Elitmus Exam Category

Find the number of numbers that can formed using all the digits 1, 2, 3, 4, 3, 2, 1 only once so that the odd digits occupy the odd places only?
A.
4!/(2!)2
B.
7!/(2!)3
C.
1! 3! 5! 7!
D.
None of these

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Elitmus Other Question

Three positive consecutive integers are raised to the first, second and third power respectively and then added. The sum so obtained is perfect square whose square root is equal to the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?
A. 1≤m≤3
B.4≤m≤6
C.7≤m≤9
D.10≤m≤12
E.3≤m≤15
First we increased the denominator of a positive fraction by 3 and then we decreased it by 5. The sum of the resulting fractions proves to be equal to 19/42. Find the denominator of the fraction if the numerator is 2
A.
7
B.
8
C.
12
D.
9