21). If \(a_{n}= 3  4n \), then what is \(a_{1} + a_{2} + a_{3} + ...... + a_{n}\) equal to \( [ 1 + 2 + 3 + ..... + n = \frac{n(n + 1)}{2}]\)
A). n(4n3) 
B). n(2n1) 
C). \(n^{2}\) 
D). n(2n1) 

22). A train travels at a speed of 40km/hr and another train at a speed of 20m/s. what is the ration of speed of the first train to that of the second train?
A). 2:01 
B). 5:09 
C). 5:03 
D). 9:05 

23). \( \left( x+y\right)\) : \( \left( xy\right)\)= 3 : 5 and xy = positive imply that
A). \(x \) and \( y\) are both positive 
B). \(x \) and \( y\) are both negative 
C). One of them is positive and one of them is negative 
D). No real solutions for \( x\) and \( y\) exist 

24). How many pairs of \( X\) and \( Y\) are possible in the number \( 763X4Y2\), if the number is divisible by 9?
A). 8 
B). 9 
C). 10 
D). 11 

25). What is the remainder when \( 4^{1012}\) is divided by 7?

26). What is the highest common facter of \( 2x^{3}\)+\( x^{2}\)\( x\)\( 2\) and \( 3x^{3}\)\( 2x^{2}\)+\( x\)\( 2\)?
A). \( x1\) 
B). \( x+1\) 
C). \( 2x+1\) 
D). \( 2x1\) 

27). What is the remainder when \( \left( 1235 \times 4523 \times 2451\right)\) is divided by 12?

28). What is the remainder when \( \left(17^{23} + 23^{23} + 29^{23}\right)\) is divided by 23?

29). \( p\),\( q\) and r are prime numbers. Such that p< q
A). 1 
B). 2 
C). 3 
D). None of these 

30). The LCM of two numbers is 90 times their HCF. The sum of DCM and HCF is 1456. If one of the numbers is 160; then what is the other number?
A). 120 
B). 136 
C). 144 
D). 184 
