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NDA Determinants questions with solutions

Determinants and their properties and applications. 13 questions from our 2016–2023 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

NDA 2023

If A is a 3×3 matrix with det A=-2, then det (adj(A^2) equalsNDA 2023 Maths · hard
The values of x for which beginvmatrixx&1&1\\1&x&1\\1&1&xendvmatrix=0 areNDA 2023 Maths · medium

NDA 2022

If A is a 3×3 matrix with |A|=5, then |adj(adjA)| equalsNDA 2022 Maths · hard

NDA 2019

The value of beginvmatrix2&0&1\\1&3&2\\1&1&4endvmatrix isNDA 2019 Maths · easy
The homogeneous system x+y+z=0, x+2y+3z=0, 2x+3y+kz=0 has a non-trivial solution for k equal toNDA 2019 Maths · medium
The value of beginvmatrix1&2&3\\2&3&4\\3&4&5endvmatrix isNDA 2019 Maths · easy
If A and B are 3×3 matrices with |A|=2 and |B|=3, then |2A^-1B| equalsNDA 2019 Maths · medium

NDA 2017

For the determinant Δ=beginvmatrix2&-1&3\\0&4&5\\1&2&-2endvmatrix, the cofactor of the element 3 isNDA 2017 Maths · medium
For the system x+y+z=6, x+2y+3z=14, x+3y+λ z=μ, the system does NOT have a unique solution when λ equalsNDA 2017 Maths · hard

NDA 2016

The value of the determinant beginvmatrix1&1&1\\1&2&4\\1&4&16endvmatrix isNDA 2016 Maths · medium
The cofactor of the element 5 in the matrix beginpmatrix1&2&3\\4&5&6\\7&8&10endpmatrix isNDA 2016 Maths · easy
If A is a 3×3 matrix with |A|=-2, then |-A^3| is equal toNDA 2016 Maths · hard
The system of equations x+y+z=0, x-y+z=0, 2x+2z=0 hasNDA 2016 Maths · medium