1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Angle between the tangents to the curve $$y = {x^2} - 5x + 6$$ at the points $$(2,0)$$ and $$(3,0)$$ is
A
$$\pi $$
B
$${\pi \over 2}$$
C
$${\pi \over 6}$$
D
$${\pi \over 4}$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is
A
$${3 \over 2}{x^2}$$
B
$$\sqrt {{{{x^3}} \over 8}} $$
C
$${1 \over 2}{x^2}$$
D
$$\pi {x^2}$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at
A
$$x=2$$
B
$$x=-2$$
C
$$x=0$$
D
$$x=1$$
4
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 $$\alpha $$
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