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
ar - 5ar-1 + 8ar-2 - 4ar-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
ar + 6ar-1 + 12ar-2 - 8ar-3 = 0 is
