x = 123 + 13, then x2 - 1

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 Multiple Choice QuestionsMultiple Choice Questions

71.

If 0 < y < 213 and xy3 - 1 = 1, then 2x + 23x3 + 25x5 + ...is equal to :

  • logy32 - y3

  • logy31 - y3

  • log2y31 - y3

  • logy31 - 2y3


72.

If f : N  Z is defined byf(n) =  2 if n = 3k, k  Z10 if n = 3k + 1,  k  Z  0 if n = 3k + 2, k  ZThen, n  N : fn > 2 is equal to

  • {3, 6, 4}

  • {1, 4, 7}

  • {4, 7}

  • {7}


73.

The value of 42 + 42 + 42 + ... is equal to

  • 7

  • - 6

  • 5

  • 4


74.

If log27log3x = 13, then the value of x is

  • 3

  • 6

  • 9

  • 27


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75.

x = 123 + 13, then x2 - 1x - x2 - 1

  • 1

  • 2

  • 3

  • 12


A.

1

Given that,      x = 123 + 13or x2 = 143 + 13 + 2 = 43Now, x2 - 1x - x2 - 1 = x2 - 1x - x2 - 1 × x + x2 - 1x +x2 - 1                                 = xx2 - 1 + x2 - 11                                 = 123 + 1343 - 1 + 43 - 1                                 = 124313 + 13               23 + 13 = 1


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76.

If a, b, c  0 and belong to the set to {0, 1, 2, 3, ..., 9}, then log10a + 10b + 102c10- 4a + 10- 3b + 10- 2c is equal to

  • 1

  • 2

  • 3

  • 4


77.

nn + 12n + 1 : n  Z 

  • 6k : k  Z

  • 12k : k  Z

  • 18k : k  Z

  • 24k : k  Z


78.

If x22x - 1x + 2x - 3 = A + B2x - 1 + Cx + 2 + Dx - 3, then A is equal to

  • 12

  • - 150

  • - 825

  • 2725


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79.

If m- 3, 4 + n4 - 3 = 10 - 11, then 3m + 7n is equal to

  • 3

  • 5

  • 10

  • 1


80.

If f : R  R is defined by f(x) = [2x] - 2[x] for x  R, where [x] is the greatest integer not exceeding x, then the range of f is :

  • x  R : 0  x  1

  • {0, 1}

  • x  R : x > 0

  • x  R : x  0


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