AP EAMCET · Maths · Determinants
If \(a, b, c\) are distinct positive real numbers, then the value of the determinant \(\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|\) is
- A \( < 0\)
- B \(>0\)
- C \(0\)
- D \(\geq 0\)
Answer & Solution
Correct Answer
(A) \( < 0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } \mathrm{A}=\left|\begin{array}{lll} a & b & c \\ b & c & a \\ c & a & b \end{array}\right| \quad\left[\mathrm{C}_1 \rightarrow \mathrm{C}_1 \rightarrow \mathrm{C}_2 \rightarrow \mathrm{C}_3\right] \\ & =\left|\begin{array}{lll} a+b+c & b & c \\…
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 sum of the coefficients of even powers of \(x\) in the expansion of \(\left(1-x+x^2\right)^{2 n}\) is 3281 , then \(\mathrm{n}=\)AP EAMCET 2023 Medium
- Observe the following statements :
\(\mathrm{A}: \int\left(\frac{x^2-1}{x^2}\right) e^{\frac{x^2+1}{x}} d x=e^{\frac{x^2+1}{x}}+c\)
\(\mathrm{R}: \int f^{\prime}(x) e^{f(x)} d x=f(x)+c\)
Then which of the following is true ?AP EAMCET 2006 Hard - If \(k>1\) and the determinant of the matrix \(A^2\), where \(A=\left[\begin{array}{ccc}k & k \alpha & \alpha \\ 0 & \alpha & k \alpha \\ 0 & 0 & k\end{array}\right]\), is \(k^2\), then \(|\alpha|\) equal toAP EAMCET 2014 Medium
- The maximum area of a rectangle that can be formed with a fixed perimeter of 20 units is sq unitsAP EAMCET 2021 Medium
- \(\int_0^{\infty}\left(x^{12}+x^{-12}\right) \frac{\log x}{x} d x=\)AP EAMCET 2022 Hard
- The equation of the plane \(\pi\) through the line of intersection of the planes \(\pi_1 \equiv x+3 y-6=0\), and \(\pi_2 \equiv 3 x-y+4 z=0\) is \(\pi_1+\lambda \pi_2=0\). If the plane \(\pi\) is at unit distance from the origin, then an equation of the plane \(\pi\) isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- The quotient when \(3 x^5-4 x^4+5 x^3-3 x^2+6 x-8\) is divided by \(x^2+x-3\) isAP EAMCET 2024 Easy
- If then lies in theAP EAMCET 2020 Easy
- The formation of ammonia from its constituent elements is an exothermic reaction. The effect of increase temperature on the reaction equilibrium isAP EAMCET 2022 Easy
- The value of isAP EAMCET 2022 Easy
- A body of mass \(1 \mathrm{~kg}\) is moving with a velocity \(10 \mathrm{~ms}^{-1}\) due to a constant force on a horizontal rough surface having coefficient of kinetic friction 0.4 . If the constant force is removed, the body comes to rest in a time (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2023 Medium
- For a binomial variate \(X \sim B(n, p)\) the difference between the mean and variance is 1 and the difference between their squares is 11 . If the probability of \(P(x=2)=m\left(\frac{5}{6}\right)^n\) and \(n=36\) then \(m: n=\)AP EAMCET 2024 Hard