1
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
If $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors satisfying
$${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2} = 9,$$ then $$\left| {2\overrightarrow a + 5\overrightarrow b + 5\overrightarrow c } \right|$$ is
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2
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Tangents are drawn to the hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,$$ parallel to the straight line $$2x - y = 1,$$ The points of contact of the tangents on the hyperbola are
A
$$\left( {{9 \over {2\sqrt 2 }},{1 \over {\sqrt 2 }}} \right)$$
B
$$\left( -{{9 \over {2\sqrt 2 }},-{1 \over {\sqrt 2 }}} \right)$$
C
$$\left( {3\sqrt 3 , - 2\sqrt 2 } \right)$$
D
$$\left( -{3\sqrt 3 , 2\sqrt 2 } \right)$$
3
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$\theta ,\,\varphi \, \in \,\left[ {0,2\pi } \right]$$ be such that
$$2\cos \theta \left( {1 - \sin \,\varphi } \right) = {\sin ^2}\theta \,\,\left( {\tan {\theta \over 2} + \cot {\theta \over 2}} \right)\cos \varphi - 1,\,\tan \left( {2\pi - \theta } \right) > 0$$ and $$ - 1 < \sin \theta \, < - {{\sqrt 3 } \over 2},$$

then $$\varphi $$ cannot satisfy

A
$$0 < \varphi < {\pi \over 2}$$
B
$${\pi \over 2} < \varphi < {{4\pi } \over 3}$$
C
$${{4\pi } \over 3} < \varphi < {{3\pi } \over 2}$$
D
$${{3\pi } \over 2} < \varphi < 2\pi $$
4
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is
A
75
B
150
C
210
D
243
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