Direction: Study the following sequence carefully and answer the questions given below:

1. If ‘-‘ stands for ‘x’,  ’x’ stands for ‘+’,  ‘+’stands for ‘÷’ and ‘÷’ stands for ‘-‘,then what is the value of 9÷18x15+3-6x12 ?

(a)24       (b)30      (c)33     (d)42     (e)58

2. If a$b=a²b²-ab , then 3$8=

(a)600    (b)552     (c)576   (d)625    (e)676

3. If pØq=p²+q²-p-q and p∆q=pq-p-q,then(6Ø5)∆ 5 =

(a)200   (b)175    (c)195   (d)179      (e)225

4. If4©5=189 and 10©8=1512,then 6©9=

(a)945    (b)1148    (c)983    (d)764    (e)932

5. If’∆’ means is less than’, ‘$’ means ‘is greater than’and £’means ‘is equal to’and given that a∆ b,c£d and c$b,then which of the following is true ?

(a)d∆a     (b)b$d      (c)a£c    (d)a∆b∆c      (e)a∆c

6. If ’x’means 'added to' ’÷’means 'multiplied by'; ’+’means 'subtracted from' and ‘-‘ means ‘divided by',then simplify 24+36-12x 8÷4= ?

(a)36    (b)53     (c)5      (d)20     (e)None of these

7. If A means ‘-‘,B means ‘÷’,C means ‘+’,and D means ‘x’,then 15B3C24A12D2 =?

(a)2     (b)5/9   (c)-23⁴/₉    (d)34     (e)5

8. If ‘W’ means ÷,X means ‘+’,Y means ‘-‘ and Z means ‘x’ then 28Z3Y4x12W6=?

(a)27    (b)82       (c)39    (d)53     (e)11

9. If ‘+’means ‘÷’,÷means ‘x’ ,’x’ means  ‘-‘ and ‘-‘ means ‘+’ ,then 10+2÷5-3÷4+2-1=?

(a)32   (b)50     (c)45     (d)120    (e)150

10. If 5@6=61 and 8@10=164,then 7@9=?

(a)125    (b)63     (c)130    (d)32       (e)95

Answer & Explanations

1. Ans (c)33. The given expression 9÷18x15+3-6x12. By converting the symbols according to the given definitions, we get 9-18+15÷3x6+12  solving this by BODMAS rule,we get the value as 33.

2.  Ans (b)552. Given a$b=a²b²-ab –ab →3$8 = 3²x8² – 3x8=9x64-24=576-24=552

3. Ans (c)195. 6Ø5 = 6²+5²-6-5=36+25-6-5=50 (6Ø5∆ 5 = 50∆5 = 50x5-50-5= 195

4. Ans (a)945. 4³+5³=64+125=189=> 4©5, 10³+8³ =1000+512=1512=>10©8

Similarly, 6©9=6³+9³=216+729=945

5. Ans (a)a∆b∆c. a∆b means a<b, c$d means c>b, b<c, c£d means c=d therefore, a<b<c=d. So a∆b∆c  is true=>a<b<c→ is true

6. Ans (b)53. 24-36÷12+8 x 4= 24-3 +32= 53.

7. Ans (e)5. 15÷3+24-12x2 , 5+24-24=5

8. Ans (b)82. 28x3-4+12÷6, 84-4+2 or 84+2-4=86-4=82

9. Ans (a)32. 10÷2x5+3x4÷2+1, 5x5+3x4÷2+1, 5x5+3x2+1, 25+6+1=32

10.Ans(c)130.5x5+6x6=25+36=61,8x8+10x10=64+100=164 so,7x7+9x9=49+81=130