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

A7500

B7560

C4000

D2000

Question - 2

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

A14

B7

C10

D12

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

A40000

B5096520

C568400

D70000

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?

A2

B30

C56

D256

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

A300(1.05)r

B200

C100(1.02)r+1

D50\(\times \) (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\(\frac { 2({ z }^{ 5 }-1) }{ z-1 } \)

DNone 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
a_{r} - 5a_{r-1} + 8a_{r-2} - 4a_{r-3} = 0 is

Aar = A1(1)r + (A2 + A3r) (2)r

Bar = (A1 + A2r2 + A3r3) (3)r

Car = (A1 + A2r + A3 r2) (-2)r

DNone of the above

Question - 9

The solution of the recurrence relation
a_{r} + 6a_{r-1} + 12a_{r-2} - 8a_{r-3} = 0 is

Aar = (A1r + A2r + 2A3 r3)(2)r

Bar = (A1 + A2r2 + A3r3)(3)r

Car = (A1 + A2r + A3r2)(-2)r

DNone of these

Question - 10

The sum of the series
1^{2} + 2^{2} + 3^{2} + ...+r^{2} is