JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations
\(\begin{aligned}
& x+2 y-3 z=2 \\
& 2 x+\lambda y+5 z=5 \\
& 14 x+3 y+\mu z=33
\end{aligned}\)
has infinitely many solutions, then \(\lambda+\mu\) is equal to :
- A 13
- B 10
- C 12
- D 11
Answer & Solution
Correct Answer
(C) 12
Step-by-step Solution
Detailed explanation
\begin{aligned} & \Delta=\left|\begin{array}{ccc} 1 & 2 & -3 \\ 2 & \lambda & 5 \\ 14 & 3 & \mu \end{array}\right|=0 \Rightarrow \lambda \mu+42 \lambda-4 \mu+107=0 \\ & \Delta_1=\left|\begin{array}{ccc} 2 & 2 & -3 \\ 5 & \lambda & 5 \\ 33 & 3 & \mu \end{array}\right|=0…
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
- Let \(S=\{x^{3}+ax^{2}+bx+c:a, b, c\in N\) and \(a, b, c\le 20\}\) be a set of polynomials. Then the number of polynomials in S, which are divisible by \(x^{2}+2,\) isJEE Mains 2026 Hard
- The value of \(\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)\) is equal toJEE Mains 2022 Easy
- Let \(a = lm\left( {\frac{{1 + {z^2}}}{{2iz}}} \right)\), where \(z\) is any non-zero complex number. The set \(A = \{ a:\left| z \right| = 1\,and\,z \ne \pm 1\} \) is equal toJEE Mains 2013 Hard
- Let \(A=\left(\begin{array}{cc}4 & -2 \\ \alpha & \beta\end{array}\right)\) . If \(A ^{2}+\gamma A +18 I = O\), then \(\operatorname{det}( A )\) is equal toJEE Mains 2022 Easy
- Let \(y = y ( x )\) be the solution of the differential equation \(\left( x ^2-3 y ^2\right) dx +3 xy dy =0, y (1)=1\). Then \(6 y^2(e)\) is equal toJEE Mains 2023 Medium
- Let \(A,B\) and \(C\) be the vertices of a variable right angled triangle inscribed in the parabola \(y^2=16x\). Let the vertex \(B\) containing the right angle be \((4,8)\) and the locus of the centroid of \(\triangle ABC\) be a conic \(C_o\). Then three times the length of latus rectum of \(C_o\) is ______JEE Mains 2026 Hard
More PYQs from JEE Mains
- Let \(A=\left[a_{i j}\right]\) be \(3 \times 3\) matrix such that \(A\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]\) and \(A\left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]\), then \(a_{23}\) equals :JEE Mains 2025 Easy
- Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \(f(x+y)=f(x) f(y)\) for all \(x, y \in \mathbf{R}\). If \(f^{\prime}(0)=4 \mathrm{a}\) and \(f\) satisfies \(f^{\prime \prime}(x)-3 \mathrm{a} f^{\prime}(x)-f(x)=0\), \(\mathrm{a}\gt0\), then the area of the region \(\mathrm{R}=\{(x, y) \mid 0 \leq y \leq f(\mathrm{a} x), 0 \leq x \leq 2\}\) is:JEE Mains 2025 Hard
- Let the mean and variance of \(12\) observations be \(\frac{9}{2}\) and \(4\) respectively. Later on, it was observed that two observations were considered as \(9\) and \(10\) instead of \(7\) and \(14\) respectively. If the correct variance is \(\frac{m}{n}\), where \(m\) and \(n\) are co-prime, then \(m + n\) is equal toJEE Mains 2023 Hard
- If the ellipse \(\frac{ x ^{2}}{ a ^{2}}+\frac{ y ^{2}}{ b ^{2}}=1\) meets the line \(\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1\) on the \(x\)-axis and the line \(\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1\) on the \(y\)-axis, then the eccentricity of the ellipse isJEE Mains 2022 Hard
- Let \(R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}\) be a relation on the set \(A= \{3, 5, 9, 12\}.\) Then, \(R\) isJEE Mains 2013 Hard
- Let \(\alpha > 0\). If \(\int \limits _0^\alpha \frac{ x }{\sqrt{ x +\alpha}-\sqrt{ x }} dx =\frac{16+20 \sqrt{2}}{15}\), then \(\alpha\) is equal to :JEE Mains 2023 Hard