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Partial Derivatives And Euler's Equation NAT

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10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Partial Derivatives And Euler's Equation NAT

Partial Derivatives And Euler's Equation NAT for Physics 2023 is part of Topic wise Tests for IIT JAM Physics preparation. The Partial Derivatives And Euler's Equation NAT questions and answers have been prepared according to the Physics exam syllabus.The Partial Derivatives And Euler's Equation NAT MCQs are made for Physics 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Partial Derivatives And Euler's Equation NAT below.

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*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 1

then the value of x²f_xx + 2xyf_xy + y²f_yy =

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 1

The correct answer is: 0

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 2

If u(x, y) = e^αx+βy satisfy the condition u_xx - 7u_xy + 12u_yy = 0. α² - 7αβ + β² = ____

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 2

We are given with u(x,y)=e^α^x+^βy

u_x=αe^{αx+ βy} , uy= βe^{αx+ βy}

u_xx=α²e^{αx+ βy}, u_yy=β²e^{αx+ βy}

u_xy= αβe^{αx+ βy}

put these values in the given relation, we get

u_xx-7u_xy+12u_yy=0

e^{αx+ βy}[α²-7αβ+12β²]=0

e^{αx+ β} ≠0=> α²-7αβ+12β²=0

The correct answer is: 0

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 3

Let f = y^x, what is at x = 2, y = 1

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 3

f = y^x

The correct answer is: 1

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 4

If z = 2(ax + by)² – (x² + y²) and a² + b² = 1 then find the value of

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 4

Correct Answer :- 0

Explanation : dz/dx = 4a(ax+by) - 2x

d²z/dx² = 4a² - 2

dz/dy = 4b(ax+by) - 2y

d2z/dy2 = 4b² - 2

d²z/dx²+ d²z/dx² = 4a² - 2 + 4b² - 2

=> 4(a²+b²) - 4

As we know that a² + b² = 1

=> 4(1) - 4

=> 0

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 5

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 5

v is homogeneous function of degree 3

The correct answer is: 3

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 6

If u = log(tan x + tan y + tan z), then (sin 2x) u_x + (sin 2y)u_y + sin 2z)u_z is equal to

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 6

The correct answer is: 2

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 7

If f(x, y) = x³y – xy³ then

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 7

1 – 12 = –11

The correct answer is: 0

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 8

If w = x²cos xy, then Find the value of a + b.

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 8

We have

= 1 - 0 = 1

a + b = 1

The correct answer is: 1

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 9

If v = log(x² + y²) then v_xx + v_yy equal to

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 9

The correct answer is: 0

*Answer can only contain numeric values

Partial Derivatives And Euler's Equation NAT - Question 10

If z = e^a^x+by f(ax - by) then the value of The value of n is

Detailed Solution for Partial Derivatives And Euler's Equation NAT - Question 10

= 2abz

The correct answer is: 2

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