31). The LCM of two integers is 1237. What is their HCF?
| A). 37 |
| B). 19 |
| C). 1 |
| D). Cannot be determined |
|
32). What is \( \Large \frac{1}{a-b} \)-\( \Large \frac{1}{a+b} \)-\( \Large \frac{2b}{a^{2}+b^{2}} \)-\( \Large \frac{4b^{3}}{a^{4}+b^{4}} \)-\( \Large \frac{8b^{7}}{a^{8}-b^{8}} \)
| A). \( a+b\) |
| B). \( a-b\) |
| C). \( 1\) |
| D). \( 0\) |
|
33). A man rides one third of the distances from A to B at the rate of \( x\)km/hr and the remainder at the rate of \( 2y\) km/hr. If he had travelled at a uniform rate of \( 6z\) km/hr, he could have ridden from A to B and back again in he same time Which one of the following is correct?
| A). \( z\) = \( x\) + \( y\) |
| B). \(3 z\) = \( x\) + \( y\) |
| C). \( \Large \frac{1}{z} \) = \( \Large \frac{1}{x} \)+\( \Large \frac{1}{y} \) |
| D). \( \Large \frac{1}{2z} \) = \( \Large \frac{1}{x} \)+\( \Large \frac{1}{y} \) |
|
34). If \( ax\) + \( by\) - \( 2\) = 0 and \( axby\) = \( 1\), where \( a\) \( \ne\)\( 0\),\( b\) \( \ne\)\( 0\) then what is \( \left( a^{2} x + b^{2 y}\right)\) equal to?
| A). \( a\) +\( b\) |
| B). \( 2ab\) |
| C). \( a^{3}\) +\( b^{3}\) |
| D). \( a^{4}\) +\( b^{4}\) |
|
35). Consider the following statements :
1. \( \left( a - b - c \right)\) is one of the factors of \( 3abc\) + \( b^{3}\) + \( c^{3}\) - \( a^{3}\)
2. \( \left( b + c - 1 \right)\) is one of the factors of \( 3abc\) + \( b^{3}\) + \( c^{3}\) - \( 1\)
Which of the above statements is/are correct?
| A). 1 only |
| B). 2 only |
| C). Both 1 and 2 |
| D). Neither 1 nor 2 |
|
36). \( 7^{10}\) - \( 5^{10}\) is divisible by
| A). 10 |
| B). 7 |
| C). 5 |
| D). 11 |
|
37). Consider the following statements in respect of four spheres A, B, C and D having respective radii 6, 8, 10 and 12 cm :
1. The surface area of sphere C is equal to the sum of surface areas of spheres A and B.
2. The volume of sphere D is equal to the sum of volumes of spheres A, B and C.
Which of the above statements is/are correct?
| A). 1 only |
| B). 2 only |
| C). Both 1 and 2 |
| D). Neither 1 nor 2 |
|
38). What is the number of divisors of 360?
| A). 12 |
| B). 18 |
| C). 24 |
| D). None of these |
|
39). The multiplication of a three-digit number \( XY5\)with digit \( Z\) yields \( X215.\)What is \( X + Y + Z \)equal to?
| A). 13 |
| B). 15 |
| C). 17 |
| D). 18 |
|
40). If the equation \( x^{2}\) + \( 2\)\( \left( 1+k\right)\)\( x\) + \( k^{2}\) = \( 0\) has equal roots, then what is the value of k?
| A). \( \Large \frac{1}{2} \) |
| B). -\( \Large \frac{1}{2} \) |
| C). \( 1\) |
| D). \( -1\) |
|
