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1
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
If $$\mathop {\lim }\limits_{x \to 0} {{a{e^x} - b\cos x + c{e^{ - x}}} \over {x\sin x}} = 2$$, then a + b + c is equal to ____________.
2
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 ___________.
3
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 __________.
f(x) = | 2x + 1 | $$-$$ 3| x + 2 | + | x2 + x $$-$$ 2 |, x$$\in$$R is not differentiable, is __________.