1
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+2
-0.5
How many moles of electron weigh one kilogram?
A
$$6.023 \times {10^{23}}$$
B
$${1 \over {9.108}} \times {10^{31}}$$
C
$${{6.023} \over {9.108}} \times {10^{54}}$$
D
$${1 \over {9.108 \times 6.023}} \times {10^8}$$
2
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+2
-0.5
The point(s) in the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are)
A
$$\left( { \pm {4 \over {\sqrt 3 }}, - 2} \right)$$
B
$$\left( { \pm \sqrt {{{11} \over 3}} ,1} \right)$$
C
$$(0,0)$$
D
$$\left( { \pm {4 \over {\sqrt 3 }}, 2} \right)$$
3
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow V = 2\overrightarrow i + \overrightarrow j - \overrightarrow k $$ and $$\overrightarrow W = \overrightarrow i + 3\overrightarrow k .$$ If $$\overrightarrow U $$ is a unit vector, then the maximum value of the scalar triple product $$\left| {\overrightarrow U \overrightarrow V \overrightarrow W } \right|$$ is
A
$$-1$$
B
$$\sqrt {10} + \sqrt 6 $$
C
$$\sqrt {59} $$
D
$$\sqrt {60} $$
4
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+4
-1
If $${\overrightarrow a }$$ and $${\overrightarrow b }$$ are two unit vectors such that $${\overrightarrow a + 2\overrightarrow b }$$ and $${5\overrightarrow a - 4\overrightarrow b }$$ are perpendicular to each other then the angle between $$\overrightarrow a $$ and $$\overrightarrow b $$ is
A
$${45^ \circ }$$
B
$${60^ \circ }$$
C
$${\cos ^{ - 1}}\left( {{1 \over 3}} \right)$$
D
$${\cos ^{ - 1}}\left( {{2 \over 7}} \right)$$
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