All India Engineering / Architecture Entrance Examination (AIEEE)

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AIEEE 2009 Maths

Q. 19. The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are

1. 
   
   
2. 6, -3, 2
   
   
3. 
   
4. 

Sol.:   Direction ratios are: 6, –3, 2

Direction cosines are:

Answer: (4)

Q. 20. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

1. at least 1000
   
   
2. less than 500
   
   
3. at least 500 but less than 750
   
   
4. at least 750 but less than 1000

Sol: 

   
Answer: (1)

Q. 21. are non-coplanar vectors and p, q are real numbers, then the equality

1. all values of (p, q)
   
   
2. exactly one value of (p, q)
   
   
3. exactly two values of (p, q)
   
   
4. more than two but not all values of (p, q)

Sol:  

Answer: (2)