61.

What is the number of different messages that can be represented by three 0's and two 1's ?

• 10

• 9

• 8

• 7

What is the number of odd integers between 1000 and 9999 with no digit repeated ?

• 2100

• 2120

• 2240

• None of the above

What is the greatest value of the positive integer n satisfying the condition :

$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... + \frac{1}{2^{\mathrm{n} - 1}} < 2 - \frac{1}{1000} ?$

• 8

• 9

• 10

• 11

How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms ?

• One

• Two

• Four

• Infinitely many

Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where p^-1 + q^-1 + r^-1 = 5/3.

What is the value of ab ?

• 10

• 9

• 8

• 6

Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where p^-1 + q^-1 + r^-1 = 5/3.

What is the value of xyz ?

• 120

• 105

• 90

• Cannot be determined

Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where p^-1 + q^-1 + r^-1 = 5/3.

What is the value of pqr ?

• $\frac{35}{243}$

• $\frac{81}{35}$

• $\frac{243}{35}$

• Cannot be determined

The sixth term of an AP is 2 and its common difference is greater than 1. What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest ?

• $\frac{8}{5}$

• $\frac{9}{5}$

• 2

• $\frac{11}{5}$

The sixth term of an AP is 2 and its common difference is greater than 1. What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest ?

•  - 4

•  - 6

•  - 8

• - 10

The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°. How many possible values can n have ?

• One

• Two

• Three

• Infinitely many