12

Progressions

Question 1
Find the Arithmetic Mean of series: 2, 6, 10, 14, 18, 22, 26, 30.
A
16
B
8
C
64
D
36
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Question 1 Explanation: 
AM = (a1+a2+a3+......+an)/n
=(n(a1+an)/2)/n
=(a1+an)/2 = (2 + 30)/2 = 16
Question 2
Find the Sum of series: 2, 6, 10, 14, 18, 22, 26, 30
A
32
B
88
C
128
D
110
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Question 2 Explanation: 
Sum of AP = (n/2)[2a+(n-1)d]
= 4*[4+7*4]
=128
Question 3
Find the AM of series: 10, 7, 4, 1, -2
A
13/2
B
14/3
C
4
D
16/5
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Question 3 Explanation: 
AM = (a1+a2+a3+......+an)/n =(n(a1+an)/2)/n =a1+a2/2 =10-2/2 = 4
Question 4
Find the Sum of series: 10, 7, 4, 1, -2
A
40
B
21
C
20
D
18
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Question 4 Explanation: 
Sum of series = (n/2)[2a+(n-1)d]
= 20
Question 5
Find sum of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........11
A
120
B
123.5
C
126.5
D
118.5
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Question 5 Explanation: 
sum of AP = (n/2)[2a+(n-1)d]
n=19, a=2, d=1/2
S = (19/2)[2*2+(19-1)1/2]
=(19/2)[4+9]
=9.5*13 = 123.5
Question 6
Find Arithmetic Mean of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........11
A
13/2
B
25/8
C
19
D
22/9
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Question 6 Explanation: 
AM of Series: (2+11)/2
=13/2
Question 7
Find the sum of series: 1, 3, 9, 27, 81, ..............39
A
[(1-310)]/(1-3)
B
18
C
10
D
20
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Question 7 Explanation: 
Sol: Sn=[a(1-rn)]/(1-r) =[1(1-310)]/(1-3) =[(1-310)]/(1-3)
Question 8
Find the sum of series: 1/3, 1/9, 1/27, 1/81.................
A
1/2
B
1/3
C
1/4
D
1/6
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Question 8 Explanation: 
Sn=a/(1-r)
= (1/3)/(1-1/3)
=1/2
Question 9
If the product of n positive integers is nn, then their sum is:
A
A negative integer
B
Equal to n
C
Equal to n+(1/n)
D
Never less than n2
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Question 9 Explanation: 
Clearly, since the given integers are positive, their sum can't be negative. Also, since the numbers are all integers their sum can't be a fraction. Let's take 1, 3 and 9. The product of these three integers is 27 = 33. This can also be written as nn where n=3. As we can see, the sum of these 3 integers is not equal to 3. Therefore, we are left with the fourth option.
Question 10
A tennis ball is initially dropped from a height of 180 m. After striking the ground, it rebounds (3/5)th of the height from which it has fallen. The total distance that the ball travels before it comes to rest is:
A
540 m
B
600 m
C
720 m
D
900 m
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Question 10 Explanation: 
The total distance traveled by the ball is the sum of two infinite series: a. Series 1: the distance traveled by the ball when it's falling down b. Series 2: the distance traveled by the ball when it's bouncing up S1 = a1 / (1 - r1) and S2 = a2 / (1 - r2) S1 = 180 / (1 - 3/5) and S2 = (180 * 3/5) / (1 - 3/5) S1 = 180 / (2/5) and S2 = 108 / (2/5) S1 = 180 * 5/2 and S2 = 108 * 5/2 S1 = 450 and S2 = 270 Therefore, S = S1+S2 = 720 m.
There are 15 questions to complete.
12

GATE CS Corner


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