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(4n-3) |
| B). -n(2n-1) |
| C). -\(n^{2}\) |
| D). -n(2n-1) |
|
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). \( \left( x+y\right)\) : \( \left( x-y\right)\)= 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). \( x-1\) |
| B). \( x+1\) |
| C). \( 2x+1\) |
| D). \( 2x-1\) |
|
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 |
|
