JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the system of equations \(x+2 y+3 z=5\), \(2 x+3 y+z=9,4 x+3 y+\lambda z=\mu\) have infinite number of solutions. Then \(\lambda+2 \mu\) is equal to :
- A \(28\)
- B \(17\)
- C \(22\)
- D \(15\)
Answer & Solution
Correct Answer
(B) \(17\)
Step-by-step Solution
Detailed explanation
\( x+2 y+3 z=5 \) \(2 x+3 y+z=9 \) \( 4 x+3 y+\lambda z=\mu\) for infinite following \(\Delta=\Delta_1=\Delta_2=\Delta_3=0\) \(\Delta=\left|\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 4 & 3 & \lambda\end{array}\right|=0 \Rightarrow \lambda=-13\)…
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
- \(\text { If } \int\limits_{0}^{2}\left(\sqrt{2 x}-\sqrt{2 x-x^{2}}\right) d x=\) \(\int\limits_{0}^{1}\left(1-\sqrt{1-y^{2}}-\frac{y^{2}}{2}\right) d y+\int\limits_{1}^{2}\left(2-\frac{y^{2}}{2}\right) d y+I\) then \(I=\dots\dots\dots\)JEE Mains 2022 Hard
- The area (in sq. units) of the region \(A=\{(x, y):(x-1)[x] \leq y \leq 2 \sqrt{x}, 0 \leq x \leq 2\}\) where \([t]\) denotes the greatest integer function, isJEE Mains 2020 Hard
- A circle \(C_{1}\) passes through the origin \(O\) and has diameter \(4\) on the positive \(x\)-axis. The line \(y =2 x\) gives a chord \(OA\) of a circle \(C _{1}\). Let \(C _{2}\) be the circle with \(OA\) as a diameter. If the tangent to \(C _{2}\) at the point \(A\) meets the \(x\)-axis at \(P\) and \(y\)-axis at \(Q\), then \(QA : AP\) is equal to.JEE Mains 2022 Hard
- \(\lim _{n \rightarrow \infty} \tan \left\{\sum_{r=1}^{n} \tan ^{-1}\left(\frac{1}{1+r+r^{2}}\right)\right\}\) is equal to..........JEE Mains 2021 Medium
- Let \(x _1, x _2 \ldots ., x _{100}\) be in an arithmetic progression, with \(x _1=2\) and their mean equal to \(200\) . If \(y_i=i\left(x_i-i\right), 1 \leq i \leq 100\), then the mean of \(y _1, y _2\), \(y _{100}\) isJEE Mains 2023 Hard
- Let \(x=4\) be a directrix to an ellipse whose centre is at the origin and its eccentricity is \(\frac{1}{2}\) If \(P (1, \beta), \beta>0\) is a point on this ellipse, then the equation of the normal to it at \(P\) isJEE Mains 2020 Hard
More PYQs from JEE Mains
- The values of \(\lambda\) and \(\mu\) for which the system of linear equations \(x+y+z=2\) \(x+2 y+3 z=5\) \(x+3 y+\lambda z=\mu\) has infinitely many solutions are, respectivelyJEE Mains 2020 Medium
- Let the line \(\mathrm{L}\) be the projection of the line \(\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}\) in the plane \(x-2 y-z=3 .\) If \(d\) is the distance of the point \((0,0,6)\) from \(\mathrm{L}\), then \(\mathrm{d}^{2}\) is equal to .... .JEE Mains 2021 Hard
- Let \(f\,:\,R \to R\) be a function such that \(f\left( x \right) = {x^3} + {x^2}f'\left( 1 \right) + xf''\left( 2 \right) + f'''\left( 3 \right)\), \(x \in R\). Then \(f(2)\) equalsJEE Mains 2019 Hard
- Let \(E ^{ C }\) denote the complement of an event \(E\). Let \(E _{1}, E _{2}\) and \(E _{3}\) be any pairwise independent events with \(P \left( E _{1}\right) > 0\) and \(P \left( E _{1} \cap E _{2} \cap E _{3}\right)=0\) Then \(P \left( E _{2}^{ C } \cap E _{3}^{ C } / E _{1}\right)\) is equal toJEE Mains 2020 Hard
- The area (in sq. units) of the region \(\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^{2}: \mathrm{x}^{2} \leq \mathrm{y} \leq 3-2 \mathrm{x}\right\},\) isJEE Mains 2020 Hard
- Let \(\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) If \(8 x^{2}+b x+c=0\) is a quadratic equation whose roots are \(\alpha^{1 / 5}\) and \(\beta^{1 / 5}\), then the value of \(c-b\) is equal to:JEE Mains 2021 Hard