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1
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
A function f is defined on [$$-$$3, 3] as

$$f(x) = \left\{ {\matrix{ {\min \{ |x|,2 - {x^2}\} ,} & { - 2 \le x \le 2} \cr {[|x|],} & {2 < |x| \le 3} \cr } } \right.$$ where [x] denotes the greatest integer $$ \le $$ x. The number of points, where f is not differentiable in ($$-$$3, 3) is ___________.
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2
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
If $$\mathop {\lim }\limits_{x \to 0} {{ax - ({e^{4x}} - 1)} \over {ax({e^{4x}} - 1)}}$$ exists and is equal to b, then the value of a $$-$$ 2b is __________.
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3
JEE Main 2021 (Online) 25th February Morning Slot
Numerical
+4
-1
The number of points, at which the function
f(x) = | 2x + 1 | $$-$$ 3| x + 2 | + | x2 + x $$-$$ 2 |, x$$\in$$R is not differentiable, is __________.
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4
JEE Main 2021 (Online) 25th February Morning Slot
Numerical
+4
-1
Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x = $$-$$1 and x = 1. If $$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^3}}} = 1$$, then $$5.f(2)$$ is equal to _________.
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