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Question 1 of 5
1. Question
The seventh term of a GP is 4 times the 5th term. What will be the first term when its 4th term is 40?
Correct
Ans-b
In the case of a G.P. the 7th term is derived by multiplying the 5th term twice by the common ratio.
(Note: this is very similar to what we had seen in the case of an A.P.) Since, the seventh term is derived
By multiplying the 5th term by 4, the relationship.
r 2= 4 must be true.
Hence, r = 2
If the 4th term is 40, the series in reverse from the 4th to the first term will look like:
40, 20, 10, 5. Hence, option (b) is correct
Incorrect
Ans-b
In the case of a G.P. the 7th term is derived by multiplying the 5th term twice by the common ratio.
(Note: this is very similar to what we had seen in the case of an A.P.) Since, the seventh term is derived
By multiplying the 5th term by 4, the relationship.
r 2= 4 must be true.
Hence, r = 2
If the 4th term is 40, the series in reverse from the 4th to the first term will look like:
40, 20, 10, 5. Hence, option (b) is correct
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Question 2 of 5
2. Question
How many terms are identical in the two A.P.s 21, 23, 25, up to 120 terms and 23, 26, 29,.. up to 80 terms?
Correct
Ans-b
The first common term is 23, the next will be 29 (Notice that the second common term is exactly 6 away from the first common term. 6 is also the LCM of 2 and3 which are the respective common differences of the two series.)
Thus, the common terms will be given by the A.P 23 29, 35.., last term. To find the answer you need to find the last term that will be common to the two series.
The first series is 23, 25, 27 ……259
While the second series is 23, 26, 29…….260
Hence, the last common term is 257.
Thus our answer becomes [(257-23)/6]+1= 40.Option (b) is correct.
Incorrect
Ans-b
The first common term is 23, the next will be 29 (Notice that the second common term is exactly 6 away from the first common term. 6 is also the LCM of 2 and3 which are the respective common differences of the two series.)
Thus, the common terms will be given by the A.P 23 29, 35.., last term. To find the answer you need to find the last term that will be common to the two series.
The first series is 23, 25, 27 ……259
While the second series is 23, 26, 29…….260
Hence, the last common term is 257.
Thus our answer becomes [(257-23)/6]+1= 40.Option (b) is correct.
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Question 3 of 5
3. Question
The sum of the first four terms of an A.P. is 56 and sum of the first eight terms of the same A.P. is 176. Find the sum of the first 16 terms of the A.P.?
Correct
Ans-c
Think like this:
The average of the first 4 terms is 14, while the average of the first 8 terms must be 22.
Now visualise this:
Hence, d = 8/2 = 4 [ Note : understand this as a property of an A.P.]
Hence, the average of the 8th and 9th term = 22+ 4.4-38 But this 38 also represents the average of the 16 term A.P.
Hence, required answer 16x 38= 608. Option (c ) is correct.
Incorrect
Ans-c
Think like this:
The average of the first 4 terms is 14, while the average of the first 8 terms must be 22.
Now visualise this:
Hence, d = 8/2 = 4 [ Note : understand this as a property of an A.P.]
Hence, the average of the 8th and 9th term = 22+ 4.4-38 But this 38 also represents the average of the 16 term A.P.
Hence, required answer 16x 38= 608. Option (c ) is correct.
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Question 4 of 5
4. Question
X and Y are two numbers whose A.M. is 41 and G.M. is 9. Which of the following may be a value of X?
Correct
Ans-c
AM= 41 means that their sum is 82 and GM = 9 means their product is 81. The numbers can only be 81 and 1. Option (c) is correct
Incorrect
Ans-c
AM= 41 means that their sum is 82 and GM = 9 means their product is 81. The numbers can only be 81 and 1. Option (c) is correct
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Question 5 of 5
5. Question
Two numbers A and B are such that A > B and their G.M. is 40% lower than their A.M. Find the ratio between the numbers.
Correct
Ans-b
Trial and error gives s that tor option (b) With the ratio 9:1, the numbers can be taken as 9x and 1x. Their AM would be 5x and their GM would be 3x. The GM can be seen to be 40% lower thanthe AM,
Incorrect
Ans-b
Trial and error gives s that tor option (b) With the ratio 9:1, the numbers can be taken as 9x and 1x. Their AM would be 5x and their GM would be 3x. The GM can be seen to be 40% lower thanthe AM,
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