### 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