1
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$P,Q,R$$ and $$S$$ be the points on the plane with position vectors $${ - 2\widehat i - \widehat j,4\widehat i,3\widehat i + 3\widehat j}$$ and $${ - 3\widehat i + 2\widehat j}$$ respectively. The quadrilateral $$PQRS$$ must be a
A
parallelogram, which is neither a rhombus nor a rectangle
B
square
C
rectangle, but not a square
D
rhombus, but not a square
2
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Equation of the plane containing the straight line $${x \over 2} = {y \over 3} = {z \over 4}$$ and perpendicular to the plane containing the straight lines $${x \over 3} = {y \over 4} = {z \over 2}$$ and $${x \over 4} = {y \over 2} = {z \over 3}$$ is
A
$$x+2y-2z=0$$
B
$$3x+2y-2z=0$$
C
$$x-2y+z=0$$
D
$$5x+2y-4z=0$$
3
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Two adjacent sides of a parallelogram $$ABCD$$ are given by
$$\overrightarrow {AB} = 2\widehat i + 10\widehat j + 11\widehat k$$ and $$\,\overrightarrow {AD} = \widehat i + 2\widehat j + 2\widehat k$$
The side $$AD$$ is rotated by an acute angle $$\alpha$$ in the plane of the parallelogram so that $$AD$$ becomes $$AD'.$$ If $$AD'$$ makes a right angle with the side $$AB,$$ then the cosine of the angle $$\alpha$$ is given by
A
$${{8 \over 9}}$$
B
$${{{\sqrt {17} } \over 9}}$$
C
$${{1 \over 9}}$$
D
$${{{4\sqrt 5 } \over 9}}$$
4
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
If the distance of the point $$P(1, -2, 1)$$ from the plane $$x+2y-2z$$$$\, = \alpha ,$$ where $$\alpha > 0,$$ is $$5,$$ then the foot of the perpendicular from $$P$$ to the planes is
A
$$\left( {{8 \over 3},{4 \over 3}, - {7 \over 3}} \right)$$
B
$$\left( {{4 \over 3},-{4 \over 3}, {1 \over 3}} \right)$$
C
$$\left( {{1 \over 3},{2 \over 3}, {10 \over 3}} \right)$$
D
$$\left( {{2 \over 3},-{1 \over 3}, {5 \over 3}} \right)$$
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