1
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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, $$\infty $$)
2
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let L be a tangent line to the parabola y2 = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$$, then the value of b is equal to :
A
20
B
14
C
16
D
11
3
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of $$\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}$$, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :
A
r
B
$${r \over 2}$$
C
0
D
2r
4
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If x, y, z are in arithmetic progression with common difference d, x $$\ne$$ 3d, and the determinant of the matrix $$\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]$$ is zero, then the value of k2 is :
A
72
B
12
C
36
D
6
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