$(10)$ If $g(x,y)=x^3{y}^2-y,$ then what is $g_{yx}(2,3)$

$($a$)71$

$($c$)107$

$($b$)72.$

$($d$)108$

$(11)$ Which of the following is an even function of $$

$($a$){}^{}{?}^2$

$($c$)sin(2)+3$

$($b$){}^2-4$

$($d$){}^3+6$

$(12)$ A periodic function is given by a function which

$($a$)$ has a period $2$

$($c$)$ satisfies $f(t+T)=-f(t)$

$($b$)$ satisfies $f(t+T)=f(t)$

$($d$)$ has a period $$

$(13)$ Which of the following differential equations is linear?

$($a$)\frac{dy}{dx}=x-y^2$

$($c$)\frac{dy}{dx}=sin(xy)$

$($b$)\frac{dy}{dx}=x^2-y$

$($d$)\frac{dy}{dx}=e^{xy}$

$(14)$ A partial differential equation has

$($a$)$ one independent variable

$($b$)$ two or more independent variables

$($c$)$ more than one dependent variable

$($d$)$ equal number of dependent and independent variables

$(15)$ The Laplacian of a function $f=f(x,y)$ is defined to be $f_{}+f_{yy}.$ Which of the following functions has Laplacian equal to zero?

$($a$)f(x,y)=x^2-2y^2+2xy$

$($c$)f(x,y)=-3x^2-3y^2+6xy$

$($b$)f(x,y)=x^2-2y^2+3xy$

$($d$)f(x,y)=3x^2-3y^2-6xy$

$(16)$ Find the divergence of the vector field vec$(F)=-sin()hat(i)+cos()hat(j)$

$($a$)$ grad$*vec(F)=sin()$

$($c$)$ grad$*vec(F)=cos()+sin()$

$($b$)$ grad$*vec(F)=-cos()-sin()$

$($d$)$ grad$*vec(F)=-cos()$