1
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+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
$${m \over {n + 1}}l\left( {m + 1,n - 1} \right)$$
2
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+4
-1
The value of $$'a'$$ so that the volume of parallelopiped formed by $$\widehat i + a\widehat j + \widehat k,\widehat j + a\widehat k$$ and $$a\widehat i + \widehat k$$ becomes minimum is
A
$$-3$$
B
$$3$$
C
$$1/\sqrt 3 $$
D
$$\sqrt 3 $$
3
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+4
-1
The value of $$k$$ such that $${{x - 4} \over 1} = {{y - 2} \over 1} = {{z - k} \over 2}$$ lies in the plane $$2x -4y +z = 7,$$ is
A
$$7$$
B
$$-7$$
C
no real value
D
$$4$$
4
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$P\left( B \right) = {3 \over 4},P\left( {A \cap B \cap \overline C } \right) = {1 \over 3}$$ and
$$P\left( {\overline A \cap B \cap \overline C } \right) = {1 \over 3},\,\,$$ then $$P\left( {B \cap C} \right)$$ is
A
$$1/12$$
B
$$1/6$$
C
$$1/15$$
D
$$1/9$$
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