the differential equation
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0%
2)
0%
0%
0%
The solution of differential equation
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0%
0%
2)
0%
0%
None of the above
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0%
0%
2)
0%
0%
A particular solution of log (dy/d
x
) = 3
x
+ 4y, y(= 0 is
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e3x + 3e-4y = 4
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4e3x - 3e-4y = 3
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3e3x + 4e-4y = 7
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4e3x + 3e-4y = 7
The solution of the differential equation e
-
x
(y + 1)dy + (cos
2
x
- sin 2
x
)y d
x
= 0 subjected to the condition that y = 1, when
x
= 0 is
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y + log y + ex cos2 x = 2
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log (y ++ ex cos2x = 1
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y + log y = ex cos2 x
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(y ++ ex cos2 x = 2
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(4x + y += tan (2x + C)
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(4x + y + 1)2 = 2 tan (2x + C)
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(4x + y + 1)3 = 3 tan (2x + C)
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(4x + y += 2 tan (2x + C)
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