1
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
$${{{4\sqrt 5 } \over 9}}$$
2
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
$$\left( {{2 \over 3},-{1 \over 3}, {5 \over 3}} \right)$$
3
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-0
Match the statement in Column-$$I$$ with the values in Column-$$II$$

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column-$$I$$
(A)$$\,\,\,\,$$ A line from the origin meets the lines $$\,{{x - 2} \over 1} = {{y - 1} \over { - 2}} = {{z + 1} \over 1}$$
and $${{x - {8 \over 3}} \over 2} = {{y + 3} \over { - 1}} = {{z - 1} \over 1}$$ at $$P$$ and $$Q$$ respectively. If length $$PQ=d,$$ then $${d^2}$$ is
(B)$$\,\,\,\,$$ The values of $$x$$ satisfying $${\tan ^{ - 1}}\left( {x + 3} \right) - {\tan ^{ - 1}}\left( {x - 3} \right) = {\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ are
(C)$$\,\,\,\,$$ Non-zero vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c \,\,$$ satisfy $$\overrightarrow a \,.\,\overrightarrow b \, = 0.$$
$$\left( {\overrightarrow b - \overrightarrow a } \right).\left( {\overrightarrow b + \overrightarrow c } \right) = 0$$ and $$2\left| {\overrightarrow b + \overrightarrow c } \right| = \left| {\overrightarrow b - \overrightarrow a } \right|.$$
If $$\overrightarrow a = \mu \overrightarrow b + 4\overrightarrow c \,\,,$$ then the possible values of $$\mu$$ are
(D)$$\,\,\,\,$$ Let $$f$$ be the function on $$\left[ { - \pi ,\pi } \right]$$ given by $$f(0)=9$$
and $$f\left( x \right) = \sin \left( {{{9x} \over 2}} \right)/\sin \left( {{x \over 2}} \right)$$ for $$x \ne 0$$
The value of $${2 \over \pi }\int_{ - \pi }^\pi {f\left( x \right)dx}$$ is

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$Column-$$II$$
(p)$$\,\,\,\,$$ $$-4$$
(q)$$\,\,\,\,$$ $$0$$
(r)$$\,\,\,\,$$ $$4$$
(s)$$\,\,\,\,$$ $$5$$
(t)$$\,\,\,\,$$ $$6$$

A
$$\left( A \right) \to t;\,\,\left( B \right) \to p,r;\,\,\left( C \right) \to q,s;\,\,\left( D \right) \to r$$
B
$$\left( A \right) \to r;\,\,\left( B \right) \to p;\,\,\left( C \right) \to q,s;\,\,\left( D \right) \to r$$
C
$$\left( A \right) \to t;\,\,\left( B \right) \to p,r;\,\,\left( C \right) \to q;\,\,\left( D \right) \to r$$
D
$$\left( A \right) \to t;\,\,\left( B \right) \to r;\,\,\left( C \right) \to q,s;\,\,\left( D \right) \to r$$
4
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is
A
0.02 mm
B
0.05 mm
C
0.1 mm
D
0.2 mm
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