41). If \( m\) and \( n\) are the roots of the equation \( x^{2}\) +\( ax\) + \( b\) = \( 0\), and \( m^{2}\) and \( n^{2}\) are the roots of the equation \( x^{2}\) - \( cx\) +\( d\) = \( 0\), then which of the following is/are correct?
1.\( 2b\) - \( a^{2}\) = \( c\)
2.\( b^{2}\)= \( d\)
Select the coorect answer using the code given below :
| A). 1 only |
| B). 2 only |
| C). Both 1 and 2 |
| D). Neither 1 nor 2 |
|
42). If \( N^{2}\) - \( 33\), \( N^{2}\) - \( 31\) and \( N^{2}\) - \( 29\) are prime numbers, then what is the number of possible values of \( N\), where \( N\) is an integer?
| A). 1 |
| B). 2 |
| C). 6 |
| D). None of these |
|
43). There are 48 cricket balls, 72 hockey balls and 84 tennis balls, and they have to be arranged in several rows in such a way that every row contains the same number of balls of one type. What is the minimum number of rows required for this to happen? (
| A). 12 |
| B). 16 |
| C). 17 |
| D). 19 |
|
44). The HCF of two natural numbers m and n is 24 and their product is 552. How many sets of values of m and n are possible? (
| A). 1 |
| B). 2 |
| C). 4 |
| D). No set of m and n is possible satisfying the given conditions |
|
45). If \( m\) and \( n\)\(\left( m > n\right) \) are the roots of the equation
\( 7\)\( \left( x + 2a\right)^{2}\) + \( 3a^{2}\) = \( 5a\)\( \left( 7x + 23a\right)\)
Where \( a>0\) then what is \( 3m\) - \( n\) equal to ?
| A). 12a |
| B). 14a |
| C). 15a |
| D). 18a |
|
46). A person selling an article for Rs.96 finds that his loss percent is one fourth of the amount of rupees that he paid for the article. What can be the cost price?
| A). Rs.160 only |
| B). Rs.240 only |
| C). Rs.160 or Rs.240 |
| D). Neither Rs.160 nor Rs.240 |
|
47). If (x + k) is the common factor of \( x^2 + ax + b \) and \( x^2 + cx + d \), then what is k equal to ?
| A). (d - b)/(c - a) |
| B). (d - b)/(a - c) |
| C). (d + b)/(c + a) |
| D). (d - b)/(c + a) |
|
48). What is the remainder when \( x^{5}\) - \( 5x^{2}\) + \( 125\) is divided by\( x\)+\( 5\)?
| A). 0 |
| B). 125 |
| C). -3125 |
| D). 3125 |
|
49). What is the lowest common multiple of \( ab\)\( \left( x^{2}+1\right)\)+\( x\)\( \left( a^{2}+b^{2}\right)\)and \( ab\)\( \left( x^{2}-1\right)\)+\( x\)\( \left( a^{2}-b^{2}\right)\)?
| A). \( \left( a^{2} x^{2}-b^{2}\right)\)\( \left( a + bx\right)\) |
| B). \( \left( a^{2} x^{2}-b^{2}\right)\)\( \left( a + bx\right)^{2}\) |
| C). \( \left( a^{2} x^{2}-b^{2}\right)\)\( \left( a - bx\right)\) |
| D). \( \left( a^{2} x^{2}-b^{2}\right)\)\( \left( a - bx\right)^{2}\) |
|
50). A certain number of two digits is three times the sum of its digits. If 45 is added to the number, the digits will be reversed. What is the sum of the squares of the two digits of the number?
| A). 41 |
| B). 45 |
| C). 53 |
| D). 64 |
|
