Which of the following mathematicians introduced a derivative notation ?

1 )  Which of the following mathematicians introduced a derivative notation ?

A )  Leibniz, Cauchy .

B )  Cauchy, Euler .

C )  Euler, Newton .

D )  Leibniz, Newton  .

E )  Cauchy, Newton

Correct Anwser : - D )  Leibniz, Newton  .

 

2 ) A solution of a differential equation that is free of arbitrary parameters is referred to as  ---------------  solution .

A )  Singular ,

B )  Implicit ,

C )  Explicit ,

D )  General ,

E )  Particular ,

Correct Anwser : - E )  Particular ,

 

 3 )   A solution of a differential equation that is identically zero on an interval "I" is called ------------- solution .

A )   Trivial ,

B )   Non-trivial ,

C )   General ,

D )   Particular ,

E )    All of above

Correct Anwser : - A )   Trivial ,

 

4 )  For what value(s) of "m" , the following function becomes a solution of   y''- 5y' +6y = 0 ?

Correct Anwser : - C )     2 , 3 .

 

5 )  The following general nth-order differential equation has  ----------  variables .

 

Correct Anwser : -   E )   n + 2 ,

 

6 )  Which of the following is a differential equation of all circles of radius " a "  ?

 

Correct Anwser : -  B ) 

 

7 )  The solution " y = 0 " is a -----------  solution of the following differential equation .

A )  Trajectory ,

B )   Singular ,

C )  Envelope ,

D )  Trajectory and Singular both ,

E )  Singular and Envelope both ,

Correct Anwser : -   B )   Singular ,

 

8 )  The following differential equation is known as --------  differential equation .

A )  Ordinary ,

B )  Partial ,

C )  Autonomous ,

D )  Laplace ,

E )  None of above ,

Correct Anwser : -    C )  Autonomous ,

 

9 )  Which of the following is an integrating factor of the differential equation ?

 

Correct Anwser : -    B )

 

 

10 )  Which of the following equations represents a nonlinear differential equation ?

 

Correct Anwser : -   C )