1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The normal to the curve
$$x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point
$$\theta\, '$$ is such that
A
it passes through the origin
B
it makes an angle $${\pi \over 2} + \theta $$ with the $$x$$-axis
C
it passes through $$\left( {a{\pi \over 2}, - a} \right)$$
D
it is at a constant distance from the origin
2
AIEEE 2005
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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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