AIEEE 2007 PYQ Mock Test

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals:

If ${\sin }^{-1}\left(\frac{x}{5}\right)+{\text{cosec}}^{-1}\left(\frac{5}{4}\right)=\frac{\pi }{2}$, then a value of $x$ is:

In the binomial expansion of $(a-b{)}^n,n\ge 5$, the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals:

The set $S=\{1,2,3,\dots ,12\}$ is to be partitioned into three sets $A,B,C$ of equal size. Thus, $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$. The number of ways to partition $S$ is:

The largest interval lying in $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ for which the function $f(x)=\left[{\cos }^{-1}\left(\frac{1-x}{2}\right)+\log (\cos x)\right]$ is defined, is: