JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(2 \mathrm{x}+2 \mathrm{ay}+\mathrm{az}=0\) ; \(2 x+3 b y+b z=0\) ; \(2 \mathrm{x}+4 \mathrm{cy}+\mathrm{cz}=0\) ; where \(a, b, c \in R\) are non-zero and distinct; has a non-zero solution, then
- A \(a, b, c\) are in \(A.P.\)
- B \(a + b + c = 0\)
- C \(a, b, c\) are in \(G.P.\)
- D \(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in \(A.P.\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in \(A.P.\)
Step-by-step Solution
Detailed explanation
For non-zero solution \(\left|\begin{array}{ccc}{2} & {2 a} & {a} \\ {2} & {3 b} & {b} \\ {2} & {4 c} & {c}\end{array}\right|=0, \Rightarrow\left|\begin{array}{ccc}{1} & {2 a} & {a} \\ {0} & {3 b-2 a} & {b-a} \\ {0} & {4 c-2 a} & {c-a}\end{array}\right|=0\)…
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
- If the line, \(2 x-y+3=0\) is at a distance \(\frac{1}{\sqrt{5}}\) and \(\frac{2}{\sqrt{5}}\) from the lines \(4 x-2 y+\alpha=0\) and \(6 x-3 y+\beta=0,\) respectively, then the sum of all possible values of \(\alpha\) and \(\beta\) isJEE Mains 2020 Medium
- If \(A = \dfrac{\sin 3^\circ}{\cos 9^\circ} + \dfrac{\sin 9^\circ}{\cos 27^\circ} + \dfrac{\sin 27^\circ}{\cos 81^\circ}\) and \(B = \tan 81^\circ - \tan 3^\circ\), then \(\dfrac{B}{A}\) is equal to _____.JEE Mains 2026 Medium
- The angle of elevation of the top of a vertical tower from a point \(A\), due east of it is \(45^o\) . The angle of elevation of the top of the same tower from a point \(B\). due south of \(A\) is \(30^o\). If the distance between \(A\) and \(B\) is \(54\sqrt 2 \,m\), then the height of the tower (in metres), isJEE Mains 2016 Hard
- Let \(\overrightarrow{ x }\) be a vector in the plane containing vectors \(\overrightarrow{ a }=2 \hat{ i }-\hat{ j }+\hat{ k }\) and \(\overrightarrow{ b }=\hat{ i }+2 \hat{ j }-\hat{ k }\). If the vector \(\overrightarrow{ x }\) is perpendicular to \((3 \hat{ i }+2 \hat{ j }-\hat{ k })\) and its projection on \(\overrightarrow{ a }\) is \(\frac{17 \sqrt{6}}{2},\) then the value of \(|\overrightarrow{ x }|^{2}\) is equal to ...... .JEE Mains 2021 Medium
- If \(\int \frac{\cos x d x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}}=f(x)\left(1+\sin ^{6} x\right)^{1 / \lambda}+c\) where \(c\) is a constant of integration, then \(\lambda f\left(\frac{\pi}{3}\right)\) is equal toJEE Mains 2020 Hard
- If \(a_1 , a_2, a_3, . . . . , a_n, ....\) are in \(A.P.\) such that \(a_4 - a_7 + a_{10}\, = m\), then the sum of first \(13\) terms of this \(A.P.\), is .............. \(\mathrm{m}\)JEE Mains 2013 Hard
More PYQs from JEE Mains
- If \(f(x)=\frac{2^x}{2^x+\sqrt{2}}, \mathrm{x} \in \mathbb{R}\), then \(\sum_{\mathrm{k}=1}^{81} f\left(\frac{\mathrm{k}}{82}\right)\) is equal toJEE Mains 2025 Medium
- The area of the region enclosed by the parabola \(y=4 x-x^2\) and \(3 y=(x-4)^2\) is equal toJEE Mains 2024 Medium
- The variance \(\sigma^2\) of the data is ...........
\(x_i\) \(0\) \(1\) \(5\) \(6\) \(10\) \(12\) \(17\) \(f_i\) \(3\) \(2\) \(3\) \(2\) \(6\) \(3\) \(3\) JEE Mains 2024 Medium - Let \(A, B\) and \(C\) be three events, which are pair-wise independence and \(\bar E\) denotes the complement of an event \(E\) . If \(P(A \cap B \cap C) = 0\) and \(P(C) > 0,\) then \(P[(\bar A \cap \bar B)|\,C]\) is equal toJEE Mains 2018 Hard
- If \(15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6,\) for some \(\alpha \in R ,\) then the value of \(27 \sec ^{6} \alpha+8 \operatorname{cosec}^{6} \alpha\) is equal to ....... .JEE Mains 2021 Medium
- Let an ellipse \(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\), \(a < b\), pass through the point \((4, 3)\) and have eccentricity \(\dfrac{\sqrt{5}}{3}\). Then the length of its latus rectum is :JEE Mains 2026 Medium