1
IIT-JEE 1980
Subjective
+4
-0
Given $${n^4} < {10^n}$$ for a fixed positive integer $$n \ge 2,$$ prove that $${\left( {n + 1} \right)^4} < {10^{n + 1}}.$$
2
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 $$x > 0,\,y > 0.$$
3
IIT-JEE 1980
Subjective
+4
-0
Find the solution set of the system
$$$\matrix{
{x + 2y + z = 1;} \cr
{2x - 3y - w = 2;} \cr
{x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr
} $$$
4
IIT-JEE 1980
Subjective
+4
-0
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.
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Questions Asked from Quadratic Equation and Inequalities (Subjective)
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