1
IIT-JEE 2004 Screening
+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
+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
$$1/3$$
3
IIT-JEE 2004 Screening
+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
$$5/2$$
4
IIT-JEE 2003 Screening
+3
-0.75
If $$l\left( {m,n} \right) = \int\limits_0^1 {{t^m}{{\left( {1 + t} \right)}^n}dt,}$$ then the expression for $$l(m, n)$$ in terms of $$l(m+n, n-1)$$ is
A
$${{{2^n}} \over {m + 1}} - {n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
B
$${n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
C
$${{{2^n}} \over {m + 1}} + {n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
D
$${m \over {n + 1}}l\left( {m + 1,n - 1} \right)$$
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