71. The value of
    

    1 -	1	+	1	-	1	+ .........correct to 5 places of decimal is :
    	20		20²		20³

    
    

1. 1. 1.05
      

   
   
   

   2. 0.95238
      

   
   
   

   3. 0.95239
      

   
   
   

   4. 10.5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let S = 1 -	1	+	1	-	1	+ ........
   	20		20²		20³

   
   It is a geometric series to infinity with first term, a = 1
   

   and common ratio ( r ) = -	1
   	20

   
   

   ∴ S∞ =	a
   	1 - r

   
   

   S∞ =			1
   	1 -		-	1
   				20

   
   

   S∞ =		1
   	1 +	1
   		20

   
   

   Correct Option: B

   Let S = 1 -	1	+	1	-	1	+ ........
   	20		20²		20³

   
   It is a geometric series to infinity with first term, a = 1
   

   and common ratio ( r ) = -	1
   	20

   
   

   ∴ S∞ =	a
   	1 - r

   
   

   S∞ =			1
   	1 -		-	1
   				20

   
   

   S∞ =		1
   	1 +	1
   		20

   
   

   S∞ =	20	= 0.9523809
   	21

   
   ∴ The value correct to 5 places of decimal = 0.95238

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72. For all integral values of n, the largest number that exactly divides each number of the sequence (n – 1) n(n + 1), n(n + 1)(n + 2), (n + 1)(n + 2)(n + 3),.... is
    

1. 1. 12
      

   
   
   

   2. 6
      

   
   
   

   3. 3
      

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   The largest number will be 6.
   For n = 2 , (n – 1) n(n + 1) = 6,
   for n = 3, (n – 1) (n) (n + 1) = 24 etc.

   Correct Option: B

   The largest number will be 6.
   For n = 2 , (n – 1) n(n + 1) = 6,
   for n = 3, (n – 1) (n) (n + 1) = 24 etc.
   Hence , required answer is 6.

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73. Given that 1 + 2 + 3 + .... x =	x(x + 1)	then 1 + 3 + 5 + ..... + 99 is equal to
    	2

    
    

1. 1. 2250
      

   
   
   

   2. 2500
      

   
   
   

   3. 2525
      

   
   
   

   4. 3775

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that ,
   

   1 + 2 + 3 + ............. + x =	x(x + 1)
   	2

   
   ∴ 1 + 3 + 5 + ............. + 99 = ( 1 + 2 + 3 + 4 + 5 +.....100) – ( 2 + 4 + 6 +.....100)
   

   Required answer =	100 × (100 + 1)	-	50 × (50 + 1)
   	2		2

   
   

   Correct Option: D

   Given that ,
   

   1 + 2 + 3 + ............. + x =	x(x + 1)
   	2

   
   ∴ 1 + 3 + 5 + ............. + 99 = ( 1 + 2 + 3 + 4 + 5 +.....100) – ( 2 + 4 + 6 +.....100)
   

   Required answer =	100 × (100 + 1)	-	50 × (50 + 1)
   	2		2

   
   Hence , Required answer = 5050 – 1275 = 3775

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74. 	1 -	1			1 -	1			1 -	1		...........		1 -	1		is equal to
    		5				6				7					100

    
    

1. 1. 0

   
   
   

   2. 1

      25

   
   
   

   3. 1

      100

   
   
   

   4. 1

      50

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given Here ,
   

   Expression =		1 -	1			1 -	1			1 -	1		.....		1 -	1
   			5				6				7					100

   
   

   Expression =		5 - 1			6 - 1			7 - 1		.....		99 - 1			100 - 1
   		5			6			7				99			100

   
   

   Expression =	4	×	5	×	6	×........ ×	98	×	99
   	5		6		7		99		100

   
   

   Correct Option: B

   Given Here ,
   

   Expression =		1 -	1			1 -	1			1 -	1		.....		1 -	1
   			5				6				7					100

   
   

   Expression =		5 - 1			6 - 1			7 - 1		.....		99 - 1			100 - 1
   		5			6			7				99			100

   
   

   Expression =	4	×	5	×	6	×........ ×	98	×	99
   	5		6		7		99		100

   
   

   Required answer =	4	=	1
   	100		25

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75. The sum of the series (1 + 0.6 + 0.06 + 0.006 + 0.0006 + ....) is
    

1. 1. 1	2
      	3

   
   
   

   2. 1	1
      	3

   
   
   

   3. 2	1
      	3

   
   
   

   4. 2	2
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given question ,
   1 + 0.6 + 0.06 + 0.006 + 0.0006 + ... = 1.666 .... = 1.6
   As we know that ,
   a.b
   where , a and b are any positive numbers .
   

   Number = a	b
   	9

   
   Here , a = 1 , b = 6
   

   Correct Option: A

   As per the given question ,
   1 + 0.6 + 0.06 + 0.006 + 0.0006 + ... = 1.666 .... = 1.6
   As we know that ,
   a.b
   where , a and b are any positive numbers .
   

   Number = a	b
   	9

   
   Here , a = 1 , b = 6
   

   Required answer = 1	6	= 1	2
   	9		3

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