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

Subjective
Find all maxima and minima of the function $$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$, the $$y$$-axis and the line $$y-2$$. ## Answer $${{10 \over 3}}$$ sq. units 2 ### IIT-JEE 1988 Subjective Investigate for maxima and minimum the function $$f\left( x \right) = \int\limits_1^x {\left[ {2\left( {t - 1} \right){{\left( {t - 2} \right)}^3} + 3{{\left( {t - 1} \right)}^2}{{\left( {t - 2} \right)}^2}} \right]} dt$$$

min at $$x = {7 \over 5}$$
max at $$x = 1$$.
3

### IIT-JEE 1987

Subjective
Find the point on the curve $$\,\,\,4{x^2} + {a^2}{y^2} = 4{a^2},\,\,\,4 < {a^2} < 8$$
that is farthest from the point $$(0, -2)$$.

$$(0, 2)$$
4

### IIT-JEE 1985

Subjective
Let $$f\left( x \right) = {\sin ^3}x + \lambda {\sin ^2}x, - {\pi \over 2} < x < {\pi \over 2}.$$ Find the intervals in which $$\lambda$$ should lie in order that $$f(x)$$ has exactly one minimum and exactly one maximum.

$$\lambda \in \left( { - {3 \over 2},0} \right) \cup \left( {0,{3 \over 2}} \right)$$

### 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