1
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
$${\tan ^{ - 1}}{{(1 + \sqrt 3 - \sqrt 2 )} \over {(1 - \sqrt 3 - \sqrt 2 )}}$$
2
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.
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Two vectors $$\overrightarrow X$$ and $$\overrightarrow Y$$ have equal magnitude. The magnitude of ($$\overrightarrow X$$ $$-$$ $$\overrightarrow Y$$) is n times the magnitude of ($$\overrightarrow X$$ + $$\overrightarrow Y$$). The angle between $$\overrightarrow X$$ and $$\overrightarrow Y$$ is :
A
$${\cos ^{ - 1}}\left( {{{ - {n^2} - 1} \over {{n^2} - 1}}} \right)$$
B
$${\cos ^{ - 1}}\left( {{{{n^2} - 1} \over { - {n^2} - 1}}} \right)$$
C
$${\cos ^{ - 1}}\left( {{{{n^2} + 1} \over { - {n^2} - 1}}} \right)$$
D
$${\cos ^{ - 1}}\left( {{{{n^2} + 1} \over {{n^2} - 1}}} \right)$$
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Match List - I with List - II

Choose the correct answer from the options given below :
A
(a) $$\to$$ (iv), (b) $$\to$$ (i), (c) $$\to$$ (iii), (d) $$\to$$ (ii)
B
(a) $$\to$$ (iv), (b) $$\to$$ (iii), (c) $$\to$$ (i), (d) $$\to$$ (ii)
C
(a) $$\to$$ (iii), (b) $$\to$$ (ii), (c) $$\to$$ (iv), (d) $$\to$$ (i)
D
(a) $$\to$$ (i), (b) $$\to$$ (iv), (c) $$\to$$ (ii), (d) $$\to$$ (iii)
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