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1

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
2

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

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
4

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

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Class 12