1
IIT-JEE 2011 Paper 2 Offline
Numerical
+4
-0
The number of distinct real roots of $${x^4} - 4{x^3} + 12{x^2} + x - 1 = 0$$
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2
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
A value of $$b$$ for which the equations $$$\matrix{ {{x^2} + bx - 1 = 0} \cr {{x^2} + x + b = 0} \cr } $$$

have one root in common is

A
$$ - \sqrt 2 $$
B
$$ - i\sqrt 3$$
C
$$i\sqrt 5 $$
D
$$\sqrt 2 $$
3
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+2
-0.5
The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.
A
$$\left( { - {3 \over 0},0} \right)$$
B
$$\left( { - {5 \over 2},2} \right)$$
C
$$\left( { - {3 \over 0},\,{5 \over 2}} \right)$$
D
(- 4, 0)
4
IIT-JEE 2011 Paper 2 Offline
Numerical
+2
-0
The straight line 2x - 3y = 1 divides the circular region $${x^2}\, + \,{y^2}\, \le \,6$$ into two parts.
If $$S = \left\{ {\left( {2,\,{3 \over 4}} \right),\,\left( {{5 \over 2},\,{3 \over 4}} \right),\,\left( {{1 \over 4} - \,{1 \over 4}} \right),\,\left( {{1 \over 8},\,{1 \over 4}} \right)} \right\}$$ then the number of points (s) in S lying inside the smaller part is
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