Free Printable CAT III: MCQ:DE&LT

1.

What is the nature of Lagrange’s linear partial differential equation?

a)

First-order, Second-degree

b)

Second-order, First-degree

c)

First-order, Third-degree

d)

First-order, First-degree

2.

Find the general solution of the linear partial differential equation, yzp+zxq=xy.

a)

$\phi\left(x^2-y^2,y^2-z^2\right)=0$

b)

$\phi\left(x^2-z^2,\ y^2-z^2\right)=0$

c)

$\phi\left(x^2-y^2,-z^2\right)=0$

d)

$\phi\left(x^2-y^2,y^2-x^2\right)=0$

3.

The solution of non-linear partial differential equation

\sqrt{p}+\sqrt{q}=x

is

a)

$z=\left(x-a\right)^3+a^2y+b$

b)

$z=\frac{\left(x-a\right)^3}{3}+a^2y+b$

c)

$z=\left(x-a\right)^3+b$

d)

$z=a^2x+\left(y-a\right)^3+c$

4.

The solution of non-linear partial differential equation

q-p+x-y=0

is

a)

$z=\frac{\left(x+a\right)^2}{2}+\frac{\left(y+a\right)^2}{2}+c$

b)

$z=\left(x+a\right)^2+\left(y+a\right)^2+c$

c)

$z=\frac{\left(x+a\right)^2}{2}+\frac{\left(y-a\right)^2}{2}+c$

d)

$z=\frac{\left(x-a\right)^2}{2}+\frac{\left(y+a\right)^2}{2}+c$

5.

Which of the following is an example for first order linear partial differential equation?

a)

Lagrange’s Partial Differential Equation

b)

Clairaut’s Partial Differential Equation

6.

Find the differential equation of all spheres of fixed radius having centre in xy -plane. hint:

\left(x-a\right)^2+\left(y-b\right)^2+z^2=r^2

a)

$z^2\left(p^2+q^2+1\right)=r^2$

b)

$z^2\left(p^2+q^2\right)=r^2$

c)

$p^2+q^2+1=r^2$

7.

What is the PDE when the arbitrary constants a and b are eliminated from

ax^2+by^2=1-z^2

a)

$zxp+zyq=z^2-1$

b)

$zxp+zyq=z^2+1$

c)

$zxp-zyq=z^2-1$

d)

$zxp+zyq=1-z^2$

8.

What is the PDE when the arbitrary constants a and b are eliminated from

z=axy+b

a)

$xp+yq=1$

b)

$xp-yq=0$

c)

None

9.

obtain PDE by eliminating arbitrary functions from the given equation

z=\phi\left(x^2-y^2\right)

a)

px+qy=0

b)

py+qx=0

c)

p/x+q/y=9

d)

x/p+y/q=0

10.

The solution of Lagrange's partial differential equation $\left(1-x\right)p+\left(2-y\right)q=3-z$

a)

$f\left(\frac{2-y}{1-x},\frac{3-z}{2-y}\right)$

b)

$f\left(\frac{3-y}{2-x},\frac{1-z}{2-y}\right)$

c)

$f\left(\frac{2-x}{1-z},\frac{3-x}{2-y}\right)$

CAT III: MCQ:DE&LT

Total questions: 10

Worksheet time: 50mins

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