NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
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 $$x+2y=0$$.

Answer

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

Answer

$$(0. 0)$$
3

IIT-JEE 1983

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

Answer

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 $$27a{b^2} \ge 4{c^3}$$.

Answer

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

Medical

NEET

CBSE

Class 12