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
If $${A^2} - A + 1 = 0$$, then the inverse of $$A$$ is :
A
$$A+I$$
B
$$A$$
C
$$A-I$$
D
$$I-A$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The system of equations

$$\matrix{ {\alpha \,x + y + z = \alpha - 1} \cr {x + \alpha y + z = \alpha - 1} \cr {x + y + \alpha \,z = \alpha - 1} \cr } $$

has infinite solutions, if $$\alpha $$ is :

A
$$-2$$
B
either $$-2$$ or $$1$$
C
not $$-2$$
D
$$1$$
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