Differential Equations Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If y = (x + )
n
, then (1 + x
2
) is
(a) n
2
y
(b) –n
2
y
(c) –y
(d) 2x
2
y
2. The solution of the differential equation
 is
(a)
(b)
(c)
Page 2


PART-I (Single Correct MCQs)
1. If y = (x + )
n
, then (1 + x
2
) is
(a) n
2
y
(b) –n
2
y
(c) –y
(d) 2x
2
y
2. The solution of the differential equation
 is
(a)
(b)
(c)
(d) None of these
3. The solution of 
(a) sin {(tan
–1
 y/x) + constant}
(b) cos {(tan
–1
 y/x) + constant}
(c) {tan (sin
–1
y/x) + constant}
(d) {tan(cos
–1
 y/x) + constant}
4. The differential equations of all conics whose axes coincide with the
co-ordinate axis
(a) 
(b) 
(c) 
(d) 
5. If for the differential equation  the general solution is
 then f (x/y) is given by
(a) – x
2
/ y
2
(b) y
2
/x
2
(c) x
2
/ y
2
(d) – y
2
/x
2
Page 3


PART-I (Single Correct MCQs)
1. If y = (x + )
n
, then (1 + x
2
) is
(a) n
2
y
(b) –n
2
y
(c) –y
(d) 2x
2
y
2. The solution of the differential equation
 is
(a)
(b)
(c)
(d) None of these
3. The solution of 
(a) sin {(tan
–1
 y/x) + constant}
(b) cos {(tan
–1
 y/x) + constant}
(c) {tan (sin
–1
y/x) + constant}
(d) {tan(cos
–1
 y/x) + constant}
4. The differential equations of all conics whose axes coincide with the
co-ordinate axis
(a) 
(b) 
(c) 
(d) 
5. If for the differential equation  the general solution is
 then f (x/y) is given by
(a) – x
2
/ y
2
(b) y
2
/x
2
(c) x
2
/ y
2
(d) – y
2
/x
2
6. The solution to the differential equation 
where f (x) is a given function is
(a)
(b)
(c)
(d)
7. The solution of the differential equation
 is
(a)
(b)
(c)
(d)
8. The line normal to a given curve at each  point (x, y) on the curve
passes through the point (3, 0). If the curve contains the point (3,  4)
then its equation is
(a)
(b)
(c)
(d) None of these
9. Differential equation of all conics of the form  a and b
being parameters is :
(a)
Page 4


PART-I (Single Correct MCQs)
1. If y = (x + )
n
, then (1 + x
2
) is
(a) n
2
y
(b) –n
2
y
(c) –y
(d) 2x
2
y
2. The solution of the differential equation
 is
(a)
(b)
(c)
(d) None of these
3. The solution of 
(a) sin {(tan
–1
 y/x) + constant}
(b) cos {(tan
–1
 y/x) + constant}
(c) {tan (sin
–1
y/x) + constant}
(d) {tan(cos
–1
 y/x) + constant}
4. The differential equations of all conics whose axes coincide with the
co-ordinate axis
(a) 
(b) 
(c) 
(d) 
5. If for the differential equation  the general solution is
 then f (x/y) is given by
(a) – x
2
/ y
2
(b) y
2
/x
2
(c) x
2
/ y
2
(d) – y
2
/x
2
6. The solution to the differential equation 
where f (x) is a given function is
(a)
(b)
(c)
(d)
7. The solution of the differential equation
 is
(a)
(b)
(c)
(d)
8. The line normal to a given curve at each  point (x, y) on the curve
passes through the point (3, 0). If the curve contains the point (3,  4)
then its equation is
(a)
(b)
(c)
(d) None of these
9. Differential equation of all conics of the form  a and b
being parameters is :
(a)
(b)
(c)
(d) None of these
10. The solution of the differential equation  is
(a) x f (y/x) = k
(b) f (y/x) = kx
(c) y f (y/x) = k
(d) f (y/x) = ky
(k is arbitrary constant)
11. The solution of  is
(a)
(b)
(c)
(d)
12. Which of the following equations represents the curve for which the
intercept cut-off by any tangent on y-axis is proportional to the square
of the ordinate of the point of  tangency?
(a)
(b)
(c)
Page 5


PART-I (Single Correct MCQs)
1. If y = (x + )
n
, then (1 + x
2
) is
(a) n
2
y
(b) –n
2
y
(c) –y
(d) 2x
2
y
2. The solution of the differential equation
 is
(a)
(b)
(c)
(d) None of these
3. The solution of 
(a) sin {(tan
–1
 y/x) + constant}
(b) cos {(tan
–1
 y/x) + constant}
(c) {tan (sin
–1
y/x) + constant}
(d) {tan(cos
–1
 y/x) + constant}
4. The differential equations of all conics whose axes coincide with the
co-ordinate axis
(a) 
(b) 
(c) 
(d) 
5. If for the differential equation  the general solution is
 then f (x/y) is given by
(a) – x
2
/ y
2
(b) y
2
/x
2
(c) x
2
/ y
2
(d) – y
2
/x
2
6. The solution to the differential equation 
where f (x) is a given function is
(a)
(b)
(c)
(d)
7. The solution of the differential equation
 is
(a)
(b)
(c)
(d)
8. The line normal to a given curve at each  point (x, y) on the curve
passes through the point (3, 0). If the curve contains the point (3,  4)
then its equation is
(a)
(b)
(c)
(d) None of these
9. Differential equation of all conics of the form  a and b
being parameters is :
(a)
(b)
(c)
(d) None of these
10. The solution of the differential equation  is
(a) x f (y/x) = k
(b) f (y/x) = kx
(c) y f (y/x) = k
(d) f (y/x) = ky
(k is arbitrary constant)
11. The solution of  is
(a)
(b)
(c)
(d)
12. Which of the following equations represents the curve for which the
intercept cut-off by any tangent on y-axis is proportional to the square
of the ordinate of the point of  tangency?
(a)
(b)
(c)
(d)
13. The equation of the curve which is such that the portion of the axis of x-
cut off between the origin and tangent at any point is proportional to the
ordinate of that point is
(a) x = y (a – b log y)
(b) log x = by
2 
+ a
(c) x
2 
= y (a – b log y)
(d) None of these
14. If y + (xy) = x (sin x + log x), then
(a) y = cos x +  sin x +  cos x +  log x –  
(b) y = – cos x –  sin x +  cos x +  log x – 
(c) y = – cosx +  sin x +  cos x –  log x – 
(d) None of these
15. The equation of the curve  passing through the point  and
satisfying the differential equation  is
(a)
(b)
(c)
(d) None of these
16. The real value of n for which the substitution y = u
n
 will transform the
differential equation  into a homogeneous equation
is