AP EAMCET · Maths · Determinants
If \(\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right| \gt 0\), then \(a b c \gt\)
- A 1
- B -8
- C 8
- D 3
Answer & Solution
Correct Answer
(B) -8
Step-by-step Solution
Detailed explanation
Since, \(\left|\begin{array}{ccc}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right| \gt 0\) \(a(b c-1)-(c-1)+(1-b) \gt 0 \Rightarrow 2+a b c \gt a+b+c\) ....(i) Since, \(A . M . \geq G . M . \Rightarrow a+b+c \geq 3(a b c)^{1 / 3}\) ....(ii)…
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 straight rod of length 4 units slides such that its ends \(A\) and \(B\) always lie on the \(X\) and \(Y\)-axes respectively. Then, the locus of the centroid of \(\triangle O A B\) isAP EAMCET 2021 Medium
- Suppose exists for all real . If and then which one among the following statements is definitely true?AP EAMCET 2019 Medium
- A point on the parabola whose axis is parallel to the \(\mathrm{X}\)-axis and which passes through the points \((0,1),(3,0),(0,-2)\) isAP EAMCET 2017 Medium
- If \(35 \hat{\mathbf{i}}+14 \hat{\mathbf{j}}-77 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) and \(5 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}\) are coplanar, then \(\lambda\) is equal toAP EAMCET 2021 Medium
- Let \(\vec{a}\) and \(\vec{b}\) be two non-collinear vectors of unit modulus.
If \(\vec{u}=\vec{a}-(\vec{a} \cdot \vec{b}) \vec{b}\) and \(\vec{v}=\vec{a} \times \vec{b}\), then \(|\vec{v}|=\)AP EAMCET 2024 Medium - The number of different ways of preparing a garland by using 6 distinct white roses and 6 distinct red roses such that no two red roses come together isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- A body is released from a height of vertically downwards. The speed of the body at which potential energy is twice that of kinetic energy is (Acceleration due to gravity )AP EAMCET 2019 Easy
- Let \(a, b\) and \(c\) be distinct and none of them is equal to 1 . If the lines \(x+a y+a=0\), \(b x+y+b=0\) and \(c x+c y+1=0\) are concurrent, then the value of \(\frac{a}{a-1}+\frac{b}{b-1}+\frac{c}{c-1}\) isAP EAMCET 2018 Medium
- If the ionization constant of hypochlorous acid (HOCl) is \(2.5 \times 10^{-5}\), the pH of \(1.0 \mathrm{M}\) of its solution is \((\log 5=0.7)\)AP EAMCET 2018 Medium
- Given below are two statements.
Statement-I: Easily liquefiable gases are readily adsorbedStatement-II: Adsorption enthalpy for physisorption is less compared to adsorption enthalpy for Chemisorption
The correct answer isAP EAMCET 2024 Medium - \(\frac{1}{e^{3 x}}\left(e^x+e^{5 x}\right)=a_0+a_1 x+a_2 x^2+\ldots\)
\(\Rightarrow \quad 2 a_1+2^3 a_3+2^5 a_5+\ldots\) is equal toAP EAMCET 2009 Medium - Relatively which conditions favour the faster Brownian movement of colloidal particles in solution?AP EAMCET 2022 Easy