1
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow a = \overrightarrow i - \overrightarrow k ,\overrightarrow b = x\overrightarrow i + \overrightarrow j + \left( {1 - x} \right)\overrightarrow k $$ and
$$\overrightarrow c = y\overrightarrow i - x\overrightarrow j + \left( {1 + x - y} \right)\overrightarrow k .$$ Then $$\left[ {\overrightarrow a \,\overrightarrow b \,\overrightarrow c } \right]$$ depends on
A
only $$x$$
B
only $$y$$
C
Neither $$x$$ Nor $$y$$
D
both $$x$$ and $$y$$
2
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+4
-1
If $$\overrightarrow a \,,\,\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors, then $${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2}$$ does NOT exceed
A
$$4$$
B
$$9$$
C
$$8$$
D
$$6$$
3
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+2
-0.5
A man from the top of a $$100$$ metres high tower sees a car moving towards the tower at an angle of depression of $${30^ \circ }$$. After some time,the angle of depression becomes $${60^ \circ }$$. The distance (in metres) travelled by the car during this time is
A
$$100\sqrt 3 $$
B
$$200\sqrt 3 /3$$
C
$$100\sqrt 3 /3$$
D
$$200\sqrt 3 $$
4
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+2
-0.5
If the sum of the first $$2n$$ terms of the A.P.$$2,5,8,......,$$ is equal to the sum of the first $$n$$ terms of the A.P.$$57,59,61,.....,$$ then $$n$$ equals
A
10
B
12
C
11
D
13
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