1
IIT-JEE 2012 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

Let $$\alpha$$(a) and $$\beta$$(a) be the roots of the equation $$(\root 3 \of {1 + a} - 1){x^2} + (\sqrt {1 + a} - 1)x + (\root 6 \of {1 + a} - 1) = 0$$ where $$a > - 1$$. Then $$\mathop {\lim }\limits_{a \to {0^ + }} \alpha (a)$$ and $$\mathop {\lim }\limits_{a \to {0^ + }} \beta (a)$$ are

A
$$ - {5 \over 2}$$
B
$$ - {1 \over 2}$$
C
$$ - {7 \over 2}$$
D
$$ - {9 \over 2}$$
2
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$\alpha $$ and $$\beta $$ be the roots of $${x^2} - 6x - 2 = 0,$$ with $$\alpha > \beta .$$ If $${a_n} = {\alpha ^n} - {\beta ^n}$$ for $$\,n \ge 1$$ then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is
A
1
B
2
C
3
D
4
3
IIT-JEE 2011 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$\left( {{x_0},{y_0}} \right)$$ be the solution of the following equations
$$\matrix{ {{{\left( {2x} \right)}^{\ell n2}}\, = {{\left( {3y} \right)}^{\ell n3}}} \cr {{3^{\ell nx}}\, = {2^{\ell ny}}} \cr } $$
Then $${x_0}$$ is
A
$${1 \over 6}$$
B
$${1 \over 3}$$
C
$${1 \over 2}$$
D
$$6$$
4
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
$$\sqrt 2 $$
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