NTA JEE Main 5th September 2020 Shift 2

The coefficient of $$x^4$$ in the expansion of $$(1 + x + x^2 + x^3)^6$$ in powers of $$x$$, is.......

Let $$A = \{a, b, c\}$$ and $$B = \{1, 2, 3, 4\}$$. Then the number of elements in the set $$C = \{f : A \to B \mid 2 \in f(A)$$ and $$f$$ is not one-one$$\}$$ is...

If the lines $$x + y = a$$ and $$x - y = b$$ touch the curve $$y = x^2 - 3x + 2$$ at the points where the curve intersects the $$x$$-axis, then $$\frac{a}{b}$$ is equal to...

Let the vectors $$\vec{a}$$, $$\vec{b}$$, $$\vec{c}$$ be such that $$|\vec{a}| = 2$$, $$|\vec{b}| = 4$$ and $$|\vec{c}| = 4$$. If the projection of $$\vec{b}$$ on $$\vec{a}$$ is equal to the projection of $$\vec{c}$$ on $$\vec{a}$$ and $$\vec{b}$$ is perpendicular to $$\vec{c}$$, then the value of $$|\vec{a} + \vec{b} - \vec{c}|$$ is...

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is.....