1
AIEEE 2005
+4
-1
A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$50$$ cm$$^3$$ /min. When the thickness of ice is $$5$$ cm, then the rate at which the thickness of ice decreases is
A
$${1 \over {36\pi }}$$ cm/min
B
$${1 \over {18\pi }}$$ cm/min
C
$${1 \over {54\pi }}$$ cm/min
D
$${5 \over {6\pi }}$$ cm/min
2
AIEEE 2005
+4
-1
Out of Syllabus
If the equation $${a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0$$
$${a_1} \ne 0,n \ge 2,$$ has a positive root $$x = \alpha$$, then the equation
$$n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ........... + {a_1} = 0$$ has a positive root, which is
A
greater than $$\alpha$$
B
smaller than $$\alpha$$
C
greater than or equal to smaller than $$\alpha$$
D
equal to smaller than $$\alpha$$
3
AIEEE 2005
+4
-1
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
A
Interval Function
(- $$\infty$$, $$\infty$$) x3 - 3x2 + 3x + 3
B
Interval Function
[2, $$\infty$$) 2x3 - 3x2 - 12x + 6
C
Interval Function
$$\left( { - \infty ,{1 \over 3}} \right]$$ 3x2 - 2x + 1
D
Interval Function
($$- \infty$$, - 4 ) x3 + 6x2 + 6
4
AIEEE 2005
+4
-1
Out of Syllabus
Let f be differentiable for all x. If f(1) = -2 and f'(x) $$\ge$$ 2 for
x $$\in \left[ {1,6} \right]$$, then
A
f(6) $$\ge$$ 8
B
f(6) < 8
C
f(6) < 5
D
f(6) = 5
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