Reasoning — Classification (Odd One Out)

The numbers 121, 144, and 169 are perfect squares (11^2, 12^2, and 13^2 respectively). The number 198 is not a perfect square. Hence, 198 is the odd one out.

Mango, Apple, and Banana are all types of fruits. Potato is a vegetable. Hence, Potato is the odd one out.

The letters A, E, and I are vowels in the English alphabet. The letter B is a consonant. Hence, B is the odd one out.

The numbers 23, 29, and 31 are prime numbers (they are only divisible by 1 and themselves). The number 33 is a composite number as it is divisible by 3 and 11 (3 x 11 = 33). Hence, 33 is the odd one out.

Chair, Table, and Sofa are primarily used for sitting or placing items on directly. A Cupboard is primarily used for storage, typically enclosing items. Hence, Cupboard is the odd one out.

Let's examine the pattern within each group of letters based on their alphabetical positions: * BDF: B(2) + 2 = D(4) + 2 = F(6) (Pattern: +2, +2) * HJL: H(8) + 2 = J(10) + 2 = L(12) (Pattern: +2, +2) * NPR: N(14) + 2 = P(16) + 2 = R(18) (Pattern: +2, +2) * TVY: T(20) + 2 = V(22) + 3 = Y(25) (Pattern: +2, +3) All groups except TVY follow the pattern of adding 2 to the alphabetical position of the preceding letter. Hence, TVY is the odd one out.

Let's examine each number: * 125 = 5 x 5 x 5 = 5^3 (a perfect cube) * 216 = 6 x 6 x 6 = 6^3 (a perfect cube) * 343 = 7 x 7 x 7 = 7^3 (a perfect cube) * 510 is not a perfect cube (8^3 = 512). Hence, 510 is the odd one out.

Let's find the square root of each number: * 16 = 4^2 (4 is an even number) * 36 = 6^2 (6 is an even number) * 64 = 8^2 (8 is an even number) * 81 = 9^2 (9 is an odd number) All numbers except 81 are squares of even numbers. 81 is the square of an odd number. Hence, 81 is the odd one out.

Let's examine the relationship between the numbers in each pair (X, Y): * (12, 144): Here, Y = X^2 (12^2 = 144). * (15, 225): Here, Y = X^2 (15^2 = 225). * (18, 324): Here, Y = X^2 (18^2 = 324). * (21, 440): Here, Y is not X^2 (21^2 = 441, not 440). All pairs except (21, 440) follow the pattern where the second number is the square of the first number. Hence, (21, 440) is the odd one out.

The numbers 2, 3, and 5 are prime numbers. The number 9 is a composite number (divisible by 1, 3, and 9). Therefore, 9 is the odd one out.

Lion, Tiger, and Leopard are wild animals. Cow is a domestic animal. Therefore, Cow is the odd one out.

Let's look at the alphabetical positions: B = 2 D = 4 F = 6 G = 7 B, D, F follow a pattern where each letter is 2 positions after the previous one (B+2=D, D+2=F). G does not follow this pattern (F+1=G, not F+2). Therefore, G is the odd one out.

Let's check if the numbers are perfect squares: 121 = 11 * 11 = 11^2 196 = 14 * 14 = 14^2 256 = 16 * 16 = 16^2 325 is not a perfect square (18^2 = 324, 19^2 = 361). Therefore, 325 is the odd one out.

Pen, Pencil, and Eraser are all stationery items used for writing or correcting. A Book is a collection of pages for reading or writing content; it is a product of writing/publishing rather than a tool for writing. Therefore, Book is the odd one out.

Let's examine the relationship between the numbers in each pair: (10, 100): 10^2 = 100. The second number is the square of the first. (12, 144): 12^2 = 144. The second number is the square of the first. (15, 225): 15^2 = 225. The second number is the square of the first. (13, 168): 13^2 = 169. The second number (168) is not the square of the first (13). Therefore, (13, 168) is the odd one out.

Let's analyze the pattern within each group of letters based on their alphabetical positions: ACE: A(1) + 2 = C(3), C(3) + 2 = E(5). Pattern: +2, +2 GIK: G(7) + 2 = I(9), I(9) + 2 = K(11). Pattern: +2, +2 MNP: M(13) + 1 = N(14), N(14) + 2 = P(16). Pattern: +1, +2 QSU: Q(17) + 2 = S(19), S(19) + 2 = U(21). Pattern: +2, +2 All groups except MNP follow the '+2, +2' pattern. MNP follows a '+1, +2' pattern. Therefore, MNP is the odd one out.

Mercury, Venus, and Earth are planets in our solar system. Moon is a natural satellite that orbits Earth. Therefore, Moon is the odd one out.