AIEEE 2005 Maths Question Paper Mock Test

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in a dictionary, then the word SACHIN appears at serial number:

The value of ${}^{50}{C}_4+{\sum }_{r=1}^6{}^{56-r}{C}_3$ is:

If $A=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, then which one of the following holds for all $n\ge 1$?

If the coefficient of $x^7$ in $[a{x}^2+(1/bx){]}^{11}$ equals the coefficient of $x^{-7}$ in $[ax-(1/b{x}^2){]}^{11}$, then $a$ and $b$ satisfy the relation:

Let $f:(-1,1)\to B$ be a function defined by $f(x)={\tan }^{-1}\frac{2x}{1-x^2}$, then $f$ is both one-one and onto when $B$ is the interval: