1

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
Let $$f\left( x \right) = \int {{e^x}\left( {x - 1} \right)\left( {x - 2} \right)dx.} $$ Then $$f$$ decreases in the interval
A
$$\left( { - \infty ,2} \right)$$
B
$$\left( { - 2, - 1} \right)$$
C
$$\left( {1,2} \right)$$
D
$$\left( {2, + \infty } \right)$$
2

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
3

IIT-JEE 1999

MCQ (Single Correct Answer)
The function $$f(x)=$$ $${\sin ^4}x + {\cos ^4}x$$ increases if
A
$$0 < x < \pi /8$$
B
$$\pi /4 < x < 3\pi /8$$
C
$$3\pi /8 < x < 5\pi /8$$
D
$$5\pi /8 < x < 3\pi /4$$
4

IIT-JEE 1998

MCQ (Single Correct Answer)
If $$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$ for every real number $$x$$, then the minimum value of $$f$$
A
does not exist because $$f$$ is unbounded
B
is not attained even though $$f$$ is bounded
C
is equal to 1
D
is equal to -1

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

Medical

NEET

CBSE

Class 12