AIEEE 2012 PYQ Mock Test

Let $a,b\in \mathbb{R}$ be such that the function $f$ given by $f(x)=\ln |x|+b{x}^2+ax,x\ne 0$ has extreme values at $x=-1$ and $x=2$.Statement 1: $f$ has local maximum at $x=-1$ and at $x=2$.Statement 2: $a=\frac{1}{2}$ and $b=-\frac{1}{4}$.

The area bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9y$, and the straight line $y=2$ is:

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:

If $f:\mathbb{R}\to \mathbb{R}$ is a function defined by $f(x)=[x]\cos \left(\frac{2x-1}{2}\pi \right)$, where $[x]$ denotes the greatest integer function, then $f$ is:

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then $k$ is equal to: