1
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
The sum of all the local minimum values of the twice differentiable function f : R $$\to$$ R defined by $$f(x) = {x^3} - 3{x^2} - {{3f''(2)} \over 2}x + f''(1)$$ is :
A
$$-$$22
B
5
C
$$-$$27
D
0
2
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let $$A = [{a_{ij}}]$$ be a 3 $$\times$$ 3 matrix, where $${a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr { - x} & , & {if\,\left| {i - j} \right| = 1} \cr {2x + 1} & , & {otherwise.} \cr } } \right.$$

Let a function f : R $$\to$$ R be defined as f(x) = det(A). Then the sum of maximum and minimum values of f on R is equal to:
A
$$- {{20} \over {27}}$$
B
$${{88} \over {27}}$$
C
$${{20} \over {27}}$$
D
$$- {{88} \over {27}}$$
3
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let 'a' be a real number such that the function f(x) = ax2 + 6x $$-$$ 15, x $$\in$$ R is increasing in $$\left( { - \infty ,{3 \over 4}} \right)$$ and decreasing in $$\left( {{3 \over 4},\infty } \right)$$. Then the function g(x) = ax2 $$-$$ 6x + 15, x$$\in$$R has a :
A
local maximum at x = $$-$$ $${{3 \over 4}}$$
B
local minimum at x = $$-$$$${{3 \over 4}}$$
C
local maximum at x = $${{3 \over 4}}$$
D
local minimum at x = $${{3 \over 4}}$$
4
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Consider the function f : R $$\to$$ R defined by

$$f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.$$. Then f is :
A
not monotonic on ($$-$$$$\infty$$, 0) and (0, $$\infty$$)
B
monotonic on (0, $$\infty$$) only
C
monotonic on ($$-$$$$\infty$$, 0) only
D
monotonic on ($$-$$$$\infty$$, 0) $$\cup$$ (0, $$\infty$$)
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