AIEEE 2009 PYQ Mock Test

One ticket is selected at random from $50$ tickets numbered $00,01,02,\dots ,49$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals:

Let $y$ be an implicit function of $x$ defined by $x^{2x}-2x^x\cot y-1=0$. Then $y^{\prime }(1)$ equals:

The area of the region bounded by the parabola $(y-2{)}^2=x-1$, the tangent to the parabola at the point $(2,3)$ and the x-axis is:

Given $P(x)=x^4+a{x}^3+b{x}^2+cx+d$ such that $x=0$ is the only real root of $P^{\prime }(x)=0$. If $P(-1)<P(1)$, then in the interval $[-1,1]$:

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is: