Data for Questions 1 to 3 : If ‘a’ means+, ‘b’ means –, ‘c’ means ¥ and ‘d’ means ∏
1. Calculate the value of 6a7b8c8d2
a) -17
b) 12
c) -19
d) none of these
Explanation: 6a7b8c8d2 = 6 + 7 – 8 ¥ 8 ∏ 2 = –19. Hence, (c) is the answer.
2. Calculate (8c7)c(7a5)b(6d3)d(3b2)
a) 650
b) 375
c) 670
d) none of these
Explanation: (8c7)c(7a5)b(6d3)d(3b2) becomes 56 ¥ 12 – 2 ∏ 1 = 670. Option (c) is the answer.
3. What is the value of 9a10b11c15d0
a)1
b) 2
c) 3
d) undefined
Explanation: The expression contains a division by 0, hence is undefined. Option (d) is the answer.
Data for Questions 4 to 7 : In each of the following questions if the given interchanges are made in signs and numbers, which one of the four equations would be correct?
4. Given interchanges, signs ‘–’ and ‘Π’ and numbers 4 and 8 (on the LHS)
a) 4 – 8 Π 12 = –23/4
b) 4 Π 8 – 2 = 8
c) 8 Π 2 – 4 = –15/4
d) none of these
Explanation: None of these, i.e. option (d) is correct.
5. Given interchanges: 3 and 2, Π and –
a) 1 + 3 ¥ 4 – 2 Π 1 = 5
b) 1 + 2 – 3 ¥ 8 Π 4 = 9
c) 3 – 1 ¥ 4 + 2 Π 1 = 11
d) none of these
Explanation: The given expression will become 1 + 3 ∏ 2 ¥ 8 – 4 = 9. Option (b) is the answer.
6. Given interchanges: 0.4 and 0.04,
a) 1 + 2 – 0.04 ¥ 0.4 = 1
b) 0.4 + 0.04 – 2 ¥ 2 = 1.76
c) 0.04 ¥ 0.4 – 1 = 0.18
d) none of these
Explanation: Checking each of the four options we will get none of these the answer. Hence, option (d) is the answer.
7. Given interchanges, ¥ and +, 10, 1
a) 5 ¥ 1 + 10 – 2 = 5
b) 8 + 8 – 10 ¥ 1 = 75
c) 4 – 6 ¥ 10 + 1 = 6
d) 3 + 4 – 12 ¥ 1 Π 10 = 10
Explanation: Option (d) becomes correct.
8. Find out the two signs to be interchanged for making the following equation to be correct:
5 + 3 – 5 ¥ 5 Π 1 = 15
a) ¥ and –
b) ¥ and +
c) Π and –
d) + and –
Explanation: If the signs are changed according to the first option the equation is satisfied. Hence, option(a) is correct.
9. Which of the following two signs need to be interchanged to make the given equation correct?
4 + 2 – 5 ¥ 7 Π 12 = – 21
a) Π and –
b) Π and +
c) ¥ and +
d) ¥ and –
Explanation: If the signs are changed according to the second option the equation is satisfied. Hence, option(b) is correct.
10. Insert proper arithmetical signs between the figures in the following equation
12_4_2_1 = 24
a) –, Π, ¥
b) ¥, Π, ¥
c) +, ¥, Π
d) none of these
Explanation: Insertion of ¥, ∏, ¥ in that order will make 12 ¥ 4 ∏ 2 ¥ 1 = 24. Hence, option (b) is correct.