Let x1, x2, ..., x15 be 15 distinct numbers chosen from 1, 2, 3,

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 Multiple Choice QuestionsMultiple Choice Questions

41.

The sum of n terms of the following series 13 + 33 + 53 + 73 + ... is

  • n2(2n2 - 1)

  • n3(n - 1)

  • n3 + 8n + 4

  • 2n4 + 3n2


42.

If w is an imginary cube root of unity, then the value of (2 - w)(2 - w2) + 2(3 - w)(3 - w2) + ... + (n - 1)(n - w)(n - w2) is

  • n24n +12 - n

  • n24n + 12 + n

  • n24n + 12

  • n24n + 1 - n


43.

If the first and (2n - 1)th terms of an AP, GP and HP are equal and their nth terms are respectively a, b, c, then always

  • a = b = c

  • a  b  c

  • a + c = b

  • ac - b2 = 0


44.

Let a, b, c and d be any four real numbers. Then, an +bn = cn + dn holds for any natural number n, if

  • a + b = c + d

  • a - b = c - d

  • a + b = c + d, a2 + b2 = c2 + d2

  • a - b = c - d, a2 - b2 = c2 - d2


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45.

The value of 1 + 3i1 - 3i64 + 1 -  3i1 + 3i64

  • 0

  • - 1

  • 1

  • i


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46.

Let x1, x2, ..., x15 be 15 distinct numbers chosen from 1, 2, 3, ..., 15. Then, the value of (x1 - 1)(x2 - 1)(x3 - 1)...(x15 - 1) is

  • always  0

  • 0

  • always even

  • always odd


B.

0

Since x1, x2, ..., x15 be 15 distinct numbers chosen from 1, 2, 3, ..., 15. So, x1 can take any value from 1, 2, 3, ... , 15. Among these values, one of the number must be 1, hence product will be 0.


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47.

Let d(n) denotes the number of divisors of n including 1 and itself. Then, d (225), d (1125) and d(640) are

  • in AP

  • in HP

  • in GP

  • consecutive integers


48.

Let S = a, b, c  N × N × N: a + b + c = 21, a  b  c and T = a, b, c  N × N × N: a, b, c are in AP, where N is the set of all natural numbers. Then, the number of elements in the set S  T

  • 6

  • 7

  • 13

  • 14


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49.

If x and y are digits such that 17! = 3556xy428096000, then x + y equals

  • 15

  • 6

  • 12

  • 13


50.

Let f(x) = x + 1/2. Then, the number of real values of x for which the three unequal terms f(x), f(2x), f(4x) are in HP is

  • 1

  • 0

  • 3

  • 2


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