JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of real values of \(\lambda \) for which the system of linear equations \(2x + 4y - \lambda z = 0\) ;\(4x + \lambda y + 2z = 0\) ; \(\lambda x + 2y+ 2z = 0\) has infinitely many solutions, is
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
Since the given system of linear equations has infinitely many solutions. \(\therefore \begin{array}{*{20}{c}} 2&4&{ - \lambda }\\ 4&\lambda &2\\ \lambda &2&2 \end{array} = 0\) \( \Rightarrow {\lambda ^3} + 4\lambda - 40 = 0\) \(\lambda \) has only \(1\) real root.
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 the point \(\left( {2,\alpha ,\beta } \right)\) lies on the plane which passes through the points \((3, 4, 2)\) and \((7, 0, 6)\) and is perpendicular to the plane \(2x - 5y = 15\) , then is equal to \({2\alpha - 3\beta }\) is equal toJEE Mains 2019 Hard
- If the differential equation representing the family of all circles touching \(x-\) axis at the origin is \(\left( {{x^2} - {y^2}} \right)\frac{{dy}}{{dx}} = g\left( x \right)y\) , then \(g(x)\) equalsJEE Mains 2014 Hard
- Four distinct points \((2 \mathrm{k}, 3 \mathrm{k}),(1,0),(0,1)\) and \((0,0)\) lie on a circle for \(k\) equal to :JEE Mains 2024 Medium
- The area (in square units) of the region enclosed by the ellipse \(x^2+3 y^2=18\) in the first quadrant below the line \(y=x\) is :JEE Mains 2024 Hard
- Two vertices of a triangle \(\mathrm{ABC}\) are \(\mathrm{A}(3,-1)\) and \(\mathrm{B}(-2,3)\), and its orthocentre is \(\mathrm{P}(1,1)\). If the coordinates of the point \(\mathrm{C}\) are \((\alpha, \beta)\) and the centre of the circle circumscribing the triangle \(\mathrm{PAB}\) is \((h, k)\), then the value of \((\alpha+\beta)+2(h+k)\) equals :JEE Mains 2024 Hard
- A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of \(4\). Then the conditional probability that the score \(4\) has appeared at least once isJEE Mains 2020 Medium
More PYQs from JEE Mains
- A differential equation representing the family of parabolas with axis parallel to \(\mathrm{y}\)-axis and whose length of latus rectum is the distance of the point \((2,-3)\) form the line \(3 x+4 y=5\), is given by :JEE Mains 2021 Hard
- The number of singular matrices of order 2 , whose elements are from the set \(\{2,3,6,9\}\) isJEE Mains 2025 Medium
- Let \(a, b\), c be three distinct real numbers, none equal to one. If the vectors \(a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+ c \hat{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal toJEE Mains 2023 Medium
- Let \(n \ge 2\) be a natural number and \(0 < \theta < \frac{\pi }{2}\). Then \(\int {\frac{{{{\left( {{{\sin }^n}\,\theta - \sin \,\theta } \right)}^{\frac{1}{n}}}\,\cos \,\theta }}{{{{\sin }^{n + 1}}\,\theta }}} d\theta \) is equal toJEE Mains 2019 Hard
- Let \(n \in N\) and \([x]\) denote the greatest integer less than or equal to \(x\). If the sum of \((n+1)\) terms \({ }^{n} C_{0}, 3 .{ }^{n} C_{1}, 5 .{ }^{n} C_{2}, 7 .{ }^{n} C_{3}, \ldots\) is equal to \(2^{100} \cdot 101\), then \(2\left[\frac{n-1}{2}\right]\) is equal to \(....\)JEE Mains 2021 Hard
- If \(\int \limits_{-0.15}^{0.15}\left|100 x ^2-1\right| dx =\frac{ k }{3000}\), then \(k\) is equal to \(..........\).JEE Mains 2023 Hard