1
IIT-JEE 1980
Subjective
+4
-0
For what values of $$m,$$ does the system of equations $$\matrix{ {3x + my = m} \cr {2x - 5y = 20} \cr }$$$has solution satisfying the conditions $$x > 0,\,y > 0.$$ 2 IIT-JEE 1980 Subjective +4 -0 Find the solution set of the system $$\matrix{ {x + 2y + z = 1;} \cr {2x - 3y - w = 2;} \cr {x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr }$$$
3
IIT-JEE 1979
Subjective
+4
-0
If $$\alpha ,\,\beta$$ are the roots of $${x^2} + px + q = 0$$ and $$\gamma ,\,\delta$$ are the roots of $${x^2} + rx + s = 0,$$ evaluate $$\left( {\alpha - \gamma } \right)\left( {\alpha - \delta } \right)\left( {\beta - \gamma } \right)$$ $$\left( {\beta - \delta } \right)$$ in terms of $$p,\,q,\,r$$ and $$s$$.

deduce the condition that the equations have a common root.

4
IIT-JEE 1978
Subjective
+4
-0
If $$\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n + 1}}} \right)} \over {\left( {1 - x} \right)\left( {1 - {x^2}} \right).........\left( {1 - {x^n}} \right)}}$$

where $$m$$ and $$n$$ are positive integers $$\left( {n \le m} \right),$$ show that
$$\left( {m,n + 1} \right) = \left( {m - 1,\,n + 1} \right) + {x^{m - n - 1}}\left( {m - 1,n} \right).$$

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