1
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
$$1/2$$
2
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
$$1$$
3
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+3
-0.75
The area enclosed between the curves $$y = a{x^2}$$ and
$$x = a{y^2}\left( {a > 0} \right)$$ is $$1$$ sq. unit, then the value of $$a$$ is
A
$$1/\sqrt 3 $$
B
$$1/2$$
C
$$1$$
D
$$1/3$$
4
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+3
-0.75
If $$f(x)$$ is differentiable and $$\int\limits_0^{{t^2}} {xf\left( x \right)dx = {2 \over 5}{t^5},} $$ then $$f\left( {{4 \over {25}}} \right)$$ equals
A
$$2/5$$
B
$$-5/2$$
C
$$1$$
D
$$5/2$$
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