1
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Let $$f:[0,3] \to R$$ be defined by $$f(x) = \min \{ x - [x],1 + [x] - x\}$$ where [x] is the greatest integer less than or equal to x. Let P denote the set containing all x $$\in$$ [0, 3] where f i discontinuous, and Q denote the set containing all x $$\in$$ (0, 3) where f is not differentiable. Then the sum of number of elements in P and Q is equal to ______________.
2
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
Consider the function

where P(x) is a polynomial such that P'' (x) is always a constant and P(3) = 9. If f(x) is continuous at x = 2, then P(5) is equal to _____________.
3
JEE Main 2021 (Online) 22th July Evening Shift
Numerical
+4
-1
Let f : R $$\to$$ R be a function defined as $$f(x) = \left\{ {\matrix{ {3\left( {1 - {{|x|} \over 2}} \right)} & {if} & {|x|\, \le 2} \cr 0 & {if} & {|x|\, > 2} \cr } } \right.$$

Let g : R $$\to$$ R be given by $$g(x) = f(x + 2) - f(x - 2)$$. If n and m denote the number of points in R where g is not continuous and not differentiable, respectively, then n + m is equal to ______________.
4
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
Let a function g : [ 0, 4 ] $$\to$$ R be defined as

$$g(x) = \left\{ {\matrix{ {\mathop {\max }\limits_{0 \le t \le x} \{ {t^3} - 6{t^2} + 9t - 3),} & {0 \le x \le 3} \cr {4 - x,} & {3 < x \le 4} \cr } } \right.$$, then the number of points in the interval (0, 4) where g(x) is NOT differentiable, is ____________.