1
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
If $$x=-1$$ and $$x=2$$ are extreme points of $$f\left( x \right) = \alpha \,\log \left| x \right|+\beta {x^2} + x$$ then
A
$$\alpha = 2,\beta = - {1 \over 2}$$
B
$$\alpha = 2,\beta = {1 \over 2}$$
C
$$\alpha = - 6,\beta = {1 \over 2}$$
D
$$\alpha = - 6,\beta = -{1 \over 2}$$
2
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \right]$$
A
lies between 1 and 2
B
lies between 2 and 3
C
lies between $$ - 1$$ and 0
D
does not exist.
3
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The intercepts on $$x$$-axis made by tangents to the curve,
$$y = \int\limits_0^x {\left| t \right|dt,x \in R,} $$ which are parallel to the line $$y=2x$$, are equal to :
A
$$ \pm 1$$
B
$$ \pm 2$$
C
$$ \pm 3$$
D
$$ \pm 4$$
4
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0$$ has extreme values at $$x=-1$$ and $$x=2$$

Statement-1 : $$f$$ has local maximum at $$x=-1$$ and at $$x=2$$.

Statement-2 : $$a = {1 \over 2}$$ and $$b = {-1 \over 4}$$

A
Statement - 1 is false, Statement - 2 is true.
B
Statement - 1 is true , Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
C
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
D
Statement - 1 is true, Statement - 2 is false.
JEE Main Subjects
EXAM MAP