Mathematics · 2020
JEE Main · 2 September 2020, Shift 2 · Q54
Let a, b, c ∈ R be all non-zero and satisfy a^3+ b^3+ c^3=2. If the matrix A= (a, b, c; b, c, a; c, a, b) satisfies A^T A = I, then a value of abc…
Let $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{R}$ be all non-zero and satisfy $\displaystyle \mathrm{a}^3+\mathrm{b}^3+\mathrm{c}^3=2$. If the matrix
$$A=\left(\begin{array}{lll}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right)
$$
satisfies $\displaystyle \mathrm{A}^{\mathrm{T}} \mathrm{A}=\mathrm{I}$, then a value of abc can be :
Official answer
(2)
$\displaystyle \frac{1}{3}$
More from Matrices and Determinants
- Let A=[a_i j] be a square matrix of order 3 such that a_i j=2^j-i, for all i, j=1,2,3. Then, the matrix A^2+A^3+…+A^10 is equal to:2022
- Let A= (2, -1; 0, 2). If B=I-^5 C_1(adj A)+^5 C_2(adj A)^2-…-^5 C_5(adj A)^5, then the sum of all elements of the matrix B is2022
- If for some α and β in R, the intersection of the following three planes x+4 y-2 z=1; x+7 y-5 z=β; x+5 y+α z=5 is a line in R^3, then α+β is equal to:2020
- If α ≠ a, β ≠ b, γ ≠ c and |α, b, c; a, β, c; a, b, γ| =0, then a/(α-a)+b/(β-b)+(γ)/(γ-c) is equal to:2024
- The values of λ and μ for which the system of linear equations x+y+z=2; x+2 y+3 z=5; x+3 y+λ z=μ has infinitely many solutions are, respectively:2020
- Let A= (1, 2; -2, -5). Let α, β ∈ R be such that α A^2+β A=2 I. Then α+β is equal to2022
- Let A=[a_i j] and B=[b_i j] be two 3 × 3 real matrices such that b_i j=(3)^(i+j-2) a_j i, where i, j=1,2,3. If the determinant of B is 81, then the…2020
- Let p and p+2 be prime numbers and let Δ= |p!, (p+1)!, (p+2)!; (p+1)!, (p+2)!, (p+3)!; (p+2)!, (p+3)!, (p+4)!| Then the sum of the maximum values of…2022
JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.