1
JEE Main 2020 (Online) 4th September Morning Slot
Numerical
+4
-0
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 ______.
2
JEE Main 2020 (Online) 3rd September Morning Slot
Numerical
+4
-0
If $$\mathop {\lim }\limits_{x \to 0} \left\{ {{1 \over {{x^8}}}\left( {1 - \cos {{{x^2}} \over 2} - \cos {{{x^2}} \over 4} + \cos {{{x^2}} \over 2}\cos {{{x^2}} \over 4}} \right)} \right\}$$ = 2-k

then the value of k is _______ .
3
JEE Main 2020 (Online) 2nd September Morning Slot
Numerical
+4
-0
If $$\mathop {\lim }\limits_{x \to 1} {{x + {x^2} + {x^3} + ... + {x^n} - n} \over {x - 1}}$$ = 820,
(n $$\in$$ N) then the value of n is equal to _______.
4
JEE Main 2020 (Online) 7th January Evening Slot
Numerical
+4
-0
If the function ƒ defined on $$\left( { - {1 \over 3},{1 \over 3}} \right)$$ by

f(x) = $$\left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + 3x} \over {1 - 2x}}} \right),} & {when\,x \ne 0} \cr {k,} & {when\,x = 0} \cr } } \right.$$

is continuous, then k is equal to_______.