Choose the correct answer.
Let A=\(\begin{bmatrix}1&sin\theta&1\\-sin\theta&1&sin\theta\\-1&-sin\theta&1\end{bmatrix}\),\(where 0≤\theta≤2\pi,then\)
\(Det(A)=0\)
\(Det (A)∈(2,∞)\)
\(Det(A)∈(2,4)\)
\(Det(A)∈[2,4]\)
A=\(\begin{bmatrix}1&sin\theta&1\\-sin\theta&1&sin\theta\\-1&-sin\theta&1\end{bmatrix}\)
\(∴|A|=1\)\((1+sin^{2}θ)-sinθ(-sinθ+sinθ)+1(sin^{2}θ+1)\)
\(=1+sin^{2}θ+sin^{2}θ+1\)
\(=2+2sin^{2}θ\)
\(=2(1+sin^{2}θ)\)
Now,
\(0≤\theta≤2\pi\)
\(⇒0≤sin\theta≤1\)
\(⇒0≤sin2\theta≤1\)
\(⇒1≤1+sin2\theta≤2\)
\(⇒1≤1+sin2\theta≤2\)
\(∴Det(A)∈[2,4]\)
The correct answer is D.
A settling chamber is used for the removal of discrete particulate matter from air with the following conditions. Horizontal velocity of air = 0.2 m/s; Temperature of air stream = 77°C; Specific gravity of particle to be removed = 2.65; Chamber length = 12 m; Chamber height = 2 m; Viscosity of air at 77°C = 2.1 × 10\(^{-5}\) kg/m·s; Acceleration due to gravity (g) = 9.81 m/s²; Density of air at 77°C = 1.0 kg/m³; Assume the density of water as 1000 kg/m³ and Laminar condition exists in the chamber.
The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in $\mu$m is .......... (round off to one decimal place).