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GATE 2023 II Engg. Mathematics Quiz 1

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Question 1

Let z = f (x, y) where x, y are function of t then according to the chain rule is equal to

Question 2

The value of definite integral is

Question 3

Value of

Question 4

Consider a function f(x, y, z) given by f(x, y, z) = (x2 – y2 + 9z2) (2y2 – z2) The partial derivative of this function with respect to x at the point
x =1, y = 1 and z = 1 is____.

Question 5

The smallest positive integers n for which

Question 6

If x = t2, y = t3, then is

Question 7

If find the value of

Question 8

The definite integral
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