Engineering Mathematics - Combinatorics

Question - 1

How many ways are there to arrange the nine letters in the word ALLAHABAD?

  • A 7500
  • B 7560
  • C 4000
  • D 2000

Question - 2

The number of diagonals which can be drawn by joining the angular points of a heptagon is

  • A 14
  • B 7
  • C 10
  • D 12

Question - 3

At certain college the housing office has decided to appoint, for each floor, one male and one female residental advisor. The pairs of advisors can be selected for a seven story building from 12 male and 15 female candidates are 

  • A 40000
  • B 5096520
  • C 568400
  • D 70000

Question - 4

Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences B and C are there such that (i) each is sorted in ascending order (ii) B has 5 and c has 3 elements and (iii) the result of merging B ans C given A?

  • A 2
  • B 30
  • C 56
  • D 256

Question - 5

A person deposiits Rs 300 in a saving account of SBI at an interest rate of 5% per annum compounded annually. The obatin amount in his account at the end of r yeras is

  • A 300(1.05)r
  • B 200
  • C 100(1.02)r+1
  • D 50\(\times \) (1.00)r

Question - 6

The generating function for thr sequence 2, 2, 2, 2, 2, 2 is

  • A \(\frac { { z }^{ 2 }+1 }{ (z-1) } \)
  • B \(\frac { 18(z-1) }{ { z }^{ 2 }+1 } \)
  • C \(\frac { 2({ z }^{ 5 }-1) }{ z-1 } \)
  • D None of these

Question - 7

The generating function for the sequence 0, 1, 2, 4, 8, ...... is

  • A \(\frac { 2z }{ 1+{ z }^{ 2 } } \)
  • B \(\frac {1+3z }{ 1+{ 8}{ z } } \)
  • C \(\frac { { Z }^{ 2 }+1 }{ { Z }^{ 2 }-1 } \)
  • D \(\frac {z }{ 1+{ 2}{ z } } \)

Question - 8

Solution of recurrence relation
ar - 5ar-1 + 8ar-2 - 4ar-3 = 0 is

  • A ar = A1(1)r + (A2 + A3r) (2)r
  • B ar = (A1 + A2r2 + A3r3) (3)r
  • C ar = (A1 + A2r + A3 r2) (-2)r
  • D None of the above

Question - 9

The solution of the recurrence relation
ar + 6ar-1 + 12ar-2 - 8ar-3 = 0 is

  • A ar = (A1r + A2r + 2A3 r3)(2)r
  • B ar = (A1 + A2r2 + A3r3)(3)r
  • C ar = (A1 + A2r + A3r2)(-2)r
  • D None of these

Question - 10

The sum of the series
12 + 22 + 32 + ...+r2 is

  • A \(\frac { r(r+1)(2r+1) }{ 6 } \)
  • B \(\frac { r(2r+1)(3r+1) }{ 6 } \)
  • C \(\frac { 2{ r }^{ 2 }9r+1)(2r+1) }{ 8 } \)
  • D None of these
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