JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For real numbers \(\alpha\) and \(\beta\), consider the following system of linear equations: \(x+y-z=2, x+2 y+\alpha z=1,2 x-y+z=\beta\). If the system has infinite solutions, then \(\alpha+\beta\) is equal to \(.....\)
- A \(4\)
- B \(5\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
For infinite solutions \(\Delta=\Delta_{1}=\Delta_{2}=\Delta_{3}=0\) \(\Delta=\left|\begin{array}{ccc}1 & 1 & -1 \\ 1 & 2 & \alpha \\ 2 & -1 & 1\end{array}\right|=0\) \(\Delta=\left|\begin{array}{ccc}3 & 0 & 0 \\ 1 & 2 & \alpha \\ 2 & -1 & 1\end{array}\right|=0\)…
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
- A software company sets up \(m\) number of computer systems to finish an assignment in \(17\) days. If \(4\) computer systems crashed on the start of the second day, \(4\) more computer systems crashed on the start of the third day and so on, then it took \(8\) more days to finish the assignment. The value of \(m\) is equal to :JEE Mains 2024 Medium
- If \(A=\left[\begin{array}{cc}0 & -\tan \left(\frac{\theta}{2}\right) \\ 0 & \tan \left(\frac{\theta}{2}\right)\end{array}\right]\) and \(\left( I _{2}+ A \right)\left( I _{2}- A \right)^{-1}=\left[\begin{array}{ll} a & - b \\ b & a \end{array}\right],\) then \(13\left( a ^{2}+ b ^{2}\right)\) is equal to ...........JEE Mains 2021 Medium
- Let \(A\,=\,\{\,x\,\in \,R\,:\,x\) is not a positive int eger \(\}\) Define a function \(f\,:\,A\,\to \,R\) as \(f\,(x)\, = \frac{{2x}}{{x - 1}}\) then \(f\) isJEE Mains 2019 Hard
- The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to a line, whose direction ratios are \(2,3,-6\) is :JEE Mains 2021 Hard
- Let \(f: R \rightarrow R\) be a function defined as \(f(x)=\left\{\begin{array}{cl}\frac{\sin (a+1) x+\sin 2 x}{2 x} & , \text { if } x<0 \\ b & , \text { if } x=0 \\ \frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x>0\end{array}\right.\) . If \(f\) is continuous at \(x=0,\) then the value of \(a + b\) is equal to ....... .JEE Mains 2021 Hard
- A pole stands vertically inside a triangular park \(ABC\). Let the angle of elevation of the top of the pole from each corner of the park be \(\frac{\pi}{3}\). If the radius of the circumcircle ot \(\Delta ABC\) is \(2 ,\) then the height of the pole is equal to :JEE Mains 2021 Medium
More PYQs from JEE Mains
- Let \(v\) be the solution of the differential equation \(\left(1-x^{2}\right) d y=\left(xy+\left(x^{3}+2\right) \sqrt{1-x^{2}}\right) d x,-1 < x < 1\) and \(y(0)=0\) if \(\int\limits_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{1-x^{2}} y(x) d x=k\) then \(k^{-1}\) is equal to:JEE Mains 2022 Hard
- Let \(S=\{1,2,3,5,7,10,11\}\). The number of nonempty subsets of \(S\) that have the sum of all elements a multiple of \(3\) , is \(........\)JEE Mains 2023 Hard
- Let \(I\) be the identity matrix of order \(3 \times 3\) and for the matrix \(\mathrm{A}=\left[\begin{array}{ccc}\lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2\end{array}\right],|\mathrm{A}|=-1\). Let B be the inverse of the matrix \(\operatorname{adj}\left(\mathrm{A} \operatorname{adj}\left(\mathrm{A}^2\right)\right)\). Then \(|(\lambda B+1)|\) is equal to _____JEE Mains 2025 Hard
- Consider :\(f\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {\frac{{1 + \sin x}}{{1 - \sin x}}} } \right),x \in \left( {0,\frac{\pi }{2}} \right)\) A normal to \(y = f\left( x \right)\) at \(x = \frac{\pi }{6}\) also passes through the point :JEE Mains 2016 Hard
- The equation of the normal to the curve \(y=(1+x)^{2 y}+\cos ^{2}\left(\sin ^{-1} x\right)\) at \(x=0\) isJEE Mains 2020 Hard
- The sum of all the elements in the set \(\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid\) \(H.C.F.\) of \(n\) and \(2040\) is \(1\,\}\) is equal to \(.....\)JEE Mains 2021 Hard