Complex Variables and Partial Differential Equations (3130005) MCQ

MCQs of First Order Partial Differential Equation

MCQ No - 1

The partial differential equation of #$$\mathrm z=\left(\mathrm x-\mathrm a\right)^2+\left(\mathrm y-\mathrm b\right)^2$$# is _____.

(A)

#$$4\mathrm z=\mathrm p^2+\mathrm q^2$$#

(B)

#$$\mathrm z=\mathrm p^2+\mathrm q^2$$#

(C)

#$$4\mathrm z=\mathrm p^2-\mathrm q^2$$#

(D)

none of these


A
MCQ No - 2

The partial differential equation of #$$\mathrm f\left(\mathrm x^2+\mathrm y^2,\;\mathrm z-\mathrm{xy}\right)=0$$# is _____.

(A)

#$$\mathrm x^2-\mathrm y^2=\mathrm{qx}-\mathrm{py}$$#

(B)

#$$\mathrm x^2+\mathrm y^2=\mathrm{qx}+\mathrm{py}$$#

(C)

#$$\mathrm x^2-=\mathrm{qx}-\mathrm{py}$$#

(D)

#$$\mathrm y^2-=\mathrm{qx}-\mathrm{py}$$#


A
MCQ No - 3

The general solution of P.D.E. #$$\mathrm{xp}+\mathrm{yq}=\mathrm x-\mathrm y$$# is _____.

(A)

#$$\mathrm f\left(\mathrm x,\;\mathrm x-\mathrm y-\mathrm z\right)=0$$#

(B)

#$$\mathrm f\left(\frac{\mathrm x}{\mathrm y},\;\mathrm x-\mathrm y-\mathrm z\right)=0$$#

(C)

#$$\mathrm f\left(\frac{\mathrm x}{\mathrm y},\;\mathrm x+\mathrm y+\mathrm z\right)=0$$#

(D)

#$$\mathrm f\left(\frac{\mathrm x}{\mathrm y},\;\mathrm x-\mathrm z\right)=0$$#


B
MCQ No - 4

Eliminating arbitrary constants a and b from #$$\mathrm z=\left(\mathrm x+\mathrm a\right)\;\left(\mathrm y+\mathrm b\right)$$#, the partial differential equation formed is _____ .

(A)

#$$\mathrm z=\mathrm p+\mathrm q$$#

(B)

#$$\mathrm z=\mathrm{pq}^2$$#

(C)

#$$\mathrm z=\mathrm{pq}$$#

(D)

none of these


C
MCQ No - 5

Eliminating the arbitrary function from #$$\mathrm z=\mathrm f\left(\mathrm x^2+\mathrm y^2\right)$$#, then the partial differential equation formed is _____ .

(A)

#$$\mathrm{py}=\mathrm{qx}$$#

(B)

#$$\mathrm{px}=\mathrm{qy}$$#

(C)

#$$\mathrm{pq}=\mathrm{xy}$$#

(D)

#$$\mathrm{pq}=1$$#


A