NTA JEE Main 3rd September 2020 Shift 2

The total number of 3-digit numbers whose sum of digits is 10, is ..........

If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $$4^{th}$$ A.M. is equal to $$2^{nd}$$ G.M., then $$m$$ is equal to:

Let $$S$$ be the set of all integer solutions $$(x, y, z)$$ of the system of equations
$$x - 2y + 5z = 0$$
$$-2x + 4y + z = 0$$
$$-7x + 14y + 9z = 0$$
such that $$15 \leq x^2 + y^2 + z^2 \leq 150$$. Then, the number of elements in the set $$S$$ is equal to ..........

If the tangent to the curve $$y = e^x$$ at a point $$(c, e^c)$$ and the normal to the parabola $$y^2 = 4x$$ at the point (1, 2) intersect at the same point on the $$x$$-axis, then the value of $$c$$ is .....

Let a plane $$P$$ contain two lines $$\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})$$, $$\lambda \in R$$ and $$\vec{r} = -\hat{j} + \mu(\hat{j} - \hat{k})$$, $$\mu \in R$$. If $$Q(\alpha, \beta, \gamma)$$ is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then $$3(\alpha + \beta + \gamma)$$ equals .......