Mathematical Operations
Questions on Mathematical operations will first start with either defining a new meaning to existing symbols or define a new symbol and its mathematical meaning.
You are then required to evaluate the value of an expression by assuming the meaning of the symbols as defined in the question.
The following questions will make this question type clear to you.Illustration 1:
which of the following will be the value of the expression?
(a) 12 (b) 20
(ñ) 0 (d) 24
Answer and Explanation: Putting the changed signs, the expression can be rewritten as
Using BODMAS rule, we have
Hence, the correct option is (d).
Illustration 2: ll'/l implies ‘+’,5 implies C implies ‘¥’, D implies i∏,, then calculate the value of the expression 2∠4354C5D1.
(a) 15 (b) 0
(c)-15 (d)-12
Answer and Explanation: Using the proper signs, the above expression can be written as
Hence, option (c) is correct.
Illustration 3: Which of the following changes would make the given expression correct?
Answer and Explanation: By making inter-changes given in ‘a’ we get the expression as:
By making interchanges given in ‘b’, we get expression as
By making interchanges given in option ‘c’, we get the expression as
Hence, option (d) is correct.
Illustration 4: IE4”# means add B to A, A,B implies subtract# from∠4, A@ B implies divide A by B, A*B means multiply A with B.
If a train travels with a speed of 51 IfompointX to B and returns with a speed of 4S,2∙ The average speed will be represented using the above explained notations?
Answer and Explanation: We know that the formula for average speed is given by
Hence the correct option is (b).
Illustration 5: If (/, m, ri) is represented as v [(/ + l)(m + 1)∕(∏ + 1)]:
What is the value of (48, 63, 80)?
(à) 56/9 (b) 55/9
(ñ) 6 (d) 7
Answer and Explanation: Putting the value in the above equation we get ÷[(48 + 1)(63 + 1)/(80 + 1)]
=÷(49 ó 64/81) - (7 ¥ 8)/9 - 56/9
Hence, the correct option is (a).
EXERCISE
Directions for Questions 1 to 5: If a + b implies a-b a-b implies a ¥ b a⅛b implies a ∏b a ∏ b implies a + b
1. Calculate 5 + 8-25¥5Ï40
(a) 5 (b) -5
(c) 0 (d) 10
2. With which statement can you find the value of 8?
(à)1+2-6¥ÇÏ8 (Ü)1-2 + 6¥ÇÏ8
(c) 1 - 2 ¥ 6 + 3 ¥ 8 (d) none of these
3. Which of the following is true?
(d) none of these
4. Which of the following is true?
5. Find the value of
(4 + 3- 5¥1Ï4)¥(5 + 2- 3¥1Ï4)
(a) -7/3 (b) -8/3
(d) none of these
(c)l
Directions for Questions 6 to 8: If ia^, means+, ib, means -,ic, means ¥ and id, means π
6. Calculate the value of 6a7b8c8d2
(a) -17 (b) 12
(c) -19 (d) none of these
7.
Calculate (8c7)c(760)⅛(6implies A ∏ BA*B implies A ¥ B
34. A man travels with a speed of f IfomX to B and returns from# to X with speed h. What is the average speed of the man over the entire journey?
35. Jadugar has a jadoo box which has a length, breadth and height which can be represented by ix,, ia∖ ic^, respectively. What is the formula for its total surface area?
(d) none of these
36. At the Wave cinemas in Sector 18 in Noida, charges for parking are as follows
1. For cycles Rs 2
2. For scooters Rs 5
3. For cars Rs 20
On a particular day there were ‘25’ cycles, ‘40’ scooters and ‘ 100’ cars parked at the stand, what was the amount collected in that particular day?
(d) none of these
Directions for Questions 37 to 41: If
AXB implies A2 + B2
AYB implies A2 - B2
AZB implies (A + B)2
AMB implies (A - B)2
37. Calculate the value of (4X5)Y(6X7)
(a) 5544 (b) -5544
(c) 500 (d) none of these
38. Calculate the value of (373)M(413)
(a) 1600 (b) 900
(c) 400 (d) 2500
39. If (AMB) = (AZB) then which of the following is true.
(a)Λ-5 = 0 (b)Λ2 = 52
(c) A.B - 0 (d) A - 0
40. Calculate (3Z4) - (5M5)
(à) 49 (b) 25
(ñ) 64 (d) none of these
41. Calculate the value of (2Z2)M(4Y4)
(a) 16 (b) 256
(c) 25 (d) none of these
Directions for Questions 42 and 43: If indicates either ‘+’ or ‘¥’, solve the following questions.
42. What is the maximum value of
I*2*3*4*5*6*7
(a) 5040 (b) 5041
(c) 7 !/2 (d) none of these
43.
What is the minimum value ofI*2*3*4
(a) 10 (b) 9
(c)ll (d) 14
Directions for Questions 44 to 46: If
A indicates >
B indicates <
C indicates =
D indicates π
E indicates +
F indicates -
G indicates *
H indicates ∏
44. Which of the following is false?
(a) (5E7)A(4E3)A(1E2)
(b) (5E6)A(6E12)A(13E6)
(c) (12H3)C(40H10)C(60H15)
(d) all of these are false
45. Calculate (32H(2H(6H3)))
(à) 16 (b) 32
(ñ) 8 (d) none of these
46. Calculate 5E3F4G6H2
(a) 1.5
(c) -4
(b)l
(d) none of these
Answer Key
| l.(a) | 2. (b) | 3.(c) | 4. (b) |
| 5. (a) | 6. (c) | 7. (c) | 8. (d) |
| 9. (d) | 10. (b) | ll.(d) | 12. (d) |
| 13. (a) | 14. (b) | 15.(b) | 16. (c) |
| 17. (a) | 18. (b) | 19. (a) | 20. (a) |
| 21. (a) | 22. (d) | 23. (b) | 24. (c) |
| 25. (b) | 26. (b) | 27. (d) | 28. (c) |
| 29. (d) | 30. (d) | 31∙(b) | 32. (c) |
| 33. (d) | 34. (d) | 35. (b) | 36. (c) |
| 37. (b) | 38. (a) | 39. (c) | 40. (a) |
| 41∙(b) | 42.(b) | 43.(b) | 44. (b) |
| 45. (b) | 46. (c) |
Solutions
1. The expression will become 5-8⅛25∏5 + 40. Using the BODMAS rule we will get:
5 - 40 + 40 = 5. Hence, option (a) is correct. 
Solutions 22 to 25:
24.
The required value will be got by the square root of the difference between 412 and 92√zE 1681 -81 = 1600. Hence, the required answer is 40. Correct answer is option (c).
26. yPz means that ó is less thanz and zNa means z = a. Thus,ó is less than a√zE yPa. Option (b) is correct.
27. IOa is greater than 6b. and 12b is greater than 20c √zE 6n is greater than 10c. Thus 10a is greater than 10c or a is greater than c. Option (d) is correct.
28. a is negative and b + 2 is less than a implies that b must be below -2. Hence, option (c) is correct.
29. Nothing can be said about the relationships between s, è or v or for that matter about è and v. Hence, cannot be determined. The correct answer is option (d).
30. Since the modulus value is always positive, all the three, i.e. the first, second and third relationships are possible. Hence, option (d) is correct.
31. Option (b) is correct since we will get 10 + 4 - 14.
32. 11 — 1.5 = 9.5. Option (c) is correct.
33. (-15)(-7) - 105. Hence, option (d) is correct.
34. It can be seen that none of these is correct. Hence, (d) is the answer.
35. The surface area of a cuboid box is equal to twice the areas of each of the sides. Hence, option (b) is correct.
36. The correct answer is option (c).
37. 412 - 852 = 1681 — 7225 - - 5544. Hence, option (b) is correct answer.
38. (- 40)2 -1600. Hence, option (a) is correct answer.
39. The given expression tells us that (A - T?)2 - (A + B)2. This can only occur when 2AB - - 2AB - 0. Hence, option (c) is correct.
40. 72 - 49. Hence, correct answer is option (a).
41. 162 - 256. Hence, correct answer is option (b).
42. The maximum value will be obtained when we use multiplication between 2 to 7 and addition between 1 and 2. Hence, option (b) is the answer.
43. The minimum value will be got if we use a multiplication between 1 and 2 and addition between 2, 3, and 4. The value will be l¥2 + 3 + 4 = 9. Hence, option
(b) is the answer.
44. It can be seen that options 1 and 3 are correct, but option (b) is wrong. Hence, option (b) is the correct answer.
45. 32/1 = 32. Hence, option (b) is correct.
46. 5 + 3-12= -4. Hence, option (c) is correct.