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  • Last Updated : 16 Sep, 2021

Question 1

Calculate the arithmetic mean of the given series: 2, 6, 10, 14, 18, 22, 26, 30.

A

8

B

16

C

32

D

None of the above

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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: 

Arithmetic mean AM of the series is given by = (a1+a2+a3+.....+an)/n ……… (1) But the given series is also an AP which sum is given by = (n/2)*(a1+an) ………..(2) From equation (1),(2) we get, AM=(a1+an)/2 AM=(2+11)/2=13/2

Question 7

Find the sum of series: 1, 3, 9, 27, 81, ..............39

A

[(1-3^(10))]/(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

Calculate the sum of given series: 1/3, 1/9, 1/27, 1/81.................

A

1/4

B

1/3

C

1/2

D

1

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Question 8 Explanation: 

The given series is an infinite GP, whose sum is given by Sn=a/(r-1) Where, a=first term of series, r=common ratio. Therefore, Sn=(1/3)/(1-1/3) Sn=1/2

Question 9

For n positive integers, if their product is nn, then what will be their sum?
 

A

Equal to n+(1/n)

B

Equal to n

C

A negative integer

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 building of height 180 m. After striking the ground, it rebounds (3/5)th of the height from which it has fallen. 

Calculate the total distance that the ball traveled before it comes to rest.

A

540 m

B

600 m

C

900 m

D

None of the above

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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.
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