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 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If $$f$$ and $$g$$ are differentiable functions in $$\left[ {0,1} \right]$$ satisfying
$$f\left( 0 \right) = 2 = g\left( 1 \right),g\left( 0 \right) = 0$$ and $$f\left( 1 \right) = 6,$$ then for some $$c \in \left] {0,1} \right[$$
A
$$f'\left( c \right) = g'\left( c \right)$$
B
$$f'\left( c \right) = 2g'\left( c \right)$$
C
$$2f'\left( c \right) = g'\left( c \right)$$
D
$$2f'\left( c \right) = 3g'\left( c \right)$$
3
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.
4
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
$$\pm 4$$
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