1

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
$$5\pi /8 < x < 3\pi /4$$
2

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
3

IIT-JEE 1998

MCQ (Single Correct Answer)
The number of values of $$x$$ where the function
$$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$ attains its maximum is
A
$$0$$
B
$$1$$
C
$$2$$
D
infinite
4

IIT-JEE 1997

MCQ (Single Correct Answer)
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

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