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1

IIT-JEE 1982

Subjective
Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real solution.

Answer

Solve it.
2

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

$$x = 1,\,y = 0,\,z = 0,\,w = 0$$
3

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

$$m \in \left( { - \alpha ,\, - {{15} \over 2}} \right) \cup \left( {30,\,\alpha } \right)$$
4

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.

Joint Entrance Examination

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Graduate Aptitude Test in Engineering

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Medical

NEET

CBSE

Class 12