NTA JEE Main 2nd September 2020 Shift 1
For the following questions answer them individually
NTA JEE Main 2nd September 2020 Shift 1 - Question 71
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ___________.
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NTA JEE Main 2nd September 2020 Shift 1 - Question 72
The number of integral values of $$k$$ for which the line, $$3x + 4y = k$$ intersects the circle, $$x^2 + y^2 - 2x - 4y + 4 = 0$$ at two distinct points is ___________.
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NTA JEE Main 2nd September 2020 Shift 1 - Question 73
If $$\lim_{x \to 1} \frac{x + x^2 + x^3 + \ldots + x^n - n}{x - 1} = 820$$, $$(n \in N)$$ then the value of $$n$$ is equal to ___________.
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NTA JEE Main 2nd September 2020 Shift 1 - Question 74
The integral $$\int_0^2 ||x - 1| - x| \; dx$$ is equal to ___________.
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NTA JEE Main 2nd September 2020 Shift 1 - Question 75
Let $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ be three unit vectors such that $$|\vec{a} - \vec{b}|^2 + |\vec{a} - \vec{c}|^2 = 8$$. Then $$|\vec{a} + 2\vec{b}|^2 + |\vec{a} + 2\vec{c}|^2$$ is equal to ___________.
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