1
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
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
2
IIT-JEE 1997
MCQ (Single Correct Answer)
+2
-0.5
If $$f\left( x \right) = {x \over {\sin x}}$$ and $$g\left( x \right) = {x \over {\tan x}}$$, where $$0 < x \le 1$$, then in this interval
A
both $$f(x)$$ and $$g(x)$$ are increasing functions
B
both $$f(x)$$ and $$g(x)$$ are decreasing functions
C
$$f(x)$$ is an increasing functions
D
$$g(x)$$ is an increasing functions
3
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+1
-0.25
The function $$f\left( x \right) = {{in\,\left( {\pi + x} \right)} \over {in\,\left( {e + x} \right)}}$$ is
A
increasing on $$\left( {0,\infty } \right)$$
B
decreasing on $$\left( {0,\infty } \right)$$
C
increasing on $$\left( {0,\pi /e} \right),$$ decreasing on $$\left( {\pi /e,\infty } \right)$$
D
decreasing on $$\left( {0,\pi /e} \right),$$ increasing on $$\left( {\pi /e,\infty } \right)$$
4
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+1
-0.25
On the interval $$\left[ {0,1} \right]$$ the function $${x^{25}}{\left( {1 - x} \right)^{75}}$$ takes its maximum value at the point
A
$$0$$
B
$${1 \over 4}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$
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