1
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
For the Hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$ , which of the following remains constant when $$\alpha $$ varies$$=$$?
A
abscissae of vertices
B
abscissae of foci
C
eccentricity
D
directrix.
2
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
Let A $$\left( {h,k} \right)$$, B$$\left( {1,1} \right)$$ and C $$(2, 1)$$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is $$1$$ square unit, then the set of values which $$'k'$$ can take is given by :
A
$$\left\{ { - 1,3} \right\}$$
B
$$\left\{ { - 3, - 2} \right\}$$
C
$$\left\{ { 1,3} \right\}$$
D
$$\left\{ {0,2} \right\}$$
3
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
In a geometric progression consisting of positive terms, each term equals the sum of the next two terns. Then the common ratio of its progression is equals
A
$${\sqrt 5 }$$
B
$$\,{1 \over 2}\left( {\sqrt 5 - 1} \right)$$
C
$${1 \over 2}\left( {1 - \sqrt 5 } \right)$$
D
$${1 \over 2}\sqrt 5 $$.
4
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
In the binomial expansion of $${\left( {a - b} \right)^n},\,\,\,n \ge 5,$$ the sum of $${5^{th}}$$ and $${6^{th}}$$ terms is zero, then $$a/b$$ equals
A
$${{n - 5} \over 6}$$
B
$${{n - 4} \over 5}$$
C
$${5 \over {n - 4}}$$
D
$${6 \over {n - 5}}$$
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