AIEEE 2009 PYQ Mock Test

For real $x$, let $f(x)=x^3+5x+1$, then:

In a binomial distribution $B(n,p=1/4)$, if the probability of at least one success is greater than or equal to $9/10$, then $n$ is greater than:

If $P$ and $Q$ are the points of intersection of the circles $x^2+y^2+3x+7y+2p-5=0$ and $x^2+y^2+2x+2y-p^2=0$, then there is a circle passing through $P,Q$ and $(1,1)$ for:

The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are:

If $|z-4/z|=2$, then the maximum value of $|z|$ is equal to: