Explanation

The pattern in the series is obtained by adding 1 to the square of consecutive integers:

(1 × 1) + 1 = 2

(2 × 2) + 1 = 5

(3 × 3) + 1 = 10

(4 × 4) + 1 = 17

(5 × 5) + 1 = 26

(6 × 6) + 1 = 37

(7 × 7) + 1 = 50

(8 × 8) + 1 = 65 (not 64)

So, the odd one in the series is: 64 (should be 65)

The correct series would be: 2, 5, 10, 17, 26, 37, 50, 65

Explanation

Taking all person of same nationality as one person, then we will have only three people.

These three person can be arranged themselves in 3! Ways.

8 Indians can be arranged themselves in 8! Way.

4 American can be arranged themselves in 4! Ways.

4 Englishman can be arranged themselves in 4! Ways.

Hence, required number of ways = 3! 8! 4! 4! Ways.

Explanation

The given series is formed by adding 1, 4, 9, 16, 25, and 36 (which are consecutive perfect squares) to the previous term. Breaking it down:

• 1 + 1 = 2
• 2 + 4 = 6
• 6 + 9 = 15
• 15 + 16 = 31
• 31 + 25 = 56

56 + 36 = 92 (not 91)

So, the correct series would be: 1, 2, 6, 15, 31, 56, 92.

Therefore, the wrong number in the series is 91.

Explanation

Two numbers are 5x and 4x

5x - 4x = 10

x = 10

Largest number is 5x = 5*10 = 50

Explanation

no/Def

1, = 0

3 = 2

6 = 3

10 = 4

15 = 5

Explanation

The sequence 5, 10, 20, 40, 80, .... is an example of a geometric sequence.

5 + 5 = 10

10 + 10 = 20

20 + 20 = 40 

40 + 40 = 80

The pattern is that we are always multiplying by a fixed number of 2 to the previous term to get to the next term.1

Explanation

D    C    X   W
H    G    T   S
L     K    P   O
P     O    L   K
T     S    H   G

Explanation

All numbers are repeated except 4 and 8.

Multiply 8 by 4 = 32

Explanation

Here's the completed series:

2 + 18 = 20

20 + 22 = 42

42 + 26 = 68

68 + 30 = 98

The pattern consists of adding consecutive multiples of 2 (18, 22, 26, 30, ...) to obtain the next term.

Explanation

A number is divisible by 132 if it is divisible by 3, 4, and 11 (as 132 = 3 × 4 × 11), given that 3, 4, and 11 are pairwise co-prime.

Solution:

⇒ 264 is divisible by 3, 4, and 11.

⇒ 396 is divisible by 3, 4, and 11.

⇒ 462 is not divisible by 4.

⇒ 792 is divisible by 3, 4, and 11.

⇒ 968 is not divisible by 3.

⇒ 2178 is not divisible by 4.

⇒ 5184 is not divisible by 11.

⇒ 6336 is divisible by 3, 4, and 11.

There are 4 numbers (264, 396, 792, and 6336) that are divisible by 132.