JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S\) be the set of values of \(\lambda\), for which the system of equations \(6 \lambda x-3 y+3 z=4 \lambda^2\) \(2 x+6 \lambda y+4 z=1\) \(3 x+2 y+3 \lambda z=\lambda \text { has no solution. Then } 12 \sum_{\lambda \in S}|\lambda|\) is equal to \(...........\).
- A \(23\)
- B \(22\)
- C \(24\)
- D \(21\)
Answer & Solution
Correct Answer
(C) \(24\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}6 \lambda & -3 & 3 \\ 2 & 6 \lambda & 4 \\ 3 & 2 & 3 \lambda\end{array}\right|=0\) (For No Solution) \(2 \lambda\left(9 \lambda^2-4\right)+(3 \lambda-6)+(2-9 \lambda)=0\) \(18 \lambda^3-14 \lambda-4=0\) \((\lambda-1)(3 \lambda+1)(3 \lambda+2)=0\)…
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 \(a, b\) and \(c\) be distinct positive numbers. If the vectors \(a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k}\) and \(c \hat{i}+c \hat{j}+b \hat{k}\) are co-planar, then \(\mathrm{c}\) is equal to:JEE Mains 2021 Easy
- Let \(\vec{a}=\hat{i}-3 \hat{j}+7 \hat{k}, \vec{b}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}\) be a vector such that \((\vec{a}+2 \vec{b}) \times \vec{c}=3(\vec{c} \times \vec{a})\). If \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=130\), then \(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}\) is equal to ....................JEE Mains 2024 Hard
- Which of the following is true for \(y ( x )\) that satisfies the differential equation \(\frac{d y}{d x}=x y-1+x-y ; y(0)=0\)JEE Mains 2021 Medium
- If \(y=\tan ^{-1}\left(\sec x^{3}-\tan x^{3}\right) \cdot \frac{\pi}{2} < x^{3} < \frac{3 \pi}{2}\), thenJEE Mains 2022 Hard
- If \((27)^{999}\) is divided by \(7\), then the remainder isJEE Mains 2017 Hard
- Suppose a class has \(7\) students. The average marks of these students in the mathematics examination is \(62\), and their variance is \(20\) . A student fails in the examination if \(he/she\) gets less than \(50\) marks, then in worst case, the number of students can fail isJEE Mains 2022 Medium
More PYQs from JEE Mains
- The coefficient of \(t^4\) in the expansion of \({\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}\) isJEE Mains 2019 Hard
- A tower \(T_1\) of height \(60\, m\) is located exactly opposite to a tower \(T_2\) of height \(80\, m\) on a straight road. From the top of \(T_1\) . if the angle of depression of the foot of \(T_2\) is twice the angle of elevation of the top of \(T_2\), then the width (in \(m\)) of the road between the feet of the towers \(T_1\) and \(T_2\) isJEE Mains 2018 Hard
- \(25 \%\) of the population are smokers. A smoker has \(27\) times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is \(\frac{ k }{10}\). Then the value of \(k\) is \(.............\)JEE Mains 2023 Hard
- Let \( \alpha, \beta \in \mathbb{R} \) be such that the function
\( f(x)=\begin{cases}2\alpha(x^{2}-2)+2\beta x&,x<1\\ (\alpha+3)x+(\alpha-\beta)&,x\ge1\end{cases} \)
be differentiable at all \( x \in \mathbb{R} \). Then \( 34(\alpha+\beta) \) is equal toJEE Mains 2026 Hard - Let \(S\) be the set of all real roots of the equation, \(3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .\) Then \(\mathrm{S}\)JEE Mains 2020 Hard
- Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}} .\) If \(\overrightarrow{\mathrm{c}}\) is a vector such that \(\vec{a} \times \vec{c}=\vec{b}\) and \(\vec{a} \cdot \vec{c}=3\), then \(\vec{a} \cdot(\vec{b} \times \vec{c})\) is equal to :JEE Mains 2021 Hard