If  then what is the value of 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. -10000
  2. -10
  3. 10
  4. 10000

Answer (Detailed Solution Below)

Option 1 : -10000
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NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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Concept:

Determinant of a 3×3 Matrix:

  • The determinant of a 3×3 matrix can be found by the cofactor expansion method.
  • It is expressed as:
  • If the matrix has a common factor across rows or columns, it can be factored out to simplify calculations.
  • is a summation notation indicating summing function values from n = 1 to n = k.
  • Important identities used:

 

Calculation:

Given,

⇒ Extract common factors 20 and 10:

⇒ Expand determinant using first column:

Now,

∴ The value is -10000.

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