KCET · Maths · Complex Number
If \(3 x+i(4 x-y)=6-i\) where \(x\) and \(y\) are real numbers, then the values of \(x\) and \(y\) are respectively,
- A 3, 9
- B 2, 4
- C 2, 9
- D 3, 4
Answer & Solution
Correct Answer
(C) 2, 9
Step-by-step Solution
Detailed explanation
\(3 x+i(4 x-y)=6-i\)
On comparing real and imaginary parts of LHS and RHS, we get
\[
\begin{aligned}
& 3 x=6 \text { and } 4 x-y=-1 \\
& \Rightarrow \quad 3 x=6 \Rightarrow x=2 \\
& \text { Put } x=2 \text { into } 4 x-y=-1 \text {, we get } \\
& 4 \times 2-y=-1 \\
& \Rightarrow \quad 8+1=y \Rightarrow y=9 \\
&
\end{aligned}
\]
On comparing real and imaginary parts of LHS and RHS, we get
\[
\begin{aligned}
& 3 x=6 \text { and } 4 x-y=-1 \\
& \Rightarrow \quad 3 x=6 \Rightarrow x=2 \\
& \text { Put } x=2 \text { into } 4 x-y=-1 \text {, we get } \\
& 4 \times 2-y=-1 \\
& \Rightarrow \quad 8+1=y \Rightarrow y=9 \\
&
\end{aligned}
\]
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
- The length of the latus rectum of \(x^2+3 y^2=12\) isKCET 2025 Easy
- The solution for the differential equation \( \frac{d y}{y}+\frac{d x}{x}=0 \)KCET 2016 Easy
- The area of the triangle with vertices \((3, 8), (-4, 2)\) and \((5, 1)\) is \(\dfrac{P}{4}\), then the value of \(P\) isKCET 2026 Easy
- If \(\sin ^{-1} a\) is the acute angle between the curves \(x^{2}+y^{2}=4 x\) and \(x^{2}+y^{2}=8\) at \((2,2)\), then \(a\) is equal toKCET 2013 Hard
- The image of the point \( (1,6,3) \) in the line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) isKCET 2018 Hard
- \(\lim _{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=\)KCET 2022 Easy
More PYQs from KCET
- If \(A=\left[\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right] B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]\), then \((A B)^{\prime}\) is equal toKCET 2021 Easy
- The percentage of \(p\)-character of the hybrid orbitals in graphite and diamond are respectivelyKCET 2012 Easy
- \(\mathrm{H}_{2}(g)+2 \mathrm{AgCl}(s) \rightleftharpoons 2 \mathrm{Ag}(s)+2 \mathrm{HCl}(a q)\) \(E_{\text {cell }}^{\circ}\) at \(25^{\circ} \mathrm{C}\) for the cell is \(0.22 \mathrm{~V}\). The equilibrium constant at \(25^{\circ} \mathrm{C}\) isKCET 2021 Hard
- If \(f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)\), then \(f'\left(\dfrac{1}{2}\right) = \)KCET 2026 Easy
- Statement A: Photorespiration decreases photosynthetic output.
Statement B: In photorespiratory pathway, neither ATP nor NADPH is produced.KCET 2014 Medium - A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii isKCET 2013 Easy