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### Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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##### If a - b = 9 and a2 + b2 = 125, the what should be the value of ab ?
 1) 16 2) 18 3) 20 4) 22 5) None of these
Explanation :

First Method::

We know that, 2ab = (a2 + b2) - (a - b)2 = 125 - 81 = 44   or   ab = 22.

Second Method:

We know that, (a - b)2 = a2 + b2 -2ab = 125- 2ab   or  81 = 125 -2ab   or  2ab = 125-81 =44

or ab =44/2=22

##### If (13+23+33+43+ 53+63+................+103) = 3025 ,then find the value of (23+43+63+83+ 103+...............+203)
 1) 6050 2) 10060 3) 12040 4) 24200 5) None of these
Explanation : We can express ,  (23+43+63+83+ 103+...............+203) =
23 x  (13+23+33+43+ 53+63+................+103) = 8 x  3025 = 24200
##### Given that, (12+22+32+42+ 52+62+72) = x +1 , the find the value of the following expressions:(22+42+62+82+102+122+ 142) =  ?
 1) 2(x+1) 2) 4(x+1) 3) 8(x+2) 4) 16(x+1) 5) None of these
Explanation : We can write, (22+42+62+82+102+122+ 142) = 22 x (12+22+32+42+ 52+62+72 =  4(x+1)
##### If  a+1/a = 6  then, a4 +1/a4 = ?
 1) 1154 2) 1158 3) 1160 4) 1164 5) None of these
Explanation : Given, a+1/a = 6
a2+1/a2 = (a +1/a)2 -2 = 36-2=34
or a4 +1/a4 = (a2+1/a2 )2 = (34)2 -2  = 1154
##### Q5.
 1) 3/2 2) 31/2 3) 127/108 4) 121/108 5) None of these
##### Q6.
 1) 0 2) 1 3) 2 4) 3 5) None of these
##### What is?
 1) 2 2) 3 3) 4 4) 5 5) None of these
##### Q8.
 1) 3/7 2) 1 3) 2 4) 4 5) None of these