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SSC MTS 11 Feb 2026 Shift 2 Paper

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Question : 16 of 90

Marks: +1, -0

14^{2}+16^{2}+24^{2}+2(14\times 16+16\times 24+24\times 14)=?

3000
2916
3200
2600

Solution:

Concept:

The expression follows the algebraic identity:

(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)

.

Explanation:

Identify

a = 14

,

b = 16

, and

c = 24

.

The given sum is

14^2 + 16^2 + 24^2 + 2(14\times16 + 16\times24 + 24\times14)

.

This matches the right-hand side of the identity.

Therefore, the value equals

(14 + 16 + 24)^2

.

Add the numbers:

14 + 16 = 30

, then

30 + 24 = 54

.

Now compute

54^2 = 54 \times 54 = 2916

.

Answer:

2916, which corresponds to option B.

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