NTA JEE Main 4th September 2020 Shift 1

Let $$(2x^2 + 3x + 4)^{10} = \sum_{r=0}^{20} a_r x^r$$. Then $$\frac{a_7}{a_{13}}$$ is equal to __________

If the system of equations
$$x - 2y + 3z = 9$$
$$2x + y + z = b$$
$$x - 7y + az = 24$$
has infinitely many solutions, then $$a - b$$ is equal to __________

Suppose a differentiable function $$f(x)$$ satisfies the identity $$f(x + y) = f(x) + f(y) + xy^2 + x^2y$$, for all real $$x$$ and $$y$$. If $$\lim_{x \to 0}\frac{f(x)}{x} = 1$$, then $$f'(3)$$ is equal to __________

If the equation of a plane P, passing through the intersection of the planes, $$x + 4y - z + 7 = 0$$ and $$3x + y + 5z = 8$$ is $$ax + by + 6z = 15$$ for some $$a, b \in R$$, then the distance of the point (3, 2, -1) from the plane P is __________

The probability of a man hitting a target is $$\frac{1}{10}$$. The least number of shots required, so that the probability of his hitting the target at least once is greater than $$\frac{1}{4}$$, is ____