AIEEE 2005 Maths Question Paper Mock Test

The area enclosed between the curve $y={\log }_e(x+e)$ and the coordinate axes is:

The parabolas $y^2=4x$ and $x^2=4y$ divide the square region bounded by the lines $x=4,y=4$ and the coordinate axes into three parts. If $S_1,S_2,S_3$ are respectively the areas of these parts numbered from top to bottom, then $S_1:S_2:S_3$ is:

If $x\frac{dy}{dx}=y(\log y-\log x+1)$, then the solution of the equation is:

The line parallel to the x-axis and passing through the intersection of the lines $ax+2by+3b=0$ and $bx-2ay-3a=0$, where $(a,b)\ne (0,0)$ is:

A spherical iron ball $10\text{ cm}$ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50{\text{ cm}}^3\text{/min}$. When the thickness of ice is $5\text{ cm}$, then the rate at which the thickness of ice decreases, is: