1
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1
Change Language

Let $$y = p(x)$$ be the parabola passing through the points $$( - 1,0),(0,1)$$ and $$(1,0)$$. If the area of the region $$\{ (x,y):{(x + 1)^2} + {(y - 1)^2} \le 1,y \le p(x)\} $$ is A, then $$12(\pi - 4A)$$ is equal to ___________.

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2
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1
Change Language

The number of elements in the set $$\{ n \in Z:|{n^2} - 10n + 19| < 6\} $$ is _________.

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3
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1
Change Language

If the mean of the frequency distribution

Class : 0-10 10-20 20-30 30-40 40-50
Frequency : 2 3 $$x$$ 5 4

is 28, then its variance is __________.

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4
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1
Change Language

The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is ___________.

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