Mathematical Tools For Economics 1 Set 4 MCQs

This set of Mathematical Tools for Economics 1 Multiple Choice Questions & Answers (MCQs) focuses on Mathematical Tools For Economics 1 Set 4

Q1 | If x + 2 is a factor of x3 – 2ax2 + 16, then value of a is

Q2 | If one of the factor of x2 + x – 20 is (x + 5). Find the other

x – 4

x + 2

x + 4

x – 5

Q3 | The value of the unknown for which equation is true is called -------- of the equation.

explanation

variable

solutions

none of the above

Q4 | The highest degree of the variables in an equation determines the nature of the equation.

lowest degree

highest degree

value

solution

Q5 | If x and y are two variables such that y = f(x) ,for any value of the x there is acorresponding y value, then x is

dependent variable

constant

independent variable

none of the above

Q6 | Which of the following is incorrect?

direct search methods are useful when the optimization function is not differentiable

the gradient of f(x,y) is the a vector pointing in the direction of the steepest slope at that point

the hessian is the jacobian matrix of second-order partial derivatives of a function.

the second derivative of the optimization function is used to determine if we have reached an optimal point.

Q7 | An initial estimate of an optimal solution is given to be used in conjunction with thesteepest ascent method to determine the maximum of the function. Which of the following statements is correct?

the function to be optimized must be differentiable.

if the initial estimate is different than the optimal solution, then the magnitude of the gradient is nonzero.

as more iterations are performed, the function values of the solutions at the end of each subsequent iteration must be increasing.

all 3 statements are correct.

Q8 | Determine the determinant of hessian of the function 2x2-2y2 − 4y +6 at point (0, 0)?

-4

-8

Q9 | Determine the minimum of the function f(x,y)= x2+y2 ? Use the point (2, 1) as the initial estimate of the optimal solution. Conduct one iteration.

(2,1)

(−6,−3)

(0,0)

(1,−1)

Q10 | The Jacobian of p,q,r w.r.t x,y,z given p=x+y+z, q=y+z, r=z is ________

-1

Q11 | Which among the following is the definition of Jacobian of u and v w.r.t x and y?

j(x,yu,v)

j(u,vx,y)

∂(x,y)∂(u,v)

∂(u,x)∂(v,y)

Q12 | What are the gradient and the determinant of the Hessian of the function f(x, y ) = x2 y 2 at its global optimum?

∇f = 0i + 0j and h > 0

∇f = 0i + 0j and h = 0

∇f = 1i +1j and h < 0

∇f = 1i +1j and h = 0