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GATE 2022 Toppers Quiz 28

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Question 1

A function is defined by f(x) = 2x3 – 3x2 – 12x + 5 for –2 ≤ x ≤ 3. Which one of the following statements is true about this function?

Question 2

The temperature at a point (x, y, z) in space is given by t(x, y, z) = x2+y2-z. A mosquito located at (4,4,2) desires to fly in such a direction that it gets cooled faster. Find the direction in which it should fly?

Question 3

Figure shows the polar plot of a system, the transfer function of the system is

Question 4

Consider the state model as shown below :

The number of closed loop poles that lie on the right half of s-plane is

Question 5

In a semiconductor sample if donor concentration is 1014/cm3and acceptor concentration is 1013 /cm3 then difference between the fermi level and intrinsic fermi level (EF – EFi) is ____ eV.

(Assume ni = 1.5 × 1012 / cm3, T = 300°k)

Question 6

A band limited low-pass signal of bandwidth 5 kHz is sampled at a sampling rate The signal is reconstructed using the reconstruction filter whose magnitude response is shown below:

The minimum sampling rate (in kHz) for perfect reconstruction of is _________.

Question 7

A bus travelling at 80 km/hr uses 40% more petrol to travel a distance than it does when it travels at a speed of 65 km/hr. If the bus can travel 58.8 km on a litre at 65 km/hr, how far (in km) can the bus travel on 10 litres at 80 km/hr?

Question 8

The input is fed to a Hilbert transformer to obtain as shown in the figure below:

Here The value (accurate to two decimal places) of is __________.

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Jan 9ESE & GATE EC