1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Statement I :

Two forces $$\left( {\overrightarrow P + \overrightarrow Q } \right)$$ and $$\left( {\overrightarrow P - \overrightarrow Q } \right)$$ where $$\overrightarrow P \bot \overrightarrow Q$$, when act at an angle $$\theta$$1 to each other, the magnitude of their resultant is $$\sqrt {3({P^2} + {Q^2})}$$, when they act at an angle $$\theta$$2, the magnitude of their resultant becomes $$\sqrt {2({P^2} + {Q^2})}$$. This is possible only when $${\theta _1} < {\theta _2}$$.

Statement II :

In the situation given above.

$$\theta$$1 = 60$$^\circ$$ and $$\theta$$2 = 90$$^\circ$$

In the light of the above statements, choose the most appropriate answer from the options given below :-
A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are true
C
Statement I is true but Statement II is false
D
Both Statement I and Statement II are false.
2
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
The resultant of these forces $$\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS}$$ and $$\overrightarrow {OT}$$ is approximately .......... N.

[Take $$\sqrt 3 = 1.7$$, $$\sqrt 2 = 1.4$$ Given $$\widehat i$$ and $$\widehat j$$ unit vectors along x, y axis]

A
$$9.25\widehat i + 5\widehat j$$
B
$$3\widehat i + 15\widehat j$$
C
$$2.5\widehat i - 14.5\widehat j$$
D
$$- 1.5\widehat i - 15.5\widehat j$$
3
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The angle between vector $$\left( {\overrightarrow A } \right)$$ and $$\left( {\overrightarrow A - \overrightarrow B } \right)$$ is :

A
$${\tan ^{ - 1}}\left( {{{ - {B \over 2}} \over {A - B{{\sqrt 3 } \over 2}}}} \right)$$
B
$${\tan ^{ - 1}}\left( {{A \over {0.7B}}} \right)$$
C
$${\tan ^{ - 1}}\left( {{{\sqrt 3 B} \over {2A - B}}} \right)$$
D
$${\tan ^{ - 1}}\left( {{{B\cos \theta } \over {A - B\sin \theta }}} \right)$$
4
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The magnitude of vectors $$\overrightarrow {OA}$$, $$\overrightarrow {OB}$$ and $$\overrightarrow {OC}$$ in the given figure are equal. The direction of $$\overrightarrow {OA}$$ + $$\overrightarrow {OB}$$ $$-$$ $$\overrightarrow {OC}$$ with x-axis will be :

A
$${\tan ^{ - 1}}{{(1 - \sqrt 3 - \sqrt 2 )} \over {(1 + \sqrt 3 + \sqrt 2 )}}$$
B
$${\tan ^{ - 1}}{{(\sqrt 3 - 1 + \sqrt 2 )} \over {(1 + \sqrt 3 - \sqrt 2 )}}$$
C
$${\tan ^{ - 1}}{{(\sqrt 3 - 1 + \sqrt 2 )} \over {(1 - \sqrt 3 + \sqrt 2 )}}$$
D
$${\tan ^{ - 1}}{{(1 + \sqrt 3 - \sqrt 2 )} \over {(1 - \sqrt 3 - \sqrt 2 )}}$$
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