In the polynomial f(x) = $x^5 + a\times x^3 + b\times x^4 +c\times x + d$, all coefficients a, b, c, d are integers. If 3 + $\sqrt{7}$ is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)?
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How many divisors (including 1, but excluding 1000) are there for the number 1000? |
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A call center agent has a list of 305 phone numbers of people in alphabetic order of names (but she does not have any of the names). She needs to quickly contact Deepak Sharma to convey a message to him. If each call takes 2 minutes to complete, and every call is answered, what is the minimum amount of time in which she can guarantee to deliver the message to Mr Sharma. |
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The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the average time per call? |
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The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively. What is the median time per call? |
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Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra?s score will be strictly higher than Eric?s score? |
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What is the largest integer that divides all three numbers 23400,272304,205248 without leaving a remainder? |
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Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20 neither like chocolate nor like cricket. How many people like both cricket and chocolate? |
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If f(x) = 2x+2 what is f(f(3))? |
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If f(x) = 7 x +12, what is f-1(x) (the inverse function)? |
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A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many times must it be applied before the numbers appear in their original order)? |
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