1
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
If $${{w - \overline w z} \over {1 - z}}$$ is purely real where $$w = \alpha + i\beta ,$$ $$\beta \ne 0$$ and $$z \ne 1,$$ then the set of the values of z is
A
$$\left\{ {z:\left| z \right| = 1} \right\}$$
B
$$\left\{ {z:z = \overline z } \right\}$$
C
$$\left\{ {z:z \ne 1} \right\}\,\,$$
D
$$\left\{ {z:\left| z \right| = 1,z \ne 1} \right\}$$
2
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
Let $$a,\,b,\,c$$ be the sides of triangle where $$a \ne b \ne c$$ and $$\lambda \in R$$.
If the roots of the equation $${x^2} + 2\left( {a + b + c} \right)x + 3\lambda \left( {ab + bc + ca} \right) = 0$$ are real, then
A
$$\lambda < {4 \over 3}$$
B
$$\lambda > {5 \over 3}$$
C
$$\lambda \in \left( {{1 \over 3},\,{5 \over 3}} \right)$$
D
$$\lambda \in \left( {{4 \over 3},\,{5 \over 3}} \right)$$
3
IIT-JEE 2006
Subjective
+6
-0
Let $$a$$ and $$b$$ be the roots of the equation $${x^2} - 10cx - 11d = 0$$ and those $${x^2} - 10ax - 11b = 0$$ are $$c$$, $$d$$ then the value of $$a + b + c + d,$$ when $$a \ne b \ne c \ne d,$$ is
4
IIT-JEE 2006
Subjective
+6
-0
If $${a_n} = {3 \over 4} - {\left( {{3 \over 4}} \right)^2} + {\left( {{3 \over 4}} \right)^3} + ....{( - 1)^{n - 1}}{\left( {{3 \over 4}} \right)^n}\,\,and\,\,{b_n} = 1 - {a_n},$$, then find the least natural number $${n_0}$$ such that $${b_n}\,\, > \,\,{a_n}\,\forall \,n\,\, \ge \,\,{n_0}$$.
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