AIEEE 2011 PYQ Mock Test

Consider $5$ independent Bernoulli's trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $p$ lies in the interval:

A man saves Rs. $200$ in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. $40$ more than the saving of immediately previous month. His total saving from the start of service will be Rs. $11040$ after:

The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is:

If the angle between the line $\frac{x-2}{1}=\frac{y-1}{2}=\frac{z-3}{\lambda }$ and the plane $x+2y+3z=4$ is ${\cos }^{-1}\sqrt{\frac{5}{14}}$, then $\lambda$ equals:

If $\vec{a}=\frac{1}{\sqrt{10}}(3\hat{i}+\hat{k})$ and $\vec{b}=\frac{1}{7}(2\hat{i}+3\hat{j}-6\hat{k})$, then the value of $(\overrightarrow{2a}-\vec{b})\cdot [(\vec{a}\times \vec{b})\times (\vec{a}+\overrightarrow{2b})]$ is: