Let two noncollinear unit vectors and from and acute angle. A point moves so that at any time the position vector (where is the origin) is given by . When is farthest form origin , let be the length of and be the unit vector along Then, 

a) 
b) 

c) 
d) 
Let two noncollinear unit vectors and from and acute angle. A point moves so that at any time the position vector (where is the origin) is given by . When is farthest form origin , let be the length of and be the unit vector along Then, 

a) 
b) 

c) 
d) 
The ratio between a twodigit number and the sum of the digits of that number is 4:1. If the digit in the unit’s place is 3 more than the digit in the ten’s place, then the number is 


(a) 
24 
(b) 
36 
(c) 
63 
(d) 
96 
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