AIEEE 2005 Maths Question Paper Mock Test

Let $a,b$ and $c$ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$, $\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then $c$ is:

If $\vec{a},\vec{b},\vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then $[\lambda (\vec{a}+\vec{b}){\lambda }^2\vec{b}\lambda \vec{c}]=[\vec{a}\vec{b}+\vec{c}\vec{b}]$ for:

Let $\vec{a}=\hat{i}-\hat{k}$, $\vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$. Then $[\vec{a}\vec{b}\vec{c}]$ depends on:

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is:

A random variable $X$ has Poisson distribution with mean $2$. Then $P(X>1.5)$ equals: