21. 

1. 1. 12

      29

   
   
   

   2. 8

      19

   
   
   

   3. 48

      29

   
   
   

   4. 2

      19

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   = 1 +		5
   	1 +	2 × 5
   		9

   
   

   = 1 +	1
   	19 + 10
   	19

   
   

   = 1 +	19	=	29 + 19	=	48
   	29		29		29

   Correct Option: C

   
   

   = 1 +		5
   	1 +	2 × 5
   		9

   
   

   = 1 +	1
   	19 + 10
   	19

   
   

   = 1 +	19	=	29 + 19	=	48
   	29		29		29

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22. 

1. 1. a

   
   
   

   2. 1 – a

   
   
   

   3. 1

   
   
   

   4. 0

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   = 1 −	a	= 1 −	a
   	1 – (1 – a)		1 – 1 + a

   
   = 1 – 1 = 0

   Correct Option: D

   
   

   = 1 −	a	= 1 −	a
   	1 – (1 – a)		1 – 1 + a

   
   = 1 – 1 = 0

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23. On simplification, the expression
    
    is equal to

1. 1. 28

      65

   
   
   

   2. 24

      53

   
   
   

   3. 56

      53

   
   
   

   4. 14

      65

   
   
   

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1. View Hint View Answer Discuss in Forum

   First part =	4	1	− 2	1
   		7		7
   	3	1	+ 1	1
   		2		7

   
   

   =	29	−	15
   	7		7
   	7	+	8
   	2		7

   
   

   =	14
   	7
   	49 + 16
   	14

   
   

   =	2	=	2 × 14	=	28
   	65/14		65		65

   
   
   

   =	1
   	2 +	24
   		53

   
   

   =	1
   	106 + 24
   	53

   
   

   =	53
   	130

   
   

   ∴  Expression =	28	÷	53	= 1
   	65		130

   
   

   =	28	×	130	=	56
   	65		53		53

   Correct Option: C

   First part =	4	1	− 2	1
   		7		7
   	3	1	+ 1	1
   		2		7

   
   

   =	29	−	15
   	7		7
   	7	+	8
   	2		7

   
   

   =	14
   	7
   	49 + 16
   	14

   
   

   =	2	=	2 × 14	=	28
   	65/14		65		65

   
   
   

   =	1
   	2 +	24
   		53

   
   

   =	1
   	106 + 24
   	53

   
   

   =	53
   	130

   
   

   ∴  Expression =	28	÷	53	= 1
   	65		130

   
   

   =	28	×	130	=	56
   	65		53		53

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24. The simplified value of :
    

1. 1. 20

      101

   
   
   

   2. 100

      101

   
   
   

   3. 2

   
   
   

   4. 90

      101

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let, a = 1 +		1
   	10 +	1
   		10

   
   

   = 1 +	1
   	100 + 1
   	10

   
   

   = 1 +	1
   	100 + 1
   	10

   
   

   = 1 +	10
   	101

   
   

   =	101 + 10	=	111
   	101		101

   
   Again,
   

   b = 1 −		1
   	10 +	1
   		10

   
   

   = 1 −	1
   	100 + 1
   	10

   
   

   = 1 −	10
   	101

   
   

   =	101 − 10	=	91
   	101		101

   
   ∴  Expression
   = (a² − b²) ÷ ab
   = {(a + b) (a – b)} ÷ ab
   

   =		111	+	91				111	−	91			÷		111	×	91
   		101		101				101		101					101		101

   
   

   =	202	×	20	×	101 × 101
   	101		101		111 × 91

   Correct Option: D

   Let, a = 1 +		1
   	10 +	1
   		10

   
   

   = 1 +	1
   	100 + 1
   	10

   
   

   = 1 +	1
   	100 + 1
   	10

   
   

   = 1 +	10
   	101

   
   

   =	101 + 10	=	111
   	101		101

   
   Again,
   

   b = 1 −		1
   	10 +	1
   		10

   
   

   = 1 −	1
   	100 + 1
   	10

   
   

   = 1 −	10
   	101

   
   

   =	101 − 10	=	91
   	101		101

   
   ∴  Expression
   = (a² − b²) ÷ ab
   = {(a + b) (a – b)} ÷ ab
   

   =		111	+	91				111	−	91			÷		111	×	91
   		101		101				101		101					101		101

   
   

   =	202	×	20	×	101 × 101
   	101		101		111 × 91

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25. The value of
    

1. 1. 1

      8

   
   
   

   2. 1

      64

   
   
   

   3. 1

      16

   
   
   

   4. 1

      32

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression
   
   

   = 4 −	5
   	1 +	9
   		31

   
   

   = 4 −	5
   	31 + 9
   	31

   
   

   = 4 −	5 × 31	=	160 − 155
   	40		40

   
   

   =	5	=	1
   	40		8

   Correct Option: A

   Expression
   
   

   = 4 −	5
   	1 +	9
   		31

   
   

   = 4 −	5
   	31 + 9
   	31

   
   

   = 4 −	5 × 31	=	160 − 155
   	40		40

   
   

   =	5	=	1
   	40		8

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