JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(2 x-3 y=\gamma+5\) ; \(\alpha x+5 y=\beta+1\), where \(\alpha, \beta, \gamma \in R\) has infinitely many solutions, then the value of \(|9 \alpha+3 \beta+5 \gamma|\) is equal to
- A \(56\)
- B \(89\)
- C \(58\)
- D \(30\)
Answer & Solution
Correct Answer
(C) \(58\)
Step-by-step Solution
Detailed explanation
\(2 x-3 y=\gamma+5\) \(\alpha x+5 y=\beta+1\) Infinite many solution \(\frac{\alpha}{2}=\frac{5}{-3}=\frac{\beta+1}{\gamma+5}\) \(\alpha=\frac{-10}{3}, \quad 5 \gamma+25=-3 \beta-3\) \(9 \alpha=-30, \quad 3 \beta+5 \gamma=-28\) \(\text { Now, } 9 \alpha+3 \beta+5 \gamma=-58\)…
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
- For the differentiable function \(f: R -\{0\} \rightarrow R\), let \(3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10\), then \(\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|\) is equal toJEE Mains 2023 Hard
- If for some positive integer \(n,\) the coefficients of three consecutive terms in the binomial expansion of \((1+x)^{n+5}\) are in the ratio \(5: 10: 14,\) then the largest coefficient in this expansion isJEE Mains 2020 Hard
- The value of \(\log _{ e } 2 \frac{ d }{ dx }\left(\log _{\cos x } \operatorname{cosec} x \right)\) at \(x=\frac{\pi}{4}\) is.JEE Mains 2022 Medium
- Let \(A_{1}=\left\{(x, y):|x| \leq y^{2},|x|+2 y \leq 8\right\}\) and \(A_{2}=\{(x, y):|x|+|y| \leq k\}\). If \(27\) (Area \(\left.A _{1}\right)=5\) (Area \(A _{2}\) ), then \(k\) is equal toJEE Mains 2022 Hard
- If \(\int \frac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^9} d x=\)
\(\frac{1}{m}\left(\left(\sqrt{1+x^2}+x\right)^n\left(n \sqrt{1+x^2}-x\right)\right)+C\)
where C is the constant of integration and \(m, n \in N\), then \(\mathrm{m}+\mathrm{n}\) is equal toJEE Mains 2025 Hard - Let \(f\) be a polynomial function such that \(\log_2(f(x)) = \left(\log_2\left(2+\dfrac{2}{3}+\dfrac{2}{9}+\ldots\infty\right)\right)\cdot\log_3\left(1+\dfrac{f(x)}{f(1/x)}\right)\), \(x>0\) and \(f(6)=37\). Then \(\displaystyle\sum_{n=1}^{10}f(n)\) is equal to ________.JEE Mains 2026 Hard
More PYQs from JEE Mains
- The number of real solution(s) of the equation \(x^2+3 x+2=\min \{|x-3|,|x+2|\} \text { is : }\)JEE Mains 2025 Medium
- Let \(\quad S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots . .+\frac{2}{5^{107}}+\frac{1}{5^{108}}\). Then the value of \(\left(16 S -(25)^{-34}\right)\) is equal to \(............\).JEE Mains 2023 Hard
- The value of \(\cot \frac{\pi}{24}\) is :JEE Mains 2021 Hard
- A stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let \(P\) be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of \(P\) isJEE Mains 2014 Hard
- Let \(f(x) = \lim_{y \to 0} \dfrac{(1 - \cos(xy)) \tan(xy)}{y^3}\). Then the number of solutions of the equation \(f(x) = \sin x\), \(x \in \mathbf{R}\) is :JEE Mains 2026 Medium
- Let the eccentricity \(e\) of a hyperbola satisfy the equation \(6e^2 - 11e + 3 = 0\). If the foci of the hyperbola are \((3, 5)\) and \((3, -4)\), then the length of its latus rectum is :JEE Mains 2026 Medium