AIEEE 2003 (Maths) Mock Test

The area of the region bounded by the curves $y=|x-1|$ and $y=3-|x|$ is:

Let $f(x)$ be a function satisfying $f^{\prime }(x)=f(x)$ with $f(0)=1$ and $g(x)$ be a function that satisfies $f(x)+g(x)=x^2$. Then the value of the integral ${\int }_0^{1}f(x)g(x)dx$, is:

The degree and order of the differential equation of the family of all parabolas whose axis is the $x$ -axis, are respectively:

The solution of the differential equation $(1+y^2)+(x-e^{{\tan }^{-1}y})\frac{dy}{dx}=0$, is:

If the equation of the locus of a point equidistant from the points $(a_1,b_1)$ and $(a_2,b_2)$ is $(a_1-a_2)x+(b_1-b_2)y+c=0$, then the value of '$c$ ' is: