AIEEE 2008 PYQ Mock Test

The solution of the differential equation $\frac{dy}{dx}=\frac{y}{x}+x$ satisfying the condition $y(1)=1$ is:

The mean of the numbers $a,b,8,5,10$ is $6$ and the variance is $6.80$. Then which one of the following gives possible values of $a$ and $b$?

The vector $\vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{j}+\hat{k}$ and bisects the angle between $\vec{b}$ and $\vec{c}$. Then which one of the following gives possible values of $\alpha$ and $\beta$?

The non-zero vectors $\vec{a},\vec{b}$ and $\vec{c}$ are related by $\vec{a}=8\vec{b}$ and $\vec{c}=-7\vec{b}$. Then the angle between $\vec{a}$ and $\vec{c}$ is:

The line passing through the points $(5,1,a)$ and $(3,b,1)$ crosses the $yz$ -plane at the point $\left(0,\frac{17}{2},-\frac{13}{2}\right)$. Then: