Maths

6. Find the area of the region in the first quadrant enclosed by x-axis,line $x=\; \surd 3y$ and the circle $x^2+y^2=4$ .

5. Find the area of the region bounded by the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=\mathrm{1 }$

4. Find the area of the region bounded by the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ .

3. Find the area of the region bounded by the curve x² = 4y ,y=2,y=4 and y-axis is the first quadrant.

2. Find the area of the region bounded by the curve y² = 9x and the lines x=2,x=4 and x-axis in the first quadrant.

1. Find the area of the region bounded by the curve y² = x the  lines x=1, x = 4 and x-axis.

1. Find the area of the region bounded by the curve y² = x the  lines x=1, x = 4 and x-axis.

113. The general solution of the differential equation  $e^{x}dy+(y{e}^x+2x)dx=0$  is:

$\begin{array}{l}(A)x{e}^y+x^2=C\\ (B)x{e}^y+y^2=C\\ (C)y{e}^x+x^2=C\\ (D)y{e}^y+x^2=C\end{array}$

112. The general equation of a differential equation of the type $\frac{dx}{dy}+P_{1}x=Q,is:$

$\begin{array}{l}(A)y{e}^{{\displaystyle \int P_{1}dy}}={\displaystyle \int \left(Q_1{e}^{{\displaystyle \int P_{1}dy}}\right)}dy+C\\ (B)y.e^{{\displaystyle \int P_{1}dx}}={\displaystyle \int \left(Q_1{e}^{{\displaystyle \int P_{1}dx}}\right)}dx+C\\ (C)x{e}^{{\displaystyle \int P_{1}dy}}={\displaystyle \int \left(Q_1{e}^{{\displaystyle \int P_{1}dy}}\right)}dy+C\\ (D)x.e^{{\displaystyle \int P_{1}dx}}={\displaystyle \int \left(Q_1{e}^{{\displaystyle \int P_{1}dx}}\right)}dx+C\end{array}$

Choose the correct answer:

111. The general solution of the differential equation  $\frac{ydx-xdy}{y}=0$ is:

$\begin{array}{l}(A)xy=c\\ (B)x=c{y}^2\\ (C)y=cx\\ (D)y=c{x}^2\end{array}$