McqMate
These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Bachelor of Arts in Economics (BA Economics) .
| 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 | |
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