# 80+ Mathematical Tools for Economics 1 Solved MCQs

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1.

A. s1
B. s
C.
D. none of these
2.

A. s1
B. s
C.
D. none of these
3.

A. 2n
B. 2n
C. 2/n
D. none of these
4.

## If a set S1 has n elements and S2 has m elements, how many ordered pairs can form in general?

A. m x n
B. m + n
C. m/n
D. none of these:
5.

A. rank
B. cofactor
C. inverse
D. none
6.

A. singleton set
B. finite set
C. proper set
D. none of these
7.

A. universal set
B. power set
C. disjoint set
D. finite set
8.

A. universal
B. disjoint
C. equivalent
D. none of these
9.

A. row matrix
B. column matrix
C. square matrix
D. none
10.

## A square matrix in which all elements except those in diagonal are zero are called:

A. diagonal matrix
B. identity matrix
C. null matrix
D. none
11.

## A diagonal matrix with all its diagonal elements equal to 1 is known as:

A. triangular matrix
B. zero matrix
C. identity matrix
D. none
12.

## A matrix in which every element is zero is called

A. scalar matrix
B. null matrix
C. square matrix
D. inverse matrix
13.

A. inverse
B. transpose
C. negative
D. none
14.

A. a2 = a
B. a = at
C. a2 = at
D. none
15.

## If A and B are square matrices such that AB = BA, then A and B are called…………..

B. multiplicative
C. divisive
D. commutative
16.

A. 1 −410 4
B. 7 9 −3 −4
C. 3 −36 7
D. none
17.

A. [19]
B. [6 0 9]
C. [6 4 9]
D. none
18.

A. ab
B. ac
C. bd
D. cd
19.

A. 14
B. 7
C. -1
D. 3
20.

A. unity
B. positive
C. negative
D. zero
21.

A. cofactor
B. minor
C. inverse
D. none
22.

A. inverse
B. minor
C. cofactor
D. transpose
23.

A. a−1
B. at
C. at
D. ai
24.

A. change
B. change sign
C. not change
D. become zero
25.

A. infinite set
B. finite set
C. unit set
D. null set
26.

A. null
B. equivalent
C. singleton
D. zero
27.

A. 1
B. 2
C. -2
D. 8
28.

A. 4
B. 8
C. 2
D. -2
29.

## The curve of a linear equation is................

A. parabola
B. a liner
C. hyper-parabola
D. none of the above
30.

## A linear equation in two variables is of the form ax + by + c = 0, where

A. a=0, b=0
B. a ≠0, b≠0
C. both a and b
D. none of the above
31.

## A positive definite Hessian fulfils the second-order conditions for

A. maximum
B. minimum
C. both maximum and minimum
D. minimax
32.

## A negative definite Hessian fulfils the second order conditions for

A. maximum
B. minimum
C. both maximum and minimum
D. minimax
33.

## The general quadratic equation ax2 +bx +c=0 can be solved by using

A. by factorization method
C. by completing the square method
D. all the above
34.

A. -
C. -
35.

## A quadratic equation is an equation of degree

A. one
B. two
C. three
D. all of the above
36.

A. constants
B. variables
C. exponents
D. all the above
37.

A. set
B. function
C. equation
D. all the above
38.

## When S1⊆ S, where S contains at least one element not in S1, S1 is called a ----- of S.

A. power of the set
B. proper subset
C. equivalent set
D. unit set
39.

## A ∪ B = B∪ A and A ∩ B= B ∩ A is known as

A. de morgan’s law
B. distributive law
C. associative law
D. commutative law
40.

## A ∪ (B∪ C) = (A ∪ B )∪C and A ∩ (B∩C)= (A ∩ B) ∩C is known as

A. de morgan’s law
B. distributive law
C. associative law
D. commutative law
41.

## A ∪ (B ∩C) = (A ∪ B ) ∩(A∪C)A ∩ (B∪C)= (A ∩ B) ∪(A∩C) is known as

A. de morgan’s law
B. distributive law
C. associative law
D. commutative law
42.

## (A ∪ B) ' = A' ∩ B' and (A ∩ B) '= A'∪ B' is known as

A. de morgan’s law
B. distributive law
C. associative law
D. commutative law
43.

## set that contains everything is known as

A. universal set
B. proper subset
C. equivalent set
D. unit set
44.

## Transpose of a rectangular matrix is a

A. rectangular matrix
B. diagonal matrix
C. square matrix
D. scalar matrix
45.

## Transpose of a column matrix is

A. zero matrix
B. diagonal matrix
C. column matrix
D. row matrix
46.

## Two matrices A and B are multiplied to get AB if

A. both are rectangular
B. both have same order
C. no of columns of a is equal to columns of b
D. no of rows of a is equal to no of columns of b
Answer» D. no of rows of a is equal to no of columns of b
47.

A. at bt
B. bt at
C. 1/ab
D. ab
48.

## Two matrices A and B are multiplied to get BA if

A. both are rectangular
B. both have same order
C. no of columns of a is equal to columns of b
D. both are square matrices
Answer» D. both are square matrices
49.

## What is the order of a matrix?

A. number of rows x number of columns
B. number of columns x number of rows
C. number of rows x number of rows
D. number of columns x number of columns
Answer» A. number of rows x number of columns
50.

A. associative
B. distributive
C. commutative
51.

A. relation
B. function
C. set
D. proposition
52.

## The set B of odd positive integers less than 10 can be expressed by _____________

A. {1, 2, 3}
B. {1, 3, 5, 7, 9}
C. {1, 2, 5, 9}
D. {1, 5, 7, 9, 11}
Answer» B. {1, 3, 5, 7, 9}
53.

A. one
B. two
C. zero
D. three
54.

## What is the Cartesian product of A = {1, 2} and B = {a, b}?

A. {(1, a), (1,
B. , (2, a), (b, b)} b) {(1, 1), (2, 2), (a, a), (b, b)}
C. {(1, a), (2, a), (1, b), (2, b)}
D. {(1, 1), (a, a), (2, a), (1, b)}
Answer» C. {(1, a), (2, a), (1, b), (2, b)}
55.

## Which of the following two sets are equal?

A. a = {1, 2} and b = {1}
B. a = {1, 2} and b = {1, 2, 3}
C. a = {1, 2, 3} and b = {2, 1, 3}
D. a = {1, 2, 4} and b = {1, 2, 3}
Answer» C. a = {1, 2, 3} and b = {2, 1, 3}
56.

A. infinite
B. finite
C. subset
D. empty
57.

A. 1
B. 11/3
C. 3/11
D. 7/12
58.

A. -13/3
B. -3/13
C. 13/3
D. 3/13
59.

A. 4/3
B. ¾
C. -4/3
D. -3/4
60.

A. 12
B. 22
C. 32
D. 42
61.

A. first power
B. second power
C. third power
D. four power
62.

## Example of linear equation involving two variables is

A. 7x+3y+4z = 20
B. 6x+2y = 10
C. 8x = 2+10
D. 7a+8b+9c = 10+5
63.

## In the linear equation 'ax+by = c' the a and b cannot be equal

A. to rational numbers
B. to one
C. to zero
D. set of even numbers
64.

A. ax+by = c
B. ab+xy = c
C. ac+bx = y
D. ax+bc = y
65.

A. linear
C. cubic
66.

A. x–2 + x–1 + 5
D. 3x2 + 7
67.

A. 1
B. 2
C. 3
D. none of these
68.

A. linear
C. cubic
69.

A. 1
B. 2
C. –3
D. 3
70.

A. 0
B. 2
C. 1
D. 3
71.

A. 260
B. –360
C. –160
D. 160
72.

A. 9984
B. 9469
C. 10234
D. 11324
73.

A. 237
B. 126
C. 56
D. 64
74.

A. 300
B. 500
C. 400
D. 600
75.

A. 1
B. 3
C. 2
D. 5
76.

A. 3
B. 1
C. 4
D. 2
77.

A. x – 4
B. x + 2
C. x + 4
D. x – 5
78.

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

A. explanation
B. variable
C. solutions
D. none of the above
79.

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

A. lowest degree
B. highest degree
C. value
D. solution
80.

## If x and y are two variables such that y = f(x) ,for any value of the x there is a corresponding y value, then x is

A. dependent variable
B. constant
C. independent variable
D. none of the above
81.

## Which of the following is incorrect?

A. direct search methods are useful when the optimization function is not differentiable
B. the gradient of f(x,y) is the a vector pointing in the direction of the steepest slope at that point
C. the hessian is the jacobian matrix of second-order partial derivatives of a function.
D. the second derivative of the optimization function is used to determine if we have reached an optimal point.
Answer» D. the second derivative of the optimization function is used to determine if we have reached an optimal point.
82.

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

A. the function to be optimized must be differentiable.
B. if the initial estimate is different than the optimal solution, then the magnitude of the gradient is nonzero.
C. as more iterations are performed, the function values of the solutions at the end of each subsequent iteration must be increasing.
D. all 3 statements are correct.
Answer» D. all 3 statements are correct.
83.

A. 2
B. -4
C. 0
D. -8
84.

A. (2,1)
B. (−6,−3)
C. (0,0)
D. (1,−1)
85.

A. 0
B. 1
C. 2
D. -1
86.

A. j(x,yu,v)
B. j(u,vx,y)
C. ∂(x,y)∂(u,v)
D. ∂(u,x)∂(v,y)
87.

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

A. ∇f = 0i + 0j and h > 0
B. ∇f = 0i + 0j and h = 0
C. ∇f = 1i +1j and h < 0
D. ∇f = 1i +1j and h = 0
Answer» A. ∇f = 0i + 0j and h > 0