1
JEE Main 2021 (Online) 24th February Morning Shift
Numerical
+4
-1
Change Language
$$\mathop {\lim }\limits_{n \to \infty } \tan \left\{ {\sum\limits_{r = 1}^n {{{\tan }^{ - 1}}\left( {{1 \over {1 + r + {r^2}}}} \right)} } \right\}$$ is equal to ______.
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2
JEE Main 2020 (Online) 6th September Morning Slot
Numerical
+4
-0
Change Language
Let f : R $$ \to $$ R be defined as
$$f\left( x \right) = \left\{ {\matrix{ {{x^5}\sin \left( {{1 \over x}} \right) + 5{x^2},} & {x < 0} \cr {0,} & {x = 0} \cr {{x^5}\cos \left( {{1 \over x}} \right) + \lambda {x^2},} & {x > 0} \cr } } \right.$$

The value of $$\lambda $$ for which f ''(0) exists, is _______.
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3
JEE Main 2020 (Online) 5th September Morning Slot
Numerical
+4
-0
Change Language
Let $$f(x) = x.\left[ {{x \over 2}} \right]$$, for -10< x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to _____.
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4
JEE Main 2020 (Online) 4th September Morning Slot
Numerical
+4
-0
Change Language
Suppose a differentiable function f(x) satisfies the identity
f(x+y) = f(x) + f(y) + xy2 + x2y, for all real x and y.
$$\mathop {\lim }\limits_{x \to 0} {{f\left( x \right)} \over x} = 1$$, then f'(3) is equal to ______.
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