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

Let $$f:( - 2,2) \to R$$ be defined by $$f(x) = \left\{ {\matrix{ {x[x],} & { - 2 < x < 0} \cr {(x - 1)[x],} & {0 \le x \le 2} \cr } } \right.$$ where $$[x]$$ denotes the greatest integer function. If m and n respectively are the number of points in $$( - 2,2)$$ at which $$y = |f(x)|$$ is not continuous and not differentiable, then $$m + n$$ is equal to ____________.

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2
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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3
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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4
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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