TS EAMCET · Maths · Determinants
If \(x=\alpha, y=\beta, z=\gamma\) is the unique solution of the system of linear equations \(2 x-3 y+5 z=12,5 x+2 y+3 z=11\) and \(x+2 y-3 z=-3\) then \(2 \alpha+5 \beta+3 \gamma=\)
- A 10
- B 11
- C 3
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text 2 x-3 y+5 z=12 \\ & 5 x+2 y+3 z=11 \\ & x+2 y-3 z=-3 \\ & D=\left|\begin{array}{ccc}2 & -3 & 5 \\ 5 & 2 & 3 \\ 1 & 2 & -3\end{array}\right| \\ & =2(-6-6)+3(-15-3)+5(10-2) \\ & =-24-54+40=-38 \text {. } \\ & D_1=\left|\begin{array}{ccc}12 & -3 & 5 \\ 11 &…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If A and B are arbitrary constants, then the differential equation having \(\mathrm{y}=\mathrm{Ae}^{\mathrm{x}}+\mathrm{B} \sin 2 \mathrm{x}\) as its general solution isTS EAMCET 2023 Medium
- \(\sin ^{-1} \frac{4}{5}+2 \tan ^{-1} \frac{1}{3}\) is equal toTS EAMCET 2005 Medium
- If \(x^y=y^x\), then \(x(x-y \log x) \frac{d y}{d x}\) is equal to :TS EAMCET 2006 Hard
- The number of common tangents to the circles \(x^2+y^2+4 x=0\) and \(x^2+y^2-2 x=0\) isTS EAMCET 2018 Easy
- If \(\mathbf{a}\) and \(\mathbf{b}\) represent two non collinear vectors, the equation \(\mathbf{r}=t \mathbf{a}+(\mathrm{l}-t) \mathbf{b}\) representsTS EAMCET 2020 Easy
- The cosine of the angle \(A\) of the triangle with vertices \(A(1,-1,2), B(6,11,2), C(1,2,6)\) isTS EAMCET 2007 Easy
More PYQs from TS EAMCET
- A microscope using appropriate photons is engaged to track an electron in an atom within distance of What will be the uncertainty involved in measuring its velocity?TS EAMCET 2021 Medium
- If \(\frac{x^4+3 x+1}{(x+1)^2(x-1)}=A x+B+\frac{C}{x+1}+\frac{D}{(x+1)^2}+\frac{E}{x-1}\). Then \(A+B+C+D+E=\)TS EAMCET 2020 Medium
- If a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively isTS EAMCET 2025 Medium
- The vertices of a triangle are \(A(1,7), B(-5,-1)\) and \(C(-1,2)\). Then, the equation of a bisector of the \(\angle A B C\) isTS EAMCET 2018 Hard
- If and are the mean deviations from mean and median of the first even integers thenTS EAMCET 2021 Easy
- If \(f(x)=|x-1|+|x-2|\), then \(f^{\prime}(-2023)+\) \(\mathrm{f}^{\prime}\left(\frac{2024}{2023}\right)+\mathrm{f}^{\prime}(2023)=\)TS EAMCET 2023 Easy