1
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
$$\left( -{3\sqrt 3 , 2\sqrt 2 } \right)$$
2
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
Let $$S$$ be the focus of the parabola $${y^2} = 8x$$ and let $$PQ$$ be the common chord of the circle $${x^2} + {y^2} - 2x - 4y = 0$$ and the given parabola. The area of the triangle $$PQS$$ is
Your input ____
3
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
Let $$f:IR \to IR$$ be defined as $$f\left( x \right) = \left| x \right| + \left| {{x^2} - 1} \right|.$$ The total number of points at which $$f$$ attains either a local maximum or a local minimum is
Your input ____
4
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
Let $$p(x)$$ be a real polynomial of least degree which has a local maximum at $$x=1$$ and a local minimum at $$x=3$$. If $$p(1)=6$$ and $$p(3)=2$$, then $$p'(0)$$ is
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