Mathematics · 2020
JEE Main · 3 September 2020, Shift 2 · Q71
Let S be the set of all integer solutions, (x, y, z), of the system of equations x-2 y+5 z=0; -2 x+4 y+z=0; -7 x+14 y+9 z=0 such that 15 ≤…
Let $\displaystyle S$ be the set of all integer solutions, $\displaystyle (x, y, z)$, of the system of equations
$$\begin{gathered}
x-2 y+5 z=0 \\
-2 x+4 y+z=0 \\
-7 x+14 y+9 z=0
\end{gathered}
$$
such that $\displaystyle 15 \leq x^2+y^2+z^2 \leq 150$. Then, the number of elements in the set $\displaystyle S$ is equal to \_\_\_\_.
Official answer
8
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.