Page 1 :
TEST-03, TOPIC- DIFFERENTIAL EQUATIONS, INSTRUCTIONS:, TIME-40 MINUTES, NO. OF QUESTIONS: 40, EACH QUESTION CARRIES 1 MARK, NO NEGATIVE MARKING, , 1) The integrating factor of, , is, , (a), (b), (c), (d), , 2) If, , is an integrating factor of the differential equation, , , then P =, , (a), (b), (c), (d), , 3), , is the general solution of the differential equation, (a) ( ), (b), (c), (d) ( ), , 4) The m is order and n is degree of the differential equation ( ) +5, (m,n)=, (a) (2,1), (b) (1,2), , then
Page 2 :
(c) (1,6), (d) (1,3), 5) The differential equation of the family of curves, , is, , (a), (b), (c), (d), , 6) The particular integral of the differential equation (, (a), (b), (c), , ), , (d), 7) The differential equation of the family of concentric circles having their centers at, origin is, (a), (b), (c), (d), 8) The integrating factor of the homogeneous differential equation, is, (a), (b), (c), (d) None of these, 9) The general solution of the differential equation, (a), (b), (c), (d) None of these
Page 3 :
), (a), , (, , (b) (, (c), , ), ), , (, , (d) (, , ), ), , ( ), , 11), , (, , ), , ( ), , ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ), , 12) For a non-homogeneous differential equation, ( ), ( ), if, and, are its solutions, then which of the following is solution of the corresponding, homogeneous differential equation, (a), (b), (c), (d) None of these, , 13) “For homogeneous linear differential equation , the linear combination of two, solutions is again a solution of the equation” This statement is, (a) True
Page 4 :
(b) False, (c) Neither true nor false, (d) Can’t say, , 14) The value of the Wronskian of the functions, , is, , (a) 0, (b), (c), (d) -10, , 15) The differential equation whose linearly independent solutions are, is, (a) (, , ), , (b) (, , ), , (c) (, , ), , (d) (, , ), , 16) Solving by variation of parameters, Wronskian is, , the value of the, , (a), (b), (c) 2, (d) None of these, , 17) Solving by variation of parameters, Wronskian is, (a), (b) 2, (c), , , The value of the
Page 5 :
(d) None of these, , 18) If V is a function in x then, (a), (b), , (, , ), , (, , ), , (c), , (, , ( ), , ), , (d) None of these, , 19) Number of arbitrary constants in singular solution of an equation of degree n is, (a) n, , (b) n-1, , (c) 0, , (d) 1, , 20) The differential equation of the family of orthogonal trajectories of the family of, curves, , (, , ), , (a) (, , ), , (b) (, , ), , (c) (, (d) (, , is, , ), ), , 21) By means of the transformation, , , the equation, (, , (a) (, (b) (, (c) (, (d) (, , ), ), ), , (, (, (, ), , ), , ), ), ), (, , ), , 22) The wronskian of the two solutions of the differential equation
Page 6 :
(a) 2, , (b) -2, , (c) 1, , 23) Integrating factor of (, (a), (b), , ), , 24) The differential equation (, , ⁄, , (d) -1, , (, , ), , is, , , then, , (c), (d), , ), , (a) Homogeneous, (b) Non-linear, , ⁄, , (, , ), , (c) variable separable, (d) Non homogeneous, , 25) Solution of the differential equation, , is, , (a), , (c), , (b), , (d), , 26) Solve the differential equation, (a), (b), , is of the type:, , is, (c), (d), ( ), , 27) Solution of th4e differential equation, (a), (b), , (c), (d), , 28) The solution of the differential equation, , represents:, , (a) a family of circles centred at (1,0), (b) a family of circles centred at (0,0), (c) a family of circles centred at (-1,0), (d) a family of straight lines with slope -1, 29) The general solution of the differential equation, (a), , ( ), , (b), , ( ), , (c), , ( ), , ( ), , ( )
Page 7 :
(d), , ( ), , 30) If y(x) is the solution of the differential equation, y(1)=1 then y(2)=?, (a) 3, , (b) 4, , (c) 2, , (d) 1, , ( )(, , ):
