Mathematics Mock Test - 9

If $\vec{a}=4\hat{i}+6\hat{j}$ and $\vec{b}=3\hat{j}+4\hat{k}$ then the component of $\vec{a}$ along $\vec{b}$ is:

A manufacturer produces two types of products, 1 and 2, at production levels of $x_1$ and $x_2$ respectively. The profit is $2x_1+5x_2$. Constraints are $x_1+3x_2\le 40$, $x_1+x_2\le 10$, $x_1\ge 0,x_2\ge 0$. The maximum profit is:

The vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$. The length of the median through $A$ is:

If $\alpha ,\beta$ are the roots of the equation $2x^2+3x+5=0$, then the value of the determinant $\left|\begin{array}{ccc}0& \beta & \beta \\ \alpha & 0& \alpha \\ \beta & \alpha & 0\end{array}\right|$ is:

Let $X$ be a discrete random variable with probability $P(X=x)=\frac{1}{2^x}$ for $x=1,2,3,\dots$. Then the expected value of $X$ is: