Jee Mains Pattern: Mathematics: Differential Equation Practice Paper - 01
Jee Mains Pattern: Mathematics: Differential Equation Practice Paper - 01
Jee Mains Pattern: Mathematics: Differential Equation Practice Paper - 01
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Practice Paper – 01
dy
1. If sin x is an integrating factor of the differential equation Py Q, then P can be
dx
(A) logsin x (B) cot x (C) sin x (D) log cos x
x dx y dy y3
2. Solution of the differential equation is given by
xdx ydy x3
3/2
3 y x 3/2 y3/2 1 y
(A) log log tan c0
2 x x 3/2 x
1 y
3/2
2 y xy
(C) log log tan 3/2 c 0
3 x x x
(D) None of the above
3. The degree of the differential equation of all curves having normal of constant length
c, is
(A) 1 (B) 3 (C) 4 (D) 2
4. The equation of the curve in which the portion of the tangent included between the
coordinate axes is bisected at the point of contact, is
(A) a parabola (B) an ellipse (C) a circle (D) a hyperbola
5. Solution of the differential equation
cos x dy y sin x y dx, 0 x is
2
(A) ysec x tan x c (B) y tan x sec x c
(C) tan x sec x c y (D) sec x tan x c y
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Differential Equation
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6. Consider the differential equation
1
y 2dx x dy 0. if y 1 1,
y
(A) xy2 x y
(B) x 2 y2 1 cy2 (C) y x 2 1 cx 2 (D) yx x 2 c
dy
8. If x y log y log x 1 , then the solution of the equation is
dx
9. Find the area of smaller portion of the circle x 2 y2 4 cut off by the line x = 1.
4 3 3 4 3 3
(A) sq unit (B) sq unit
3 6
3
(C) sq unit (D)
4 2 5 3
log 2 sq unit
2 log 2 2 2
11. The order and degree of the differential equation, of which xy cex be x x 2 is a
solution, is
(A) 1, 3 (B) 2, 1 (C) 3, 2 (D) None of these
12. The order of the differential equation whose general solution is given by
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Differential Equation
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13.
The degree of the differential equation satisfying 1 x 4 1 y4 a x 2 y2 , is
17. A curve passes through the point 1, and its slope at any point is given by
4
y y
cos 2 . Then, the curve has the equation
x x
e
(A) y x tan 1 ln (B) y x tan 1 ln 2
x
1 e
(C) y tan 1 ln (D) None of these
x x
18. Solution of the equation
y
f
x dy y x dx is
x
y
f '
x
x y y
(A) f cy (B) f cx (C) f cxy (D) None of these
y x x
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Differential Equation
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19. A function y f x satisfies the condition f ' x sin x f x cos x 1, f x being
/2
bounded when x 0. If I f x dx, then
0
2 2
(A) I (B) I (C) 1 I (D) 0 I 1
2 4 4 2 2
2
20.
A function y f x satisfies x 1 .f ' x 2 x x f x
2
ex
x 1
, x 1. If
f 0 5, then f x is
3x 5 x 2 6x 5 x 2 6x 5 2 5 6x x 2
(A) .e (B) .e (C) .e x
(D) .e
x 1 x 1 x 12 x 1
dy x 2 y 2 1
21. The solution of , satisfying y 1 0 is given by
dx 2xy
(C) y2 x 1 x 10 (D) x 2 y 3 5
2 2
(A) a hyperbola (B) a circle
x dy y dx
22. Solution of the equation x dx y dy 0 is
x 2 y2
c x 2 y2 c x 2 y2
(A) y x tan (B) x y tan
2 2
c x 2 y2
(C) y x tan (D) None of these
2
y 1 is
2
(A) sin x 2 y2 e x 1
(B) sin x 2 y2 x
(C) cos x y x 0
2 2
(D) sin x y e.e
2 2 x
dy
24. The solution of x 3 4x 2 tan y e x sec y satisfying y 1 0, is
dx
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Differential Equation
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25. If normal at every point to a curve passes through a fixed point then the curve must be
(A) circle (B) parabola (C) ellipse (D) hyperbola
26. Solution of the differential equation
dx
e x 2 e y2 y dy e x 2 xy 2 x 0
y 1 e x 1 e
2 y2 2 x2
(A) ex 2
C (B) e y 2
C
y 1 e y 1 e y
2 x2 2 2
(C) e y 2
C (D) ex C
27. The equation of the curve which passes through the point (2a, a) and for which the
sum of the Cartesian sub tangent and the abscissa is equal to the constant a, is
28. Water is drained from a vertical cylindrical tank by opening a valve at the base of the
tank. It is known that the rate at which the water level drops is proportional to the
square root of water depth y, where the constant of proportionality k > 0 depends on
the acceleration due to gravity and the geometry of the hole. If t is measured in
1
minutes and k , then the time to drain the tank, if the water is 4 meter deep to
15
start with is
(A) 30 min (B) 45 min (C) 60 min (D) 80 min
29. A ray of light coming from origin after reflection at the point P(x, y) of any curve
becomes parallel to x-axis, if the curve passes through (8, 6) then its equation is
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