GATE EE 2018 Question Paper (10-Feb-2018) (Shift 2)

In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain 𝛽 = 100. The base-emitter voltage drop is a constant, 𝑉${}_{\text{BE}}$ = 0.7 𝑉. The value of the Thevenin equivalent resistance 𝑅${}_{\text{Th}}$ (in Ω) as shown in the figure is ______ (up to 2 decimal places).

As shown in the figure, 𝐶 is the arc from the point (3, 0) to the point (0, 3) on the circle 𝑥² + 𝑦² = 9. The value of the integral $\underset{c}{\int }\left(y^2+2yx\right)dx+\left(2xy+x^2\right)dy$ is _____ (up to 2 decimal places).

Let f(x) = 3x³ – 7x² + 5x + 6. The maximum value of f(x) over the interval [0, 2] is _______ (up to 1 decimal place).

Let A = ≤ft[ {*20c 1&0& - 1\\ - 1&2&0\\ 0&0& - 2 } ] and B = A³ – A² – 4A + 5I, where I is the 3 × 3 identity matrix. The determinant of B is _______ (up to 1 decimal place).

The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is __________ (up to 2 decimal places).