1
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
The value of $$x$$ for which $$sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}}\,x} \right)$$ is
A
$$1/2$$
B
$$1$$
C
$$0$$
D
$$-1/2$$
2
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$f\left( x \right) = {x^3} + b{x^2} + cx + d$$ and $$0 < {b^2} < c,$$ then in $$\left( { - \infty ,\infty } \right)$$
A
$$f\left( x \right)$$ is a strictly increasing function
B
$$f\left( x \right)$$ has a local maxima
C
$$f\left( x \right)$$ is a strictly decreasing function
D
$$f\left( x \right)$$ is bounded
3
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$f\left( x \right) = {x^a}\log x$$ and $$f\left( 0 \right) = 0,$$ then the value of $$\alpha $$ for which Rolle's theorem can be applied in $$\left[ {0,1} \right]$$ is
A
$$-2$$
B
$$-1$$
C
$$0$$
D
$$1/2$$
4
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+3
-0.75
The value of the integral $$\int\limits_0^1 {\sqrt {{{1 - x} \over {1 + x}}} dx} $$ is
A
$${\pi \over 2} + 1$$
B
$${\pi \over 2} - 1$$
C
$$-1$$
D
$$1$$
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