Mathmetics

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

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Q1.
The 3rd and 8th term of an arithmetic progression are -13 and 2 respectively. What is the 14th term?
1) 18 2) 20
3) 28 4) 32
5)None of these
Answer : 20
Explanation :
Let,the first term of an AP = a and the common difference = d
3th term of AP = A3= a+2d =-13 -------(i)
8th term = A8= a+7d =2 ------- (ii)
Subtracting equation (i) from (ii), we get :
or 7d-2d=2-(-13)
or 5d =15
or d=15/5=3
Substituting it in equation (ii),a=2-7(3)=2-21=-19 
Therefore,  14th term = 
A14= a + 13d = -19 + 13(3) = -19 + 39 = 20

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Q2.
What is the sum of the first 12 terms of an arithmetic progression if the first term is -19 and last term is 36 ?
1) 84 2) 102
3) 106 4) 108
5)None of these
Answer : 102
Explanation :
First term of AP = a=-19 and last term = l=36
Number of terms = n=12
Sum of AP = n/2(a+l)
= 12/2(-19+36) = 17x6=102
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Q3.
What is the sum of the first 17 terms of an arithmetic progression if the first term is -20 and last term is 28 ?
1) 68 2) 70
3) 72 4) 76
5)None of these
Answer : 68
Explanation :
Given, First term of AP = a =- 20 and last term = l = 28 
Number of terms = n = 17
Sum of AP = n/2(a+l)= 17/2(-20+28)= 17x4 = 68 
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Q4.
If the 3rd and the 5th term of an arithmetic progression are 13 and 21, what is the 13th term ?

1) 53 2) 57
3) 63 4) 72
5)None of these
Answer : 53
Explanation :
Given,T3 = a + 2d = 13-------(1)
T5 = a + 4d = 21-------(2)
on solving (1) and (2)
d = 4 & a = 5
T 13= a + 12d = 5 + 12(4) = 5 + 48 = 53
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Q5.
In an AP, the ratio of the 7th term to the 10th term is -1. If the 16th term is -15, what is the 3rd term ?
1) 11 2) 13
3) -11 4) -13
5)None of these
Answer : 11
Explanation : Given, the 7th and the 10th terms are (a + 6d) and (a + 9d) respectively. 
The ratio of these terms is -1. 
Solving this ratio, we get -2a = 15d. The 16th term is (a + 15d) = -15. 
Substituting for a, we get a = 15 and d = -2. Therefore, the 3rd term is (a + 2d) = 11.
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Q6.
How many terms of the A.P.  6,  12,  18,  24, …… must be taken to make the sum 816 ?
1) 14 2) 16
3) 17 4) 20
5)None of these
Answer : 16
Explanation :
Given,a1= 6 and d =12-6 = 6
Since S n=816
Sum of n terms of A.P. is given as, Sn=n/2[2a+(n-1)d]
816= n/2[2x6+(n-1)6]
or 1632= n[12+6n-6]     or    1632= n[6n+6]
or 1632= 6n2 + 6n          or     6n2 + 6n -1632 = 0
Divide both sides by 6, we get,n2 + n-272= 0     or n2 + 17n -16n -272 = 0
or n(n+17) - 16(n+17) = 0   or  n = 16

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Q7.
If 7 times the seventh term of an Arithmetic Progression (AP) is equal to 11 times its eleventh term, then the 18th term of the AP will be - 
1) 1 2) 0
3) 12 4) 18
5)None of these
Answer : 0
Explanation :
Let, the first term of the AP be 'a' and the common difference be 'd'.
7th term = A 7= a + 6d
11th term = A 11 = a + 10d
A.T.Q., 7(a+6d)=11(a+10d) = 7a + 42d = 11a + 110d
11a-7a = 42d-110d
4a = -68d   a = -17d  
A18 = a+17d = -17d+ 17d = 0

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Q8.
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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Q9.
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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Q10.
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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