1
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
$$- 1.5\widehat i - 15.5\widehat j$$
2
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
$${\tan ^{ - 1}}\left( {{{B\cos \theta } \over {A - B\sin \theta }}} \right)$$
3
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
$${\tan ^{ - 1}}{{(1 + \sqrt 3 - \sqrt 2 )} \over {(1 - \sqrt 3 - \sqrt 2 )}}$$
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that $$\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|$$, then $$\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} = 4\overrightarrow {AO} + \overrightarrow {OB} + \overrightarrow {OC}$$

Reason R : Polygon law of vector addition yields $$\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CD} + \overrightarrow {AD} = 2\overrightarrow {AO}$$

In the light of the above statements, choose the most appropriate answer from the options given below :
A
A is correct but R is not correct.
B
A is not correct but R is correct.
C
Both A and R are correct and R is the correct explanation of A.
D
Both A and R are correct but R is not the correct explanation of A.
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