AIEEE 2013 PYQ Mock Test

The number of values of $k$, for which the system of equations$(k+1)x+8y=4k$$kx+(k+3)y=3k-1$ has no solution, is:

If $y=\sec ({\tan }^{-1}x)$, then $\frac{dy}{dx}$ at $x=1$ is equal to:

If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then $k$ can have:

Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A\times B$ having $3$ or more elements is:

If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$, then the length of the median through $A$ is: