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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 + c = m and 1/a + 1/b + 1/c = 0 , then the average of a2, b2 and c2 is
 1) m2 2) m2/3 3) m2/9 4) m2/27 5) None of these
Explanation : Given, 1/+ 1/+ 1/c = (ab + bc + ca)/abc = 0
Or ab + bc + ca = 0
And  a + b + c = m
Squaring both sides, we get, (a + b + c)2 = m2
Or a2 + b2 + c+2(ab + bc + ca) =m2
Or a2 + b2 + c 2+2(0) = m2
So, the average = ( a2 + b2 + c 2) /3 = m2/3 View Answer
##### If  x + y+ z = 9 and x2+y2+z2 = 31 , then what should be the value of  x3+y3+z3
 1) 3 2) 9 3) 27 4) 54 5) None of these
Explanation : Given,  x + y+ z = 9 and x2+y2+z2 = 31
Then, (x + y+ z)2 = 92
Or  x2+y2+z2 + 2( xy + yz + zx) = 81
Or 31 + 2( xy + yz + zx) = 81
Or ( xy + yz + zx) = 25
So, x2+y2+z- 3xyz = (x + y + z) [x2+y2+z2 -(xy + yz + zx)] = 9[31-25] = 54 View Answer
##### If a + b = 2c, then find the value of a/(a - c) + c/ (b-c)
 1) 0 2) 1 3) -1 4) 2 5) None of these
Explanation : Given, a + b = 2c
Put, a = 1, b = 2, then c = 3
So,1/(1-2) + 2/(3-2) = -1+2 = 1 View Answer
##### If x2+1/x2=1, then find the value of x18+x12+x6+1
 1) 0 2) 1 3) -1 4) -2 5) None of these
Explanation :  Given, x2+1/x=1, Or x4+1=x2
Or x4-x2+1=0
Multiplying both sides by (x2+1), we get
(x2+1)(x4-x2+1) =0x(x2+1)
Or x6+1 =0
So,x18+x12+x6+1 = x12(x6+1)+x6+1 =x12x0+0=0 View Answer
##### If 1/a(a2+1)=3,then what should be the value of (a6+1)/a3
 1) 1 2) 9 3) 18 4) 27 5) None of these
Explanation : Given, 1/a(a2+1) = 3
Or a+1/a =3
Or a3+1/a3+3a.1/a.(a+1/a) = 33
Or a3+1/a3 +3x3= 27
Or a3+1/a3 =18
Or (a6+1)/a3= 18 View Answer
##### If x+(1/x) = 5, the find the value of 5x/(x2+5x+1)
 1) 1/3 2) 1/4 3) 1/2 4) 1/s 5) None of these
Explanation : Given, x+(1/x) = 5
or (x2+x)/x = 5
or x2+x = 5x
Now,5x/(x2+5x+1)= 5x/(x2+1+5x) =5x/(5x+5x) =5x/10x=1/2 View Answer
##### If x=2015, y=2014 and 2013 , then x2+y2+z2 -xy-yz-zx = ?
 1) 2 2) 3 3) 4 4) 6 5) None of these
Explanation : ATQ: x2+y2+z2 -xy-yz-zx
= x2-xy+y2 -yz+z2-zx
x(x-y) + y((y-z) + z(z-x)
= 2015(2015-2014) + 2014(2014-2013)+2013(2013-2015)
= 2015 + 2014 + 4026
=4029-4026 =3 View Answer
##### 1) 8 2) 9 3) 10 4) 12 5) None of these
Explanation :
Given, x2 + 9/x = 6x
Or x2 - 6x = 9
Or (x-3)2 = 0
Or x = 3
So, x2 + 9/x= 10 View Answer
##### If  a = 4/3, then, what is the value of 27a3 -108a2 + 144a - 317  ?
 1) 221 2) -231 3) -253 4) 0 5) None of these
Explanation :
Given, a = 4/3
Or  3a = 4
Or 3a - 4 = 0
Or (3a-4)3 = 27a3 - 108a2 + 144a - 64 = 03
Or 27a3 - 108a2 + 144a - 317 = (27a3 - 108a2 + 144a -64) - 153 = 0 - 253 = - 253 View Answer
##### 1) 0 2) 1 3) 2 4) 3 5) None of these
Explanation :  View Answer