1
JEE Main 2020 (Online) 5th September Morning Slot
Numerical
+4
-0
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 _____.
2
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 ______.
3
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 _______ .
4
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 _______.