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1

### IIT-JEE 1985

Subjective
Find all the tangents to the curve
$$y = \cos \left( {x + y} \right),\,\, - 2\pi \le x \le 2\pi ,$$ that are parallel to the line $$x+2y=0$$.

$$2x + 4y - \pi = 0$$
$$2x + 4y + 3\pi = 0$$
2

### IIT-JEE 1983

Subjective
Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$
where the tangent to the curve has the greatest slope.

$$(0. 0)$$
3

### IIT-JEE 1983

Subjective
Show that $$1+x$$ $$In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}}$$ for all $$x \ge 0$$

Solve it.
4

### IIT-JEE 1982

Subjective
If $$a{x^2} + {b \over x} \ge c$$ for all positive $$x$$ where $$a>0$$ and $$b>0$$ show that $$27a{b^2} \ge 4{c^3}$$.

Solve it.

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12