1
IIT-JEE 2003
Subjective
+4
-0
If $${x^2} + \left( {a - b} \right)x + \left( {1 - a - b} \right) = 0$$ where $$a,\,b\, \in \,R$$ then find the values of a for which equation has unequal real roots for all values of $$b$$.
2
IIT-JEE 2003
Subjective
+2
-0
Prove that there exists no complex number z such that $$\left| z \right| < {1 \over 3}\,and\,\sum\limits_{r = 1}^n {{a_r}{z^r}} = 1$$ where $$\left| {{a_r}} \right| < 2$$.
3
IIT-JEE 2003
Subjective
+2
-0
If nth divisions of the main scale coincide with (n+1)th divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.
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