1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The set of points where $$f\left( x \right) = {x \over {1 + \left| x \right|}}$$ is differentiable is
A
$$\left( { - \infty ,0} \right) \cup \left( {0,\infty } \right)$$
B
$$\left( { - \infty ,1} \right) \cup \left( { - 1,\infty } \right)$$
C
$$\left( { - \infty ,\infty } \right)$$
D
$$\left( {0,\infty } \right)$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If $${x^m}.{y^n} = {\left( {x + y} \right)^{m + n}},$$ then $${{{dy} \over {dx}}}$$ is
A
$${y \over x}$$
B
$${{x + y} \over {xy}}$$
C
$$xy$$
D
$${x \over y}$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Let $$f:R \to R$$ be a differentiable function having $$f\left( 2 \right) = 6$$,
$$f'\left( 2 \right) = \left( {{1 \over {48}}} \right)$$. Then $$\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt} $$ equals
A
$$24$$
B
$$36$$
C
$$12$$
D
$$18$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The value of $$a$$ for which the sum of the squares of the roots of the equation $${x^2} - \left( {a - 2} \right)x - a - 1 = 0$$ assume the least value is
A
$$1$$
B
$$0$$
C
$$3$$
D
$$2$$
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