1
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_0^1 {{{{x^4}{{\left( {1 - x} \right)}^4}} \over {1 + {x^2}}}dx} $$ is (are)
A
$${{22} \over 7} - \pi $$
B
$${2 \over {105}}$$
C
$$0$$
D
$${{71} \over {15}} - {{3\pi } \over 2}$$
2
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
The value of $$\mathop {\lim }\limits_{x \to 0} {1 \over {{x^3}}}\int\limits_0^x {{{t\ln \left( {1 + t} \right)} \over {{t^4} + 4}}} dt$$ is
A
$$0$$
B
$${1 \over 12}$$
C
$${1 \over 24}$$
D
$${1 \over 64}$$
3
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$ABC$$ be a triangle such that $$\angle ACB = {\pi \over 6}$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposite to $$A$$, $$B$$ and $$C$$ respectively. The value(s) of $$x$$ for which $$a = {x^2} + x + 1,\,\,\,b = {x^2} - 1\,\,\,$$ and $$c = 2x + 1$$ is (are)
A
$$ - \left( {2 + \sqrt 3 } \right)$$
B
$${1 + \sqrt 3 }$$
C
$${2 + \sqrt 3 }$$
D
$${4 \sqrt 3 }$$
4
IIT-JEE 2010 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

The number of $3 \times 3$ matrices A whose entries are either 0 or 1 and for which the system

$\mathrm{A}\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is

A
0
B
$2^9-1$
C
168
D
2
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