Mathmetics

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

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Q1.
If a + b + c = m and 1/+ 1/+ 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
Answer : m2/3
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


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Q2.
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
Answer : 54
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
 

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Q3.
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
Answer : 1
Explanation : Given, a + b = 2c
Put, a = 1, b = 2, then c = 3 
So,1/(1-2) + 2/(3-2) = -1+2 = 1
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Q4.
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
Answer : 0
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

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Q5.
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
Answer : 18
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  
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Q6.
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
Answer : 1/2
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
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Q7.
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
Answer : 3
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

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Q8.
1) 8 2) 9
3) 10 4) 12
5)None of these
Answer : 10
Explanation :
Given, x2 + 9/x = 6x
Or x2 - 6x = 9
Or (x-3)2 = 0  
Or x = 3
So, x2 + 9/x= 10
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Q9.
If  a = 4/3, then, what is the value of 27a3 -108a+ 144a - 317  ?
1) 221 2) -231
3) -253 4) 0
5)None of these
Answer : -253
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
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Q10.
1) 0 2) 1
3) 2 4) 3
5)None of these
Answer : 3
Explanation :
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