AIEEE 2010 PYQ Mock Test

The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is:

A person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{\text{th}}$ minute. If $a_1=a_2=\cdots =a_{10}=150$ and $a_{10},a_{11},\dots$ are in A.P. with common difference $-2$, then the time taken by him to count all notes is:

Let $f:\mathbb{R}\to \mathbb{R}$ be a positive increasing function with ${\lim }_{x\to \infty }\frac{f(3x)}{f(x)}=1$. Then ${\lim }_{x\to \infty }\frac{f(2x)}{f(x)}=$

Let $p(x)$ be a function defined on $\mathbb{R}$ such that $p^{\prime }(x)=p^{\prime }(1-x)$, for all $x\in [0,1]$, $p(0)=1$ and $p(1)=41$. Then ${\int }_0^{1}p(x)dx$ equals:

Let $f:(-1,1)\to \mathbb{R}$ be a differentiable function with $f(0)=-1$ and $f^{\prime }(0)=1$. Let $g(x)=[f(2f(x)+2){]}^2$. Then $g^{\prime }(0)=$