Vikas

It is challenging to prepare in last 30 days, but not impossible. GATE is based on Four years of engineering syllabus. GATE tests the fundamentals of engineering. So see the past 5-10 years of question paper, decide your maximum scoring areas, decide your weak areas & then schedule your study accordingly. Understanding the fundamentals is very important as after clearing Written GATE exam you have Interview, technical Discussion to clear.

In vector calculus, divergence is a vector operator that produces a signed scalar field giving the quantity of a vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region. The divergence of the velocity field in that region would thus have a positive value. While the air is cooled and thus contracting, the divergence of the velocity has a negative value. In physical terms, the divergence of a three-dimensional vector field is the extent to which the vector field flow behaves like a source at a given point. It is a local measure of its "out goingness"– the extent to which there is more exiting an infinitesimal region of space than entering it. If the divergence is nonzero at some point then there must be a source or sink at that position.

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 59620 fruits, how many of them are apples?

The figures in the question seems to be wrong as answer is coming in decimals. Nevertheless the approach is Find Au = Unripe Apple = 45% of Unripe Fruits = 45 % (of 15% Total Fruits) Find Ar = Ripe Apple = (100-66)% of Ripe Fruits = 34% (of 85% Total Fruits) We need number of Apples = Au + Ar = Unripe Apples + Ripe Apples = 0.45*0.15*59620 + 0.34*0.85*59620 = 4024.35 + 17230.18 = 21254.53 Nos of Apples = 21254.53 (As the nos are integer it seems in question some the data is incorrect) But one can follow the approach given above to find the number of Apples

Michael lives 10 km away from where i live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, What is one possible distance (in km) at which I live from Arun’s place?

Assume you are at the center of circle, and possible location of other individual is on the perimeter of circle. Radius = distance between individuals. So we have 3 circles around you i.e., 5 km circle on which Ahmed lives, 7 km circle on which Susan lives, 10 km circle on which Michael Leaves. Arun's location is somewhere between 5 km to 7 km , as he is away from Ahmed (5 km Circle) , but closer than Susan (7 km Circle). Hence Arun's location is given by range in between 5 km to 7 km i.e., 5 km