1
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let O be the origin. Let $$\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k$$ and $$\overrightarrow {OQ} = - \widehat i + 2\widehat j + 3x\widehat k$$, x, y$$\in$$R, x > 0, be such that $$\left| {\overrightarrow {PQ} } \right| = \sqrt {20} $$ and the vector $$\overrightarrow {OP} $$ is perpendicular $$\overrightarrow {OQ} $$. If $$\overrightarrow {OR} $$ = $$3\widehat i + z\widehat j - 7\widehat k$$, z$$\in$$R, is coplanar with $$\overrightarrow {OP} $$ and $$\overrightarrow {OQ} $$, then the value of x2 + y2 + z2 is equal to :
A
2
B
9
C
7
D
1
2
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the integral

$$\int_0^{10} {{{[\sin 2\pi x]} \over {{e^{x - [x]}}}}} dx = \alpha {e^{ - 1}} + \beta {e^{ - {1 \over 2}}} + \gamma $$, where $$\alpha$$, $$\beta$$, $$\gamma$$ are integers and [x] denotes the greatest integer less than or equal to x, then the value of $$\alpha$$ + $$\beta$$ + $$\gamma$$ is equal to :
A
0
B
10
C
20
D
25
3
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of the limit

$$\mathop {\lim }\limits_{\theta \to 0} {{\tan (\pi {{\cos }^2}\theta )} \over {\sin (2\pi {{\sin }^2}\theta )}}$$ is equal to :
A
0
B
$$-$$$${1 \over 2}$$
C
$${1 \over 4}$$
D
$$-$$$${1 \over 4}$$
4
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, $$\infty $$)
JEE Main Papers
2023
2021
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