1
AIPMT 2005
MCQ (Single Correct Answer)
+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
$$\sqrt {{a \over {{v^2} - {v_1}^2}}} $$
2
AIPMT 2005
MCQ (Single Correct Answer)
+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.
3
AIPMT 2005
MCQ (Single Correct Answer)
+4
-1
If a vector $$2\widehat i + 3\widehat j + 8\widehat k$$ is perpendicular to the vector $$4\widehat j - 4\widehat i + \alpha \widehat k,$$ then the value of $$\alpha $$ is
A
1/2
B
$$-$$ 1/2
C
1
D
$$-$$ 1.
4
AIPMT 2004
MCQ (Single Correct Answer)
+4
-1
If $$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \overrightarrow A .\overrightarrow B $$ then the value of $$\left| {\overrightarrow A + \overrightarrow B } \right|$$ is
A
(A2 + b2 + AB)1/2
B
$${\left( {{A^2} + {B^2} + {{AB} \over {\sqrt 3 }}} \right)^{1/2}}$$
C
A + B
D
(A2 + B2 + $${\sqrt 3 }$$AB)1/2.
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