Maths-
General
Easy

Question

# Assertion  If  then Reason  If   is a homogeneous function in  of degree '  ' then

Hint:

## The correct answer is: Both A and  are true, but  is not the correct explanation of

### We will check both the statements one by one.A: The given function is We have to find the value of We will first simplify the given function and find it's degree. The function should be homogeneous for further operations. Hence, we need to simplify it.z= f(u)So, xuxx + 2xyuxy + yuyy = g(u)[g'(u) - 1]    ...(1)We will find all the values.Substituting the values in equation (1) we get,x2uxx + 2xyuxy + y2uyy = 1(0 - 1)= -1So, the first statement is true.R: The second statement is directly the property of homogeneous equation of degree n and function of x and y. So, the second statement is true.Now, if we see the first statement has z as function of f(u). It cannot be directly found from the second statement. We have to make the changes to find the value for the first statement.Both the statements are true but, R is not correct explanation of A.

For such questions, we should know the formulas related to homogeneous equation. Before solving the equation, we have to see if the given function is a homegenous function. A homegenous function has same degree for all its terms.