MBA Exam

If α and β are roots of the equation x2 - px + q = 0 and α1 and β1 are the roots of the equation x2 - qx + p = 0, then the equation whose roots are is:

1) pqx<sup>2</sup> - pqx + p<sup>2</sup> + q<sup>2</sup> + 4pq = 0
2) p<sup>2</sup>q<sup>2</sup>x<sup>2</sup> - p<sup>2</sup>q<sup>2</sup>x + p<sup>3</sup> + q<sup>3</sup> - 4pq = 0
3) (p+q)x<sup>2</sup> - (p+q)x + p<sup>2</sup> + q<sup>2</sup> + pq = 0
4) p<sup>2</sup>q<sup>2</sup>x<sup>2</sup> + p<sup>2</sup>q<sup>2</sup>x + p<sup>3</sup> + q<sup>3</sup> = 0

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MBA Other Question

Out of 210 interviews of IIM- Ahmedabad, 105 CAT crackers were offered tea by the interview panel, 50 were offered biscuits, and 56 were offered toffees. 32 CAT crackers were offered tea and biscuits, 30 were offered biscuits and toffees, and 45 were offered toffees and tea. What is the1) maximum and minimum number of CAT crackers who were offered all three snacks?2) maximum and minimum number of CAT crackers who were offered at least one snack?
Don't know whether it's a repeated question or not ? Anyways enjoy if you have not done it m/

1) 30,19,149,116
2) 45,12,123,116
3) 30,19,134,123
4) 45,12,149,116
If n is any 3-digit prime number then which of the following statement(s) is(are) definitely true?n divides 2n â€“ 2.an + bn is always divisible by (a + b) for a + b â‰ 0.There always exist n consecutive composites numbers.I did not understand the 3rd option

1) Only 1
2) Only 2
3) Both 1 & 2
4) All are correct