1
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $$2,3,4,5,6$$ (repetition of digits is not allowed) and divisible by 55 is _________.

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2
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

$$ \text { If } \sum\limits_{k=1}^{10} K^{2}\left(10_{C_{K}}\right)^{2}=22000 L \text {, then } L \text { is equal to }$$ ________.

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3
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

If $$[t]$$ denotes the greatest integer $$\leq t$$, then the number of points, at which the function $$f(x)=4|2 x+3|+9\left[x+\frac{1}{2}\right]-12[x+20]$$ is not differentiable in the open interval $$(-20,20)$$, is __________.

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4
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

If the tangent to the curve $$y=x^{3}-x^{2}+x$$ at the point $$(a, b)$$ is also tangent to the curve $$y = 5{x^2} + 2x - 25$$ at the point (2, $$-$$1), then $$|2a + 9b|$$ is equal to __________.

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