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- 1. Multiple Choice
If we eliminate a and b from z = (x+a)(y+b)
z = p/q
z = p - q
z = p + q
z = pq
- 2. Multiple Choice
If the number of constants to be eliminated is equal to number of independent variables, then the result is_____
First order PDE
Second order PDE
third order PDE
Second order linear PDE
- 3. Multiple Choice
If the number of constants to be eliminated is greater than the number of independent variables, then the result is_____
First order PDE
Second and higher order PDE
Second and higher order PDE
only Second order linear PDE
- 4. Multiple Choice
The Clairaut’s equation is of the form____
y=px+f(p)
y=px+f(q)
x=qy+f(p)
x=py+f(q)
- 5. Multiple Choice
If the equation is in the form f(x, p, q)=0, then we assume
p=a
z=pq
q=a
p=aq
- 6. Multiple Choice
The solution of the equation z = px + qy + pq is____
z = ax + by + pq
z = ax + by + ab
z = bx + ay + ab
z = px + qy + ab
- 7. Multiple Choice
Eliminate the arbitrary function from z = f(x2+y2)
px = qy
py+qx=0
px+qy=0
py = qx
- 8. Multiple Choice
Eliminate the arbitrary constants c and r from x2+y2+(z-c)2=r2
px = qy
px+qy=0
py = qx
py+qx=0
- 9. Multiple Choice
A solution containing as many arbitrary constants as there are independent variables is called____
complete integral
particular integral
singular integral
general integral
- 10. Multiple Choice
A solution obtained by giving particular values to the arbitrary constants in a complete integral is called____
complete integral
particular integral
singular integral
general integral
- 11. Multiple Choice
A partial differential equation which is not linear then it is called_____
semi linear
collinear
Quasi linear
non-linear
- 12. Multiple Choice
A partial differential equation requires
exactly one independent variable
two or more independent variables
more than one dependent variable
equal number of dependent and independent variables
- 13. Multiple Choice
Form a PDE by eliminating arbitrary constants from z= ax + by
z = px + qy
z = px - qy
z = qx + py
z = qx - py
- 14. Multiple Choice
Form a PDE by eliminating arbitrary constants from z= a(x+y) + b
p+q=0
px = qy
qx = py
p-q=0
- 15. Multiple Choice
z = yf(x)+g(x)
z = yf(y)+g(x)
z = xf(x)+g(x)
z = xf(y)+g(x)
- 16. Multiple Choice
The solution z = ax + g(a)y +c is getting from
f(x,p,q)=0
f(p,q)=0
f(x,p)=g(y,q)
f(z,p,q)=0
- 17. Multiple Choice
If the PDE is of the type f(p,q)=0, then we will take____
f(y,q)=a
f(x,p)=a
p=q
p=a
- 18. Multiple Choice
If the PDE is of the type f(z,p,q)=0, then we will take____
f(x,p)=a
p=aq
p=a
p=q
- 19. Multiple Choice
If the PDE is of the type f(x,p)=g(y,q), then we will take____
f(x,p)=a=g(y,q)
p=q
p=aq
p=a
- 20. Multiple Choice
The solution of simultaneous linear differential equations is of the form___
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