1
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Solution of the differential equation

$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x <{\pi \over 2}$$ is :
A
$$y\sec x = \tan x + c$$
B
$$y\tan x = \sec x + c$$
C
$$\tan x = \left( {\sec x + c} \right)y$$
D
$$\sec x = \left( {\tan x + c} \right)y$$
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Four numbers are chosen at random (without replacement) from the set $$\left\{ {1,2,3,....20} \right\}.$$

Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is $${1 \over {85}}.$$

Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is $$\left( { \pm 1, \pm 2, \pm 3, \pm 4, \pm 5} \right).$$

A
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement - 2 is false.
C
Statement - 1 is false, Statement -2 is true.
D
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
3
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :
A
$${2 \over 7}$$
B
$${1 \over 21}$$
C
$${1 \over 23}$$
D
$${1 \over 3}$$
4
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Statement-1 : The point $$A(3, 1, 6)$$ is the mirror image of the point $$B(1, 3, 4)$$ in the plane $$x-y+z=5.$$

Statement-2 : The plane $$x-y+z=5$$ bisects the line segment joining $$A(3, 1, 6)$$ and $$B(1, 3, 4).$$
A
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement - 2 is false.
C
Statement - 1 is false , Statement - 2 is true.
D
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
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