Mathmetics

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

Q11.
Alok borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow ?
1) Rs.8000 2) Rs.10,000
3) Rs.12,000 4) Data Inadequate
5)None of these
Answer : Rs.8000
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Q12.
In a triangle ABC, the sides AB and AC have been produced to D and E. Bisectors of angle CBD and angle BCE meet at O. If angle A = 64°, then angle BOC is -
1) 54° 2) 56°
3) 58° 4) 60°
5)None of these
Answer : 58°
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Q13.
In triangle ABC, if D and E are the points on the sides AB and AC respectively such that DE parallel to BC and if AD = x , DB = x - 2 , AE = x + 2 and EC = x -1. then find the value of x .
1) 2 2) 3
3) 4 4) 5
5)None of these
Answer : 5
Explanation :
Since, DE parallel to BC   
so, (AD / DB) = (AE / EC)
or {x / (x – 2)} = {(x + 2) / (x – 1)}
or x(x – 1) = (x + 2) (x – 1)
or x2 – x = x2 – 4
or x = 4 . 
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Q14.
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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Q15.
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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Q16.
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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Q17.
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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Q18.
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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Q19.
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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Q20.
An article is marked x% above the cost price. A discount of 2x/3% is given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then what should be the value of 50% of x ?
1) 12 2) 14
3) 15 4) 20
5)None of these
Answer : 15
Explanation :
Let, the cost price of the article is Rs.100. Marked price (MP) = Rs.100+x
Selling price of the price (SP) = MP - discount = Rs.100+x - 2x/3 *(Rs.100+x)/100
Also, SP = CP + 4% profit = 100+4 = Rs.104
Hence,(100+x)-2/3x * (100+x)/100 = 104 
or 100+x - 2x/300 (100+x) = 104 
or x² - 50x + 600 = 0
On solving the above equation, we get possible values of x as 20 and 30. But as x lies between 25 and 50, the value should be 30. 
So, x = 30.
The value of 50% of x is = 15
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