AP EAMCET · Maths · Determinants
The system of equations \(3 x+2 y+z=6\), \(3 x+4 y+3 z=14\) and \(6 x+10 y+8 z=a\), has infinite number of solutions, if \(a\) is equal to
- A \(8\)
- B \(12\)
- C \(24\)
- D \(36\)
Answer & Solution
Correct Answer
(D) \(36\)
Step-by-step Solution
Detailed explanation
Given system of equation is \[ \begin{gathered} 3 x+2 y+z=6 \\ 3 x+4 y+3 z=14 \\ 6 x+10 y+8 z=a \\ A=\left[\begin{array}{rrr} 3 & 2 & 1 \\ 3 & 4 & 3 \\ 6 & 10 & 8 \end{array}\right], B=\left[\begin{array}{r} 6 \\ 14 \\ a \end{array}\right] \end{gathered} \] Here,…
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 \(A\) and \(B\) are any two events such that \(P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}\) and \(P(\bar{A})=\frac{1}{4}\), then the events \(A\) and \(B\) areAP EAMCET 2017 Easy
- The transformed equation of \(2 x^2+3 y^2-z^2-8 x+18 y\) \(+2 z+9=0\) when the axes are translated to the point \((2,-3,1)\) isAP EAMCET 2023 Easy
- The point \((1,3)\) with respect to the ellipse \(4 x^2+9 y^2-16 x-54 y+61=0\) liesAP EAMCET 2021 Easy
- If the position vectors of the points \(A\) and \(B\) are \(2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}-\hat{j}+2 \hat{k}\) respectively, then the unit vector along \(\overrightarrow{\mathrm{BA}}\) and in the direction of \(\overrightarrow{\mathrm{AB}}\) isAP EAMCET 2023 Easy
- If three numbers are drawn at random successively without replacement from a set \(S=\{1,2, \ldots 10\}\), then the probability that the minimum of the chosen numbers is 3 or their maximum is 7 .AP EAMCET 2017 Medium
- \(\tan ^{-1}\left[\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x\right]=\)AP EAMCET 2019 Medium
More PYQs from AP EAMCET
- Curl the palm of your right hand around the circular wire with the fingers pointing in the direction of current and the thumb gives the direction of the magnetic field. In this case the upper side of the loop may be thought of asAP EAMCET 2023 Easy
- Two dice are thrown and the sum of the numbers appeared on the dice is noted. If \(A\) is the event of getting a prime number as their sum and \(B\) is the event of getting a number greater than 8 as their sum, then \(\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=\)AP EAMCET 2025 Medium
- The displacement of a particle of mass 2 g executing simple harmonic motion is \(x=8 \cos \left(50 t+\frac{\pi}{12}\right) m\), where \(t\) is time in second. The maximum kinetic energy of the particle isAP EAMCET 2024 Easy
- If one of the lines given by the pair of lines \(3 x^2-2 y^2+a x y=0\) is making an angle \(60^{\circ}\) with x -axis then \(\mathrm{a}=\)AP EAMCET 2025 Medium
- Let \(f(x)=\operatorname{Max}\{\cos x, \sin x, 0\}\). If the number of points at which \(f(x)\) is not differentiable in \((0,2024 \pi)\) is \(1012 k\), then \(\mathrm{k}=\)AP EAMCET 2023 Medium
- In \(\triangle \mathrm{ABC},\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{c}{2}=\)AP EAMCET 2024 Easy