Mathmetics

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

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Q1.
The 7th and 12th term of an arithmetic progression are -15 and 5 respectively. What is the 16th term ?

1) 18 2) 19
3) 21 4) 24
5)None of these
Answer : 21
Explanation :
 T7 = a + 6d = -15 ....... (1)
T12 = a + 11d = 5 ...... (2)
On solving (1) and (2), d = 4 & a = -39
T16 = a + 15d = -39 + 15(4) = -39 + 60 = 21
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Q2.
In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school ?

1) 72 2) 80
3) 100 4) 120
5)None of these
Answer : 100
Explanation :
Let, the Total Number of Students be x.
20% of Students are below 8 years of age.
The Number of Students above or equal 8  years of age =80% of x............(i)
  Number of Students of 8 years of age = 48 .....(ii)
Number of Students above 8 years of age =  2/3 ×  Number of Students of 8 years of age.
Number of Students of 8 years of age.
  Number of Students above age of 8 =2/3 × 48=32---(iii)
From equation (i), (ii) and (iii),
       80% of x = 48+2/3 of 48
80% of x  = 80
x = 100.
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Q3.
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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Q4.
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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Q5.
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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Q6.
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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Q7.
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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Q8.
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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Q9.
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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Q10.
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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