Mathematics Tes...

Evaluate \(\underset{{{x \rightarrow 0}}}{\lim}\frac{\tan 2 x}{{e}^{2 x}-1}\)

Let the image of the point (1,0,7) in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ be the point (α,β,γ). Then which one of the following points lies on the line passing through (α,β,γ) and making angles $\frac{2\pi }{3}$and$\frac{3\pi }{4}$ with y-axis and z-axis respectively and an acute angle with x-axis?

The distance of the point \(\mathrm{Q}(0,2,-2)\) form the line passing through the point \(P(5,-4,3)\) and perpendicular to the lines \(\vec{r}=(-3 \hat{i}+2 \hat{k})+ \lambda(2 \hat{i}+3 \hat{j}+5 \hat{k}), \quad \lambda \in \mathbb{R}\) and \(\vec{r}=(\hat{i}-2 \hat{j}+\hat{k})+\mu(-\hat{i}+3 \hat{j}+2 \hat{k}), \mu \in \mathbb{R}\) is:

In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?

A coin is tossed \(6\) times. The probability of getting Exactly head three times is:

Corner points of the feasible region for an LPP are \((0,3),(3,2),(6,0)\) and \((5,5)\). Let \(F=4 x\) \(+6 y\) be the objective function. Find the value of the maximum value of \(\mathrm{F}\).

If the total number of observations is \(20, \sum x_{i}=1000\) and \(\sum x _{ i }^{2}=84000\), then what is the variance of the distribution?

If \(f(x)=\left\{\begin{array}{ll}\frac{\sin 3 x}{e^{2 x}-1}, & x \neq 0 \\ k-2, & x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=\)?

If \(x+2 y=\left[\begin{array}{cc}2 & -3 \\ 1 & 5\end{array}\right]\) and \(2 x+5 y=\left[\begin{array}{ll}7 & 5 \\ 2 & 3\end{array}\right]\), then \(y\) is equal to:

The solution of the differential equation \(\frac{d y}{d x}=y\left(1-3 x^{2}\right)\) is: