1
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1 If $$\mathop {\lim }\limits_{x \to 1} {{\sin (3{x^2} - 4x + 1) - {x^2} + 1} \over {2{x^3} - 7{x^2} + ax + b}} = - 2$$, then the value of (a $$-$$ b) is equal to ___________.

2
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1 Let $$f(x) = \left[ {2{x^2} + 1} \right]$$ and $$g(x) = \left\{ {\matrix{ {2x - 3,} & {x < 0} \cr {2x + 3,} & {x \ge 0} \cr } } \right.$$, where [t] is the greatest integer $$\le$$ t. Then, in the open interval ($$-$$1, 1), the number of points where fog is discontinuous is equal to ______________.

3
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
Let $$f(x) = {x^6} + 2{x^4} + {x^3} + 2x + 3$$, x $$\in$$ R. Then the natural number n for which $$\mathop {\lim }\limits_{x \to 1} {{{x^n}f(1) - f(x)} \over {x - 1}} = 44$$ is __________.
4
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
Let [t] denote the greatest integer $$\le$$ t. The number of points where the function $$f(x) = [x]\left| {{x^2} - 1} \right| + \sin \left( {{\pi \over {[x] + 3}}} \right) - [x + 1],x \in ( - 2,2)$$ is not continuous is _____________.
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