The number of divisors of 9600 including 1 and 9600 are

a) 60

b) 58

c) 48

d) 46

If   , where a, b ∈ N, then the ordered pair (a, b) is

a) (9, 10)

b) (10, 9)

c) (7, 10)

d) (10, 7)

Let E = (2n + 1) (2n + 3) (2n + 5).  .  . (4n – 3) (4n – 1); n > 1 then E is divisible by

a) ⁿC_n/2

b) ²ⁿC_n

c) ³ⁿC_n

d) ⁴ⁿC_2n

 ^jC_i  is equal to

a) 2¹⁰ – 1

b) 2¹⁰

c) – 1

d) None of these

 is equal to

a)

b)

c)

d) None of these

The number of ways of arranging m numbers out of 1, 2, 3, .  .  ., n so that maximum is (n – 2) and minimum is 2 (repetition of numbers is allowed) such that maximum and minimum both occur exactly once, (n > 5, m > 3) is

a) ^{n – 3}C_{m – 2}

b) ^mC₂ (n – 3)^{m – 2}

c) m (m – 1) (n – 5)^{m – 2}

d) ⁿC₂ . ⁿC_m

If  then the value of x is

a) –7

b) –9

c) –10

d) –12

The number of ways of dividing 15 men and 15 women into 15 couples each consisting of a man and a woman is

a) 1240

b) 1840

c) 1820

d) 2005

Ten persons numbered 1, 2, .  .  ., 10 play a chess tournament each player playing against every other player exactly one game. It is known that no game ends in a draw. Let w₁, w₂, .  .  ., w₁₀ be the number of games won by players1, 2, 3, .  .  ., 10 respectively and l₁, l₂, .  .  ., l₁₀ be the number of games lost by the players1, 2, .  .  ., 10 respectively. Then

a)

b)

c)

d) None of these

Let T_n denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If  then n equals

a) 5

b) 7

c) 6

d) 4

If p, q ε {1, 2, 3, 4}. The number of equations of the form  having real roots is

a) 15

b) 9

c) 7

d) 8

Find the sum of the digits of the tens place of all numbers formed with the help of 2, 3, 4, 5 taken all at a time.

a) 78

b) 84

c) 92

d) 96

Find  the sum of the digits in the units place of all the numbers formed with the help of a₁, a₂, .  .  .  ., a_n taken all at a time. (Repetition of digits not allowed)

If ⁵⁶P_r+6 : ⁵⁴P_r+3 = 30800 : 1, find r.

a) 61

b) 41

c) 21

d) 71

How many different signals can be made by hoisting 6 differently coloured flags one above the other, when any number of them may be hoisted at once?

a) 1936

b) 1986

c) 1946

d) 1956

If ²⁸C_2r : ²⁴C_2r−4 = 225 : 11, find r.

a) 7

b) 8

c) 9

d) 10

How many different permutations can be made out of the letters of the word “ASSASSINATION” taken all together?

a) 10810800

b) 10010800

c) 10180800

d) 10801800

How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1, so that the odd digits always occupy the odd places?

a) 20

b) 22

c) 24

d) 18

How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

a) 420

b) 430

c) 360

d) 340

On three different days a man has to drive to a railway station, and he can choose from 5 conveyances: in how many ways can he make the three journeys?

a) 150

b) 145

c) 125

d) 130

A telegraph has 5 arms and each arm is capable 0f 4 distinct positions, including the position of rest; what is the total number of signals that can be made?

a) 1034

b) 1032

c) 1042

d) 1023

Find the number of different ways of dividing mn things into n equal groups?

There are p points in space, no four of which are in the same plane with the exception of q, which are all in the same plane; find how many planes there are each containing three of the points?