1
IIT-JEE 2003
Subjective
+2
-0
Find a point on the curve $${x^2} + 2{y^2} = 6$$ whose distance from
the line $$x+y=7$$, is minimum.
2
IIT-JEE 2003
Subjective
+4
-0
Using the relation $$2\left( {1 - \cos x} \right) < {x^2},\,x \ne 0$$ or otherwise,
prove that $$\sin \left( {\tan x} \right) \ge x,\,\forall x \in \left[ {0,{\pi \over 4}} \right]$$
3
IIT-JEE 2001
Subjective
+5
-0
Let $$ - 1 \le p \le 1$$. Show that the equation $$4{x^3} - 3x - p = 0$$
has a unique root in the interval $$\left[ {1/2,\,1} \right]$$ and identify it.
4
IIT-JEE 2000
Subjective
+5
-0
Suppose $$p\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + .......... + {a_n}{x^n}.$$ If
$$\left| {p\left( x \right)} \right| \le \left| {{e^{x - 1}} - 1} \right|$$ for all $$x \ge 0$$, prove that
$$\left| {{a_1} + 2{a_2} + ........ + n{a_n}} \right| \le 1$$.
JEE Advanced Subjects
EXAM MAP