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1

IIT-JEE 1980

Subjective
Find the solution set of the system $$$\matrix{ {x + 2y + z = 1;} \cr {2x - 3y - w = 2;} \cr {x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr } $$$

Answer

$$x = 1,\,y = 0,\,z = 0,\,w = 0$$
2

IIT-JEE 1980

Subjective
For what values of $$m,$$ does the system of equations $$$\matrix{ {3x + my = m} \cr {2x - 5y = 20} \cr } $$$

has solution satisfying the conditions $$x > 0,\,y > 0.$$

Answer

$$m \in \left( { - \alpha ,\, - {{15} \over 2}} \right) \cup \left( {30,\,\alpha } \right)$$
3

IIT-JEE 1980

Subjective
Given $${n^4} < {10^n}$$ for a fixed positive integer $$n \ge 2,$$ prove that $${\left( {n + 1} \right)^4} < {10^{n + 1}}.$$

Answer

Solve it.
4

IIT-JEE 1980

Subjective
Let $$y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}} $$

Find all the real values of $$x,$$ for which $$y$$ takes real values.

Answer

$$\left[ { - 1,\left. 1 \right)\, \cup \left[ {3,\left. \alpha \right)} \right.} \right.$$

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