1
AIPMT 2006
+4
-1
For angles of projection of a projectile at angle (45o $$-$$ $$\theta$$) and (45o + $$\theta$$), the horizontal range described by the projectile are in the ratio of
A
2 : 1
B
1 : 1
C
2 : 3
D
1 : 2.
2
AIPMT 2006
+4
-1
The vectors $$\overrightarrow A$$ and $$\overrightarrow B$$ are such that $$\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A - \overrightarrow B } \right|.$$ The angle between the two vectors is
A
45o
B
90o
C
60o
D
75o
3
AIPMT 2005
+4
-1
Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is
A
$${a \over {\sqrt {{v^2} + {v_1}^2} }}$$
B
$${a \over {v + {v_1}}}$$
C
$${a \over {v - {v_1}}}$$
D
$$\sqrt {{a \over {{v^2} - {v_1}^2}}}$$
4
AIPMT 2005
+4
-1
If the angle between the vectors $$\overrightarrow A$$ and $$\overrightarrow B$$ is $$\theta$$, the value of the product $$\left( {\overrightarrow B \times \overrightarrow A } \right).\overrightarrow A$$ is equal to
A
BA2sin$$\theta$$
B
BA2cos$$\theta$$
C
BA2sin$$\theta$$cos$$\theta$$
D
zero.
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