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Saturday, 31 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 1, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let A=[α−16β]A=\begin{bmatrix}\alpha&-1\\6&\beta\end{bmatrix}, α>0\alpha>0, such that det⁡(A)=0\det(A)=0 and α+β=1\alpha+\beta=1. If I denotes 2×22\times2 identity matrix, then the matrix (I+A)8(I+A)^8 is :
  1. (1)[4−16−1]\begin{bmatrix}4&-1\\6&-1\end{bmatrix}
  2. (2)[257−64514−127]\begin{bmatrix}257&-64\\514&-127\end{bmatrix}
  3. (3)[766−2551530−509]\begin{bmatrix}766&-255\\1530&-509\end{bmatrix}Official answer
  4. (4)[1025−5112024−1024]\begin{bmatrix}1025&-511\\2024&-1024\end{bmatrix}

Official answer

Option 3

NTA final key.

Chapter
Matrices
Topic
Matrix Multiplication
Idea tested
Idempotent and Nilpotent Matrices

Same idea in other shifts

Asked 2× in all
  1. 25 Jun 2022, Shift 2 · Q21Let A=(2−21−1)A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix} and B=(−12−12)B = \begin{pmatrix} -1 & 2 \\ -1 & 2 \end{pmatrix}. Then the number of…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.