80+ Mathematical Tools for Economics 1 Solved MCQs

1.

Suppose there is a Set S, which is the largest possible subset of S

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

Suppose there is a set S, which is the smallest possible subset of S

A. s1
B. s
C.
D. none of these
Answer» C. ∅
3.

If a set has n elements, the total number of subsets will be

A. 2n
B. 2n
C. 2/n
D. none of these
Answer» A. 2n
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:
Answer» A. m x n
5.

2 24.……………. is known as a signed minor

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

A set which contains only one element is called

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

If all the sets under consideration are subsets of a fixed set say ∪, then this set ∪ is called

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

Two sets A and B are said to be …………………. sets if no element of A is in B and no element of B is in A.

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

A matrix with equal number of rows and columns is called:

A. row matrix
B. column matrix
C. square matrix
D. none
Answer» C. square matrix
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
Answer» A. diagonal matrix
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
Answer» C. identity matrix
12.

A matrix in which every element is zero is called

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

Matrix obtained by inter changing the rows and columns is called ………… of a matrix

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

The matrix A is idempotent if:

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

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

A. additive
B. multiplicative
C. divisive
D. commutative
Answer» D. commutative
16.

If =1 23 −4 =0 −67 8, then A+B is equal to

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

If = [1 0 6] = [5 4 3], A+B is:

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

If A is a 3 × 2 matrix, B is a 2 × 3 matrix, C is a 2 × 2 matrix and D is a 3 × 3 matrix, then which of the following products does not exist?

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

The determinant of matrix =4 6 3 8 is:

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

If all the elements of any row or column are zero, the determinant is zero.

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

The determinant that results when the row and column in which that element lies are deleted is called:

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

An adjoint matrix is the ……………… of the cofactor matrix.

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

Inverse of A is denoted as

A. a−1
B. at
C. at
D. ai
Answer» A. a−1
24.

If the rows and columns of a determinant are interchanged, its value will:

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

If a set consists of a specific number of different elements, it is called

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

In …………………… sets, the number of elements in the two sets is equal.

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

The value of x in the equation 4x+3=2x+5

A. 1
B. 2
C. -2
D. 8
Answer» A. 1
28.

The values of x satisfying the equations is given by 3x+2=x+6

A. 4
B. 8
C. 2
D. -2
Answer» C. 2
29.

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

A. parabola
B. a liner
C. hyper-parabola
D. none of the above
Answer» B. a liner
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
Answer» B. a ≠0, b≠0
31.

A positive definite Hessian fulfils the second-order conditions for

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

A negative definite Hessian fulfils the second order conditions for

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

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

A. by factorization method
B. by quadratic formula
C. by completing the square method
D. all the above
Answer» D. all the above
34.

In a quadratic equation ax2+bx+c=0, sum of roots: α+β =

A. -
C. -
Answer» A. -
35.

A quadratic equation is an equation of degree

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

A polynomial can have:

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

A ------------ is a relation in which each input has only one output.

A. set
B. function
C. equation
D. all the above
Answer» B. function
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
Answer» B. proper subset
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
Answer» 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
Answer» C. associative 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
Answer» B. distributive 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
Answer» A. de morgan’s law
43.

set that contains everything is known as

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

Transpose of a rectangular matrix is a

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

Transpose of a column matrix is

A. zero matrix
B. diagonal matrix
C. column matrix
D. row matrix
Answer» 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.

In a matrix multiplication for A and B, (AB)t

A. at bt
B. bt at
C. 1/ab
D. ab
Answer» B. bt at
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.

Which of the following property does not hold for matrix multiplication?

A. associative
B. distributive
C. commutative
D. additive inverse
Answer» C. commutative
51.

A __________ is an ordered collection of objects.

A. relation
B. function
C. set
D. proposition
Answer» C. set
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.

Power set of empty set has exactly _________ subset.

A. one
B. two
C. zero
D. three
Answer» A. one
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.

The set of positive integers is _____________

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

The value of ‘x’ in 3x – 4 = 7 is

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

On solving x/2 + 5/3 = -1/2, we get x =

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

In 15/4 – 7x = 9, x=

A. 4/3
B. ¾
C. -4/3
D. -3/4
Answer» D. -3/4
60.

Sum of two numbers is 84. One of the numbers is 20 more than the other. The smaller number is

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

Variables of linear equation is implicitly raised to

A. first power
B. second power
C. third power
D. four power
Answer» A. first 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
Answer» B. 6x+2y = 10
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
Answer» C. to zero
64.

Two variables x and y if involved in linear equation then the equation is

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

The polynomial px2 + qx + rx4 + 5 is of type

A. linear
B. quadratic
C. cubic
D. biquadratic
Answer» D. biquadratic
66.

Identify the polynomial

A. x–2 + x–1 + 5
D. 3x2 + 7
Answer» D. 3x2 + 7
67.

The number of zeros of x2 + 4x + 2

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

The polynomial of type ax2 + bx + c, a = 0 is of type

A. linear
B. quadratic
C. cubic
D. biquadratic
Answer» A. linear
69.

The value of k, if (x – 1) is a factor of 4x3 + 3x2 – 4x + k, is

A. 1
B. 2
C. –3
D. 3
Answer» C. –3
70.

The degree of polynomial is

A. 0
B. 2
C. 1
D. 3
Answer» C. 1
71.

If 3 + 5 – 8 = 0, then the value of (3)3 + (5)3 – (8)3 is

A. 260
B. –360
C. –160
D. 160
Answer» B. –360
72.

. If value of 104 × 96 is

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

The value of 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37 is

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

The value of

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

If x + y = 3, x2 + y2 = 5 then xy is

A. 1
B. 3
C. 2
D. 5
Answer» C. 2
76.

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

A. 3
B. 1
C. 4
D. 2
Answer» B. 1
77.

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

A. x – 4
B. x + 2
C. x + 4
D. x – 5
Answer» A. x – 4
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
Answer» C. solutions
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
Answer» B. highest degree
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
Answer» C. independent variable
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.

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

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

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

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

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

A. 0
B. 1
C. 2
D. -1
Answer» B. 1
86.

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

A. j(x,yu,v)
B. j(u,vx,y)
C. ∂(x,y)∂(u,v)
D. ∂(u,x)∂(v,y)
Answer» B. j(u,vx,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
Tags
  • Question and answers in Mathematical Tools for Economics 1,
  • Mathematical Tools for Economics 1 multiple choice questions and answers,
  • Mathematical Tools for Economics 1 Important MCQs,
  • Solved MCQs for Mathematical Tools for Economics 1,
  • Mathematical Tools for Economics 1 MCQs with answers PDF download