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1. There is an AP 11, 13, 15.... Which term of this AP
is 65?

Correct Answers :

[D]

Explanation :

The number of terms in a series are found by:

Option (d) is correct.

2. Find the 25th term of the sequence 50, 45, 40, ...

Correct Answers :

[C]

Explanation :

The first term is 50 and the common difference is −5,
thus the 25th term is: 50 + 24 *x* (−5) = −70. Option
(c) is correct.

3. If Ajit saves Rs. 400 more each year than he did the year before and if he saves Rs. 2000 in the first year, after how many years will his savings be more than
Rs.100000 altogether?

Correct Answers :

[A]

Explanation :

We need the sum of the series 2000 + 2400 + 2800 to cross 100000. Trying out the options, we can see
that in 20 years the sum of his savings would be: 2000 + 2400 + 2800 +…+ 9600. The sum of the series would be 20 × 5800 = 116000. If we remove
the 20th year we will get the saving for 19 years.

The series would be 2000 + 2400 + 2800 + … + 9200. Sum of the series would be 116000 − 9600
= 106400. If we remove the 19th year’s savings the savings would be 106400 − 9200 which would go below 100000. Thus, after 19 years his savings
would cross 100000. Option (a) is correct.

4. The 6th and 20th terms of an AP are 8 and −20
respectively. Find the 30th term.

Correct Answers :

[B]

Explanation :

*a* + 5*d* = 8 and *a* + 19*d* = −20. Solving we get 14*d*= −28 --> *d* = −2. 30th term = 20th term + 10*d* = −20 + 10 × (−2) = −40. Option (b) is correct.

5. How many terms are there in the AP 10, 15, 20,
25,... 120?

Correct Answers :

[C]

Explanation :

In order to count the number of terms in the AP, use the shortcut: [(last term − first term)/ common difference] + 1. In this case it would become: [(120 − 10)/5] + 1 = 23. Option (c) is correct.

6. Find the number of terms of the series 1/27, 1/9,
1/3,... 729.

Correct Answers :

[A]

Explanation :

r = 3. 729=(3)^{n-1},n-1 =9 or n=10 option (a) is correct.

7. If the fifth term of a G.P. is 80 and first term is 5,
what will be the 4th term of the G.P.?

Correct Answers :

[C]

Explanation :

5r^{4} = 80 --> r^{4}=80/5-->r=2, thus 4th term =ar^{3}=5 x (2)^{3} = 40. Option C is correct.

8. Binay was appointed to Mindworkzz in the pay scale
of 12000–1500–22,500. Find how many years he will
take to reach the maximum of the scale.

Correct Answers :

[A]

Explanation :

12000 − 1500 − 22500 means that the starting scale is
12000 and there is an increment of 1500 every year.

Since, the total increment required to reach the top
of his scale is 10500, the number of years required
would be 10500/1500 = 7. Option (a) is correct.

9. How many natural numbers between 100 to 500 are
multiples of 9?

Correct Answers :

[A]

Explanation :

The series will be 108, 117, 126,…. 495. Hence, Answer = + 1 = 44. Option (a) is correct.

10. The sum of the first 20 terms of an AP whose first
term and third term are 25 and 35, respectively is

Correct Answers :

[D]

Explanation :

*a* = 25, *a* + 2*d* = 35 means *d* = 5. The 20th term
would be *a*+ 19*d* = 25 + 95 = 120. The sum of the series would be given by: [20/2] × [25 + 120] =
1450. Option (d) is correct.

11. A number 39 is divided into three parts which are
in A.P. and the sum of their squares is 515. Find the
largest number.

Correct Answers :

[B]

Explanation :

The three parts are 11, 13 and 15 since 11^{2} + 13^{2}
+ 15^{2} = 515. Since, we want the largest number, the answer would be 15. Option (b) is correct.

12. Sushil agrees to work at the rate of 10 rupee on the
first day, 20 rupees on the second day, 40 rupees on the third day and so on. How much will Sushil get if he starts working on the 1st of April and finishes on the 20th of April?

Correct Answers :

[B]

Explanation :

Sum of a G.P. with first term 10 and common ratio 2 and no. of terms 20. .Option (b) is correct.

13. Find the sum of all numbers in between 1–100 excluding all those numbers which are divisible by 7. (Include 1 and 100 for counting.)

Correct Answers :

[A]

Explanation :

The answer will be given by:

[1 + 2 + 3 +…+ 100]-[7 + 14 + 21 +… + 98]

= 50 × 101 − 7 × 105

= 5050 − 735 = 4315. Option (a) is correct.

14. The 3rd and 8th term of a GP are 1/3 and 81, respectively. Find the 2nd term.

Correct Answers :

[D]

Explanation :

3rd term ar^{2} = 1/3, 8th term ar^{7} = 81

r^{5}=243 Gives us: r = 3.
Hence, the second term will be given by (3rd term/r) = 1/3

1/3 = 1/9. Option (d) is correct.

[Note: To go forward in a G.P. you multiply by the common ratio, to go backward in a G.P. you divide by the common ratio.]

15. The sum of 5 numbers in AP is 35 and the sum of
their squares is 285. Which of the following is the
third term?

Correct Answers :

[B]

Explanation :

Since the sum of 5 numbers in AP is 35, their average would be 7. The average of 5 terms in an AP is also equal to the value of the 3rd term (logic of the middle term of an AP). Hence, the third term’s value would be 7. Option (b) is correct.

16. The number of terms of the series 26 + 24 + 22 +...
such that the sum is 182 is

Correct Answers :

[C]

Explanation :

Use trial and error by using various values from the
options.

If you find the sum of the series till 13 terms the
value is 182. The 14th term of the given series is 0,
so also for 14 terms the value of the sum would be
182. Option (c) is correct.

17. Find the lowest number in an AP such that the sum
of all the terms is 105 and greatest term is 6 times the least.

Correct Answers :

[D]

Explanation :

Trying Option (a), We get least term 5 and largest term 30 (since the
largest term is 6 times the least term). The average of the A.P becomes (5 + 30)/2 = 17.5

Thus, 17.5 × n = 105 gives us:

to get a total of 105 we need n = 6 i.e. 6 terms in this A.P. That means the A.P. should look like: 5, _,_, _, _, 30.

It can be easily seen that the common difference
should be 5. The A.P, 5, 10, 15, 20, 25, 30 fits the
situation.

The same process used for option (b) gives us the
A.P. 10, 35, 60. (10 + 35 + 60 = 105) and in the
third option 15, 90 (15 + 90 = 105).

Hence, all the three options are correct.

18. Find the general term of the GP with the third term
1 and the seventh term 8.

Correct Answers :

[A]

Explanation :

Go through the options. The correct option should give value as 1, when n = 3 and as 8 when n = 7. Only option (a) satisfies both conditions.

19. The sum of the first and the third term of a geometric
progression is 15 and the sum of its first three terms
is 21. Find the progression.

Correct Answers :

[C]

Explanation :

The answer to this question can be seen from the options. Both 3, 6, 12 and 12, 6, 3 satisfy the required conditions— viz, GP with sum of first and third terms as 15. Thus, option (c) is correct.

20. Ishita’s salary is Rs.5000 per month in the first year.
She has joined in the scale of 5000-500-10000. After
how many years will her expenses be 64,800?

Correct Answers :

[D]

Explanation :

The answer to this question cannot be determined because the question is talking about income and asking about expenses. You cannot solve this unless you know the value of the expenditure she incurs over the years. Thus, "Cannot be Determined" is the correct answer.

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