NTA JEE Main 7th January 2020 Shift 2

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, $$x$$ and $$y$$ be 10 and 25 respectively, then $$x \cdot y$$ is equal to

Let $$X = \{n \in N : 1 \le n \le 50\}$$. If $$A = \{n \in X : n \text{ is a multiple of } 2\}$$ and $$B = \{n \in X : n \text{ is a multiple of } 7\}$$, then the number of elements in the smallest subset of X, containing both A and B, is

If the system of linear equations,
$$x + y + z = 6$$
$$x + 2y + 3z = 10$$
$$3x + 2y + \lambda z = \mu$$
has more than two solutions, then $$\mu - \lambda^2$$ is equal to

If the function $$f$$ defined on $$\left(-\frac{1}{3}, \frac{1}{3}\right)$$ by $$f(x) = \begin{cases} \frac{1}{x}\log_e\left(\frac{1+3x}{1-2x}\right), & \text{when } x \neq 0 \\ k, & \text{when } x = 0 \end{cases}$$, is continuous, then $$k$$ is equal to

If the foot of the perpendicular drawn from the point $$(1, 0, 3)$$ on a line passing through $$(\alpha, 7, 1)$$ is $$\left(\frac{5}{3}, \frac{7}{3}, \frac{17}{3}\right)$$, then $$\alpha$$ is equal to