1. If ‘a’ implies ‘+’, ‘b’ implies ‘–’, ‘c’ implies ‘¥’ and ‘d’ implies ‘Π’, insert proper letter
between the figures in the following equation
40__ 20__ 30__6 = 55
a) a,b,c
b) b, c, d
c) a, b, d
d) d, b, a
Explanation: 40 + 20 – 30 ∏ 6 = 60 – 5 = 55. Hence, a, b, d. Option (c) is correct.
2. If ‘+’ implies ‘–’, ‘–’ implies ‘Π’, ‘¥’ implies ‘Π’ and ‘Π’ implies ‘+’ , then insert the
proper signs between the figures in the given equation
12__8__4__2__1 = 15
a) Π, ¥, –, +
b) Π, –, +, ¥
c) +, –, ¥, Π
d) –, +, Π, ¥
Explanation: 12 ∏ 8 ¥ 4 – 2 + 1 would mean 12 + 8 ∏ 4 ¥ 2 – 1 = 12 + 4 – 1 = 15. Hence, the order given in option (a) is correct.
3. If a = +, b = –, g = ¥, d = Π
Insert the proper notations between the figures in the following sum
10__8__6__4__2 = 6
a) b, a, d, g
b) a, b, g, d
c) b, d, g, a
d) none of these
Explanation: Option (b) is correct.
Data for Questions 4 to 6 :
If 12 + 2 = 6
27 + 9 = 3
15 + 5 = 3
4. Calculate the value of 182 + 13
a) 14
b) 1.4
c) 0.14
d) none of these
Explanation: It is clear that the + sign means ∏. Hence,
182 + 13 would give us a value of 14. Hence, (a) is the answer.
5. Calculate the value of 50 + [50 + 10]
a) 10
b) 100
c) 110
d) 5
Explanation: 50/5 = 10. Hence, (a) is the answer.
6. Calculate (10 + (6 + (3 + (2 + 1))))
a) 4
b) 5
c) 8
d) none of these
Explanation: 10/2.5 = 4. Hence, correct option is (a)
Data for Questions 7 to 10 :
If 3 ¥ 4 = 5
5 ¥ 12 = 13
7. Calculate the value of 7 ¥ 24
a) 12
b) 48
c) 10
d) none of these
Explanation: The relationship that is defined through a ¥ b = \[\sqrt{(a^{2}+b^{2})}\]
Thus, 3 ¥ 4 = \[\sqrt{25}\] = 5
5 ¥ 12 = \[\sqrt{25+144}\] = 13
7 ¥ 24 = \[\sqrt{625}\] = 25. Hence, option (d) is the answer.
8. Calculate the value of 8 ¥ 9
a) 145
b) \[\sqrt{145}\]
c) 12
d) 12.5
Explanation: 8 ¥ 9 = \[\sqrt{(64+81)}\] = \[\sqrt{145}\]
Hence, option (b) is the answer.
9. 9 ¥ ? = 41
a) 35
b) 30
c) 40
d) none of these
Explanation: The required value will be got by the square root of the difference between 412 and 92
1681 – 81 = 1600.
Hence, the required answer is 40. Correct answer is option (c)
10.Obtain {3 ¥ (5 ¥ 6)} = ?
a) 5
b) \[\sqrt{70}\]
c) \[5\sqrt{3}\]
d) none of these
Explanation: The required value would be square root of 61 + 9 = \[\sqrt{70}\]
Hence, option (b) is the answer