1
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
$$1$$
2
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
$$5/2$$
3
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$y=y(x)$$ and $${{2 + \sin x} \over {y + 1}}\left( {{{dy} \over {dx}}} \right) = - \cos x,y\left( 0 \right) = 1,$$
then $$y\left( {{\pi \over 2}} \right)$$ equals
A
$$1/3$$
B
$$2/3$$
C
$$-1/3$$
D
$$1$$
4
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
If three distinct numbers are chosen randomly from the first $$100$$ natural numbers, then the probability that all three of them are divisible by both $$2$$ and $$3$$ is
A
$$4/25$$
B
$$4/35$$
C
$$4/33$$
D
$$4/1155$$
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