1
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$f\left( x \right) = x{e^{x\left( {1 - x} \right)}},$$ then $$f(x)$$ is
A
increasing on $$\left[ { - 1/2,1} \right]$$
B
decreasing on $$R$$
C
increasing on $$R$$
D
decreasing on $$\left[ { - 1/2,1} \right]$$
2
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+2
-0.5
The triangle formed by the tangent to the curve $$f\left( x \right) = {x^2} + bx - b$$ at the point $$(1, 1)$$ and the coordinate axex, lies in the first quadrant. If its area is $$2$$, then the value of $$b$$ is
A
$$-1$$
B
$$3$$
C
$$-3$$
D
$$1$$
3
IIT-JEE 2001 Screening
MCQ (Single Correct Answer)
+2
-0.5
Let $$f\left( x \right) = \left( {1 + {b^2}} \right){x^2} + 2bx + 1$$ and let $$m(b)$$ be the minimum value of $$f(x)$$. As $$b$$ varies, the range of $$m(b)$$ is
A
$$\left[ {0,1} \right]$$
B
$$\left( {0,\,1/2} \right]$$
C
$$\left[ {1/2,\,1} \right]$$
D
$$\left( {0,\,1} \right]$$
4
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
Consider the following statements in $$S$$ and $$R$$
$$S:$$ $$\,\,\,$$\$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interval $$\left( {{\pi \over 2},\pi } \right)$$
$$R:$$$$\,\,\,$$ If a differentiable function decreases in an interval $$(a, b)$$, then its derivative also decreases in $$(a, b)$$.
Which of the following is true ?
A
Both $$S$$ and $$R$$ are wrong
B
Both $$S$$ and $$R$$ are correct, but $$R$$ is not the correct explanation of $$S$$
C
$$S$$ is correct and $$R$$ is the correct explanation for $$S$$
D
$$S$$ is correct and $$R$$ is wrong
JEE Advanced Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEE
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Medical
NEET
© ExamGOAL 2023