All India Engineering / Architecture Entrance Examination (AIEEE)

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AIEEE 2010 Mathematics

Q. 7. If two tangents drawn from a point P to the parabola  are at right angles, then the locus of p is.

1. 2x +1=0 
2. x = -1
3. 2x +1=0
4. x = 1

Sol.  

Locus of point P is directrix of parabola i.e.,  x=-1

Answer: (2)

Q. 8. If the vectors  and  are mutually orthogonal ,
then

1. (2,-3)
2. (-2,3)
3. (3,-2)
4. (-3,2)

Sol :

Answer (c)

Q. 9. Consider the following relations:

R = {(x, y) | x, y are real numbers and x=wy for some rational number w };

Then

1. neither R nor S is an equivalence relation
2. S is an equivalence relation but R is not an equivalence relation
3. R and S both are equivalence relations
4. R is an equivalence relation but S is not an equivalence relation

Sol : 

R is not equivalence  but 
  S in equivalence 
 

Answer : (2)