31). What is the HCF of \( 8\)\( \left( x^{5}-x^{3}+x\right)\) and \( 28\)\( \left( x^{6}+1\right)\)?
| A). \( 4\)\( \left( x^{4}-x^{2}+1\right)\) |
| B). \( 2\)\( \left( x^{4}-x^{2}+1\right)\) |
| C). \( \left( x^{4}-x^{2}+1\right)\) |
| D). None of the these |
|
32). Two chairs and one table cost Rs 700 and 1 chair and 2 tables cost Rs 800. If the cost of m tables and m chairs is Rs 30,000, then what is In equal to ?
| A). 60 |
| B). 55 |
| C). 50 |
| D). 45 |
|
33). Consider the following statements :
1. No integer of the form 4k + 3, where k is an integer, can be expressed as the sum of two squares.
2. Square of an odd integer can be expressed in the form 8k + 1, where k is an integer.
Which of the above statements is/are correct?
| A). 1 only |
| B). 2 only |
| C). Both 1 and 2 |
| D). Neither 1 nor 2 |
|
34). For any integer n, what is HCF (22n + 7, 33n + 10) equal to?
| A). n |
| B). 1 |
| C). 11 |
| D). None of these |
|
35). In a fire range, 4 shooters are firing at their respective targets. The first, the second, the third and the fourth shooter hit the target once every 5s, 6s, 7s and 8s respectively. If all of them hit their target at 9:00 am, when will they hit their target together again?
| A). 9:04am |
| B). 9:08am |
| C). 9 : 14am |
| D). None of these |
|
36). If A is a non-empty subset of a set E, then what is \( E\cup\)\( \left(A\cap \phi \right) - \)\( \left( A-\phi\right)\) equal to?
| A). A |
| B). Complement of A |
| C). \( \phi\) |
| D). E |
|
37). If A:B=2:3, B:C=5:7 and C:D=3:10 then what is A : D equal to?
| A). 1 : 7 |
| B). 2 : 7 |
| C). 1 : 5 |
| D). 5 : 1 |
|
38). If the average of A and B is 30, the average of C and D is 20, then which of the following is/are correct ?
1. The average ofB and C must be greater than 25.
2. The average of A and D must be less than 25.
Select the correct answer using the code given below:
| A). 1 only |
| B). 2 only |
| C). Either I or 2 |
| D). Neither 1 nor 2 |
|
39). Out of 105 students taking an examination for English and Mathematics, 80 students pass in English, 75 students pass in Mathematics and 10 students fail in both the subjects. How many students pass in only one subject?
| A). 26 |
| B). 30 |
| C). 35 |
| D). 45 |
|
40). At what point of time after 3 'o'clock, do the hour hand and the minute-hand of a clock occur at right angles for the first time?
| A). 9 'o'clock |
| B). 4 hours \( 37\)\( \Large \frac{1}{6} \) minutes |
| C). 3 hours \( 30\)\( \Large \frac{8}{11} \) minutes |
| D). 3 hours \( 32\)\( \Large \frac{8}{11} \) minutes |
|
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