GATE EC 2012 Question Paper (12-Feb-2012) (Shift 2)

The maximum value of f(x) = x³ - 9x²+ 24x + 5 in the interval [1, 6] is

Given that

$A=\left[\begin{array}{ccc}-5& & -3\\ 2& & 0\end{array}\right]andI=\left[\begin{array}{ccc}1& & 0\\ 0& & 1\end{array}\right]$ the value of A³ is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

i) 1 Ω connected at port B draws a current of 3 A

ii) 2.5 Ω connected at port B draws a current of 2 A

In the three dimensional view of a silicon n-channel MOS transistor shown below, d = 20 nm. The transistor is of width 1 μm. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of SiO₂ and Si, respectively, are 3.9 and 11.7, and ε₀ = 8.9 × 10⁻¹² F/m.

In the three dimensional view of a silicon n-channel MOS transistor shown below, d = 20 nm. The transistor is of width 1 μm. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of SiO₂ and Si, respectively, are 3.9 and 11.7, and ε₀ = 8.9 × 10⁻¹² F/m.