Business Mathematics Online MCQ Set 8

QN01. The probability of a bomb hitting a bridge is ½ and two direct hits are needed to destroy it. The least number of bombs required so that the probability of the bridge being destroyed is greater than 0.9 is

1. 8
2. 9
3. 10
4. 11

Answer

(B)9

QN02. Find the number of non-congruent rectangles that can be found on a normal 8*8 chessboard

1. 24
2. 36
3. 48
4. None of these

Answer

(B)36

QN03. Solve -x +2y -3z = 2
-2y = 3
2x -y +z = 9

1. x =5/2, y =7/2, z=-7/2
2. x=-3/2, y=-11/2, z=-7/2
3. x=11/2, y=-3/2, z=-7/2
4. x=-7/2, y= -3/2, z=-11/2

Answer

(C)x=11/2, y=-3/2, z=-7/2

QN04. Is (x+y)(x-y) = -7

1. Linear
2. Non linear
3. Monomial
4. None

Answer

(B)Non linear

QN05. The number of non zero rows of a matrix in its row echelon form is a

1. Row matrix
2. Column matrix
3. Rank of matrix
4. Augmented matrix

Answer

(C)Rank of matrix

QN06. A square matrix with each of its diagonal elements equal to unity and all non diagonal elements equal to zero is

1. Scalar matrix
2. Null matrix
3. Identity matrix
4. Column matrix

Answer

(C)Identity matrix

QN07. Find the transpose of A= 1 -1
2 3

1. 2 3
   1 -1

2. 1 2
   -1 3

3. 3 2
   1 -1

4. 3 1
   2 -1

Answer

(B)1 2
-1 3

QN08. Which of the following is correct:

1. Determinant is a square matrix
2. Determinant is a number associated to a square matrix.
3. Determinant is a number associated to a matrix.
4. None of these.

Answer

(B)Determinant is a number associated to a square matrix.

QN09. Find values of k if area of triangle is 3sq. units and vertices are (1,3), (0,0) and (k,0)

1. +3
2. -3
3. ± 1
4. ±2

Answer

(D)±2

QN10. Let A be a non singular matrix of order 3 x3.Then |adj A | is equal to

1. |A |
2. |A |²
3. | A |³
4. 3 | A|

Answer

(B)

|A |²

QN11. The equation x -y =a is consistent for
z +w =b
y -w = c
x +z =d

1. a = b +c +d
2. c = a +b +d
3. b = a +c +d
4. d = a +b +c

Answer

(D)d = a +b +c

QN12. Solve 2x +5y =24 using matrix inversion
3x +8y =38

1. x=3, y=4
2. x=1, y=3
3. x=1, y=4
4. x=2, y=4

Answer

(D)x=2, y=4

QN13. Solve x +2y -z =3 using Cramer’s rule
3x +y +z =4
x -y +2z = 6

1. x=-3, y=6, z=5
2. x=-5, y=9, z=10
3. x=-6, y=7, z=10
4. x=-4, y=8, z=5

Answer

(B)x=-5, y=9, z=10

QN14. Solve 5x + 2y =3-x – 4y =3

1. x = -1 y =1
2. x = 1 y = -1
3. x = 0 y = 1
4. x =1 y = 0

Answer

(B)x = 1 y = -1

QN15. In a class of 200 students, 70 played cricket, 60 played hockey and 80 played football. 30 played cricket and football, 30 played hockey and football, 40 played cricket and hockey. Find the maximum number of people playing all three games and also the minimum number
of people playing at least one game.

1. 200, 100
2. 30,110
3. 30, 120
4. None of these

Answer

(B)30,110

QN16. Find the range for the relation : {(3, 5), (2, 5), (2, 6), (3, 7)

1. {2, 3}
2. {5, 6, 7}
3. {3, 2, 6}
4. {2, 3, 5}

Answer

(B){5, 6, 7}

QN17. If R is a relation on a finite set having a elements, then the number of relations on A is

1. 2a
2. 2a2
3. a²
4. a^a

Answer

(B)2a2

QN18. Let A ={1,2,3} and R= {(1,2), (1,1), (2,3)}be a relation on A.What minimum number of elements may be adjoined with the elements of R so that it becomes transitive.

1. (1,2)
2. (1,3)
3. (2,3)
4. (1,1)

Answer

(B)(1,3)

QN19. Find the 5th term from the end of the G.P. 3, 6, 12, 24, …, 12,288

1. 384
2. 192
3. 1536
4. 768

Answer

(D)768

QN20. Write the modulus of 2+ √-3.

1. √ 7
2. √ 5
3. √ 13
4. √8

Answer

(A)√ 7

QN21. Solve log √8/log 8 is the same as

1. 1/√8
2. 1/8
3. ¼
4. ½

Answer

(D)½

QN22. Evaluate Log 243 / Log 9

1. 3/2
2. 5/2
3. 7/2
4. 9/2

Answer

(B)5/2

QN23. The conjugate of a complex number z = (a + ib) is

1. – a – ib
2. b – ai
3. b + ai
4. a – ib

Answer

(D)a – ib

QN24. (-3/5) x (-10/9) x (21/-4) x (-6)

1. 21
2. 42
3. 35
4. 15

Answer

(A)21

QN25. The additive inverse of (-11 / -14) is

1. 11 / 14
2. – 14 / 11
3. 14 / 11
4. – 11 / 14

Answer

(D)- 11 / 14

QN26. Thickness of a pile of 12 cardboards is 35 mm. Hence the thickness of a pile of 294 cardboards is

1. 80.50 cm
2. 83.75 cm
3. 85.75 cms
4. 81.50 cms

Answer

(C)85.75 cms

QN27. The set of irrational numbers is

1. Finite
2. Countable
3. Uncountable
4. Infinite

Answer

(C)Uncountable

QN28. The product of r consecutive positive integers is divisible by

1. r!
2. (r – 1)!
3. ( r + 1)!
4. None of these

Answer

(A)r!

QN29. If ²⁰C_r = 20C_r-10-10, then ¹⁸C_r is equal to

1. 4896
2. 816
3. 1632
4. None of these

Answer

(B)816

QN30. Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?

1. 265
2. 263
3. 264
4. 275

Answer

(C)264

QN31. Find the 5th term from the end in the expansion of (x³/2 – 2/x²)⁹

1. -252 x²
2. -252 x³
3. -250 x²
4. -250 x³

Answer

(A)

-252 x²

QN32. The coefficient of x-15 in the expansion of ( 3x² -a/3x³) is

1. -42/27 a⁷
2. -40/27 a⁷
3. – 43/27 a⁶
4. -38/27 a⁶

Answer

(B)

-40/27 a⁷

QN33. Find the 5th term from the end in the expansion of (x³/2 – 2/x²)9

1. 4000
2. 4096
3. 4069
4. 4009

Answer

(B)4096

QN34. Find the number of integral solutions of equation x + y + z + t = 29, x > 0, y > 0 < z > 0 and t > 0

1. ²⁷C₃
2. ²⁸C₃
3. 2600
4. ²⁹C₄

Answer

(C)2600

QN35. Is 3x -4y +5z =6

1. Linear
2. Non linear
3. Binominal
4. None

Answer

(A)Linear

QN36. Find P-¹, if it exist, given P = 10 -2
-5 1

1. P-¹ =0
2. P-¹ = 1/10 0 1/2 1
3. P-¹ =1
4. P-¹ does not exist

Answer

(D)

P-¹ does not exist

QN37. The equation x +ky +3z = 0 posses a non trivial solution for k if
2x +ky -2z =0
2x +3y -4z =0

1. k= 2
2. k= 3
3. k= 4
4. k=5

Answer

(C)k= 4

QN38. Solve 2x + y +z =7 using Cramer’s rule
3x -y -z =-2
x +2y -3z =-4

1. x=1, y=2, z=3
2. x=2, y=4, z=3
3. x=1, y=3, z=2
4. x=2, y=3, z=4

Answer

(A)x=1, y=2, z=3