∣A∣=211C11=k=1∑2a1k⋅A1k=a11 A11+a12 A12=∣A∣=211C12=k=1∑2a1k⋅A2k=0C21=k=1∑2a2k⋅A1k=0C22=k=1∑2a2k⋅A2k=∣A∣=211C=[11/20011/2]∣C∣=41218∣C∣=242
Let A= [ a_i j ]= [ … ]. If A_i j is the cofactor of a_i j, C_i j=Σ_ k=1^2 a_i k A_j k, 1 ≤ i, j ≤ 2, and C= [ C_i j ], then 8| C| is equal to :
JEE Main 2025 — Mathematics Algebra
2025mcqeasy
Let A=[aij]=[log5128log58log45log425]. If Aij is the cofactor of aij,Cij=k=1∑2aikAjk,1≤i,j≤2, and C=[Cij], then 8∣C∣ is equal to :
Official previous-year question
Held on 29 Jan 2025 · Verified 6 Jul 2026.
Options
- A
288
- B
222
- C
242
- D
262
Did you get this right?
Sign in to track your attempts and accuracy.
Your note
Sign in to keep a private note on this question. Nothing you write is ever public.
JEE Main Algebra in other years
More JEE Main Algebra questions
The number of elements in the set $S = \left\{(r, k) : k \in \mathbb{Z} \text{ and } {}^{36}C_{r+1} = \dfrac{6\left({}^{35}C_r\right)}{(k^2 - 3)}\right\}$, is :
2026medium
Suppose $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $\mathrm{a}^{2}, 2 \mathrm{~b}^{2}, \mathrm{c}^{2}$ are in G.P. If $\mathrm{a}<\mathrm{b}<\mathrm{c}$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}=1$, then $9\left(\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\right)$ is equal to $\_\_\_\_$ .
2026medium
Let $S=\left\{z \in \mathbb{C}: 4 z^{2}+\bar{z}=0\right\}$. Then $\sum_{z \in S}|z|^{2}$ is equal to:
2026medium
Let $S=\{z: 3 \leqslant|2 z-3(1+i)| \leqslant 7\}$ be a set of complex numbers. Then $\min _{z \in S}\left|\left(z+\frac{1}{2}(5+3 i)\right)\right|$ is equal to :
2026medium
Let $A = \begin{bmatrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{bmatrix}$ and $B = [b_{ij}]$, $1 \leq i, j \leq 3$. If $B = A^{99} - I$, then the value of $\dfrac{b_{31} - b_{21}}{b_{32}}$ is :
2026medium
Other Mathematics topics for JEE Main
Keep practicing Algebra
Work through every JEE Main Algebra PYQ, year by year.