The questions asked under this test are based on number or letter. Through this test, the candidates have to check the ability to calculate faster. Also, it is also examined by how quickly you determine the relations between them, depending on their status between different letters or digits, through such questions. The questions asked under this test can be categorized into the following sections.

** Number Series **

Under this, a series of Numbers are given in the questions asked. This series is based on addition, subtraction, multiplication, division, square, square root, cube, cube root etc. To solve related questions, it is necessary to focus on the key points given below.

** (i) **If the value of the given series Numbers is going to increase in general, then surely there is just the work of Joint.

** (ii)** If the value of the given series Numbers is going to be normal, then there is definitely a depletion function.

** (iii)** If the number of given series is increasing with a lot of intensity, then surely there is a work of multiplication or ambition, addition to addition and subtraction or addition or subtraction Together it is possible.

** (iv)** If the numeric value of the chain is decreasing with intensity, then the work of the part is being done. Also, addition or subtraction is also possible.

** (v) **If the series increases with intensity first and later decreases, then there are multiplication and division actions being followed one by one.

** (vi)** If the value of digits in the chain increases first then decreases but at least the difference, then the function of addition and subtraction is changing and changing.

** Normally two types of questions are asked under the number series **

**(a) Complete the given series: **In this given sequence order, a particular place is left blank or denoted by a question mark (?) , Then it is expected from the candidates to select the appropriate number to be given in place of the question mark (?) Given by finding that sequence.

Now observe the examples given for explanation of the above facts carefully

**Example 1. **Which of the following options will be replaced in place of the question mark (?) in the following series?

16, 23, 31, 40, 50, 61,?

** (a) 81 (b) 77 (c) 83 (d) 81**

** Solution:** (a) Carefully observing the above series, we find that the series is increasing in order of +7, +8, +9, + 10. Thus, it can be expressed as follows.

Therefore, the appropriate number of questionable mark (?) Will be 73.

**Example 2. **In the series of the following points, which of the following options will be replaced in place of the question mark (?)?

12, 6, 6, 9,? , 45, 135

** (a) **18** (b) **24

So the appropriate number of question marks (?) Will be ’18 ‘.

**Example 3. **What will happen in place of the question mark (?) in the following series?

144, 100, 64,?, 16, 4

** (a) **49** (b) **42

So the number of points in place of the question mark (?) Will be 36.

**Example 4. **What number will come in place of the question mark (?) in the following series?

2, 5, 1441, 122, 365, 2

** (a) **1000** (b) **1094

** Solution:** (b) After carefully observing the series, we find that each next post is increasing with more difference, so we can guess that the action of multiplication in it will be. Also, addition or subtraction is also possible. So we find that series**
**× 3 – 1, × 3 – 1, increasing in the order of ….. like

So the intended number will be ‘1094’ in place of the question mark (?).

**(b)** **Finding the wrong post in a given series (Finding the Wrong Term in the Given Series)**

In the series sequence given below, any wrong digit is added instead of the number coming to a particular place, which is to find the wrong position used in the series by identifying the order given to the candidates. For this, the candidates should first know that the posts in the category are changing according to which rule, then it should be known that according to the rule, which post is not changing, that is the wrong post.

Now, observe some examples carefully for clarification of the above facts.

**Example 1. **Only one post in the following numbers category is incorrect, find out the wrong post.

3, 4, 7, 11, 20, 29, 47, 76

** (a) **7** (b) **11

Can be expressed as follows

That is 3+ 4 = 7, 4 +7 = 11, 7 + 11 = 18, 11 + 18 = 29, 18 + 29 = 47, 29 + 47 = 76

Hence the number ’20 ‘in the series is an inappropriate number because the number of 20 should be ’18’.

**Example 2. **What is the number in the series that is inappropriate in the series?

5, 3, 6, 10, 9, 12, 17, 15, 18, 23

** (a) **6** (b) **10

** Solution: **(b) After carefully observing the above series we find that given series – 2, + 3, + 5, – 2, + 3, + 5,. Decreasing and increasing in the order of which can be expressed as follows

Since the above series should have ’11 “after issue 6. So there is an inappropriate number 10 in the series.

**Example 3. **One post in the following numbers category is incorrect, by knowing the wrong post, let’s know what would be the correct position in place of that wrong post? All posts are one of the alternate answers given.

105, 114, 127, 138, 153, 170, 189

** (a) **114** (b) **125

** Solution: **(b) After careful observation of the above series, it is known that the difference of two successive terms is 9, 13, 15, 17 and 19, respectively. In these, except for the second and the third difference, the difference of two to two is two, if 125 is done at the place of 127, then the gradual two posts of the class will be 9, 11, 13, 15, 17 and 19 respectively. Which are growing uniformly. So 127 is wrong and it should be 125 in its place. It can also be expressed as follows

So wrong post = 127 and correct position = 125

**Example 4. **What is the number in the following series that is inappropriate, namely incompatible?

1, 4, 3, 16, 5, 32, 7, 64

** (a) **4** (b) **3

** Solution: **(a) The given series is divided into two sections. In this, the number of each odd places is increasing + 2 + 2 + 2, respectively, while the number of places is increasing in the sequence of × 2 × 2 × 2, … In the given series, there will be number 8 in place of number 4, it has been expressed as

So incompatible numbers = [4]

**⇒ Apart from the rules of Progression, questions can also be asked which are usually of two types **

** (a) Parallel category** is called a category in which the difference of two consecutive terms is the same, in the parallel division, in the rank of its previous post, the numbers received Is called.

So if the first position of the parallel class (A) is a and the common difference is d, then the parallel range will be

a, (a + d), (a +2d), (a + 3d), ……

Therefore, the nth grade of the parallel class is T = a + (n-1) d (where a is the first term and d)

** Example 1. **Category 3, 5, 7, 9,. What will be the 10th rank?

** Solution: **10th position T _{ 10} = a + (10-1) d

= 3 + (10-1) 2 = 21

(Since the first term here a = 3 and the derivative d = 5 – 3 = 7 – 5 = 9 – 7, i.e. 2)

** Example 2. **Category 357, 363, 369, 375, …. Which of the following is the 12th term?

(a) 423 (b) 411 (c) 442 (d) 449

** Solution:** (a) 12th term T _{ 12} = a + (12 – 1) d

= 357 + 11 * 6 = 357 + 66 = 423

** Example 3. **Find out the number of posts if the first step of an AP is 5, the decimal 3 and the last position is 80.

** (a) **24** (b) **23

** Solution: **(c) here a = 5, d = 3, T_{n} = 80, n =?

T_{n} = a + (n-1) d ** ⇒ **80 = 5 + (n-1) 3

⇒ (n -1) = (80 – 5) / 3 = 25 ⇒ n = 25 + 1 = 26

Hence the number of terms n = 26

** (b) Geometric Progression: **A category in which the ratio of two consecutive terms is the same, the ratio is called the class. This ratio is called a common ratio of GP. The ratio of the ratio is obtained by dividing the post in its post from its previous post.

If the first term of a ratio category is a and r is the r, then the GP’s nth term Tn = a.r ^{ n-1 }

** Example 1. **Which of the following is the 6th wager of class 3, 9, 27, 81, ..?

** (a) **243** (b) **729

** Solution: (b) **The first position here is a = 3 and the result is = 3

6th position T _{ 6} = ar ^{ n-1 }= 3.3 ^{ 6-1} = 3 × 3 ^{ 5} = 3 × 243 = 729

Normally r = 9/3 = 27/9 = 81/27 that is 3

** Example 2 .** Series 7, 14, 28,. What will be the 10th post?

** (a) **3584** (b) **2684

Solution: (a) Here the first term a = 7 and the ratio r = 2

10th term T _{ 10} = a.r ^{ n-1 }= 7.2 ^{ 10-1}

= 7 × 2 ^{ 9} = 7 × 512 = 3584

**Alphabet Series **

Under this series, a series of letters related to the English alphabet are given in the given series, in which one or two letters are lost or the location is denoted by the question mark (?), Then the questioning The correct letter to replace the mark (?) Is to be selected. For this, the candidates are given a careful observation of the series given to know that the series is changing according to which rule and according to this changed rule, what is appropriate in place of the question mark (?).

To easily solve the questions related to this series, it is necessary to remember the numeric values of the alphabet like A = 1, B = 2, C = 3, similarly Z = 26.

Now, let’s carefully examine some examples and their interpretive solution for explanation of the above facts.

**TYPE 1
**

**⇒ instructions (example 1-4)** Each question given below is given a series of letters. One or two letters have been omitted in these series and the question mark (?) Has been shown in place of them. Carefully study the given series, find out one of the four options given below, which is suitable in place of the question mark (?) In the series.

** 1. J K M P T ?**

** (a) **X** (b) **W

** 2. Z L X J V H T F? ?**

** (a) **SE** (b) **RD

** 3. M P N Q O R? ? Q T**

** (a)** SU** (b) **PS

** 4. AZX BVT CR? ?**

** (a)** PD** (b) **EQ

** Solution:
1. **(c) After carefully observing given alphabet sequence, we find that the letters used in the range are + 1, + 2 + 3 + 4, respectively, from their alphabetical order. Is growing in order.

So the appropriate letter “Y” to the place of the question mark (?) Will be.

** 2. **(b) givenUpon careful observation of the series, we find that the letter chain is divided into two sections. Under the first volume, the alphabet used in the odd location in the series is in alphabetical order according to the numerical value, then under the second volume, the letters used in place of the even numbers are also in alphabetical serial value, decreasing by 2. , It can be displayed in the following form.

So the appropriate letter in place of the question mark (?) = Rd will be.

** 3. **(b) On careful observation of the given letter series, we find that the series is divided into two sections, the letter + 1, + 1, + 1 on the odd position, . . . . . . . Are moving in the order of + 1 + 1 + 1. Are growing in order, it can be expressed as follows

So the appropriate letter PS will be in place of the question mark (?).

** 4. **(a) The given series is organized in the following order

So the correct letter to replace the question mark (?) Is PD.

**TYPE 2
**

**Example 1**. Which of the following options in the series of the following characters comes in place of the question mark (?)?

BXF, DVI, FTL, HRO?

** (a) **JOL** (b)** KPM

** Solution:** (d) After carefully observing the given letter series, we find that the first letter of each group of the letter series + 2 + 2 + 2, …….. increasing In the sequential order, the second letter of each group- 2, – 2, – 2, ……… and the third letter of each group + 3 + 3 + 3. Is organized in increasing order, which is expressed as follows

So the appropriate group of letters coming in place of the question mark (?) Will be ‘JPR’.

**Example 2 .** Which of the following options in the series of the following letters comes in place of the question mark (?)?

EDBA, KJHG, QPNM?

** (a) **ZXUV** (b) **WVTS

** Solution:** (b) After carefully observing the above letter series, we find that the first letter used in each group of the series is + 6 + 6 + 6, rather than its alphabet serial value. Similarly, the second letter of each group, the third letter and the fourth letter is also being changed in this order. It is expressly expressed as follows

So the appropriate letter group “WVTS” will be in place of the question mark (?).

**TYPE 3
**

**⇒ instructions (example 1-3)** Each question given below has a combined series of letters and digits. In this series, a few digits and letters have been omitted and the question mark is displayed in its place (?), By carefully studying the given series, find out one of the four options given below in the series, which That fit in place of the question mark (?) In the chain.

1. L7C N9F P12I R16L?

** (a)** T21O** (b) **S20O

2. KM5 IP8 GS11 EV14?

** (a)** BY17** (b) **CZ17

3. B8Y9 D7W7 F8U8 H5S6 J4O4?

** (a) **L5O6** (b) **L5O7

** Solution: 1. **(a) Carefully observing the series, we find that the first letter of each group is 2 places ahead of the first letter of its previous group, then the middle number in each group Number + 2 + 3 + 4,. And the last letter of each group is 3 places ahead of the last letter of its previous group, it has been expressed in the following form

So instead of the question mark (?), There will be appropriate digits T21O.

**2. **(d) After carefully observing the given series, we find that the first letter of each group is based on its alphabet serial number – 2 – 2 – 2 from the first letter of the previous group. In the order of the order, then the letter + 3 + 3 + 3 between each group. In addition to this, in addition to each other, there is a digit at the end of each group, which is increasing in order of + 3 + 3 + 3.. The above fact is expressed in the following form

Hence CY17 will be there in place of (?).

** 3. **(d) Having a careful overview of the given series, we find that the first letter of each group used in the series + 2 + 2 + 2. In the order of progressing, then in the second place of each group and at the fourth position, the first 1 point in each of the three groups decreases, then 1 digit decreases and each group has the alphabet in the third place, respectively – 2 – 2 – 2. is decreasing in sequence, it can be understood as the following form

So ? = L5O5

**TYPE 4
**

**⇒ instructions (example 1-4)** Each of the following questions is given a series of letters. Some characters have been abolished in these series and they are given in the sequence given below in the sequence of the series as it should be in the series. By carefully studying the given series, find out one of the four options given below,

Appropriate in place of missing letters

** 1.** ab_baabc_aabcb_abcb_

** (a)** bcaa** (b) **cbaa

2. a_bbaa_baa_baab aab

** (a) **abab** (b) **baba

3. aaa_bb_aab_baaa_bb

** (a)** abab** (b) **bbaa

4. _sr_tr_SrS_r_SrSt_

** (a)** ttsSrr** (b) **tsrtSr

** Solution:
1. **(b) At the beginning of the series given to solve such questions, we see that the letter ‘b’ is used on either side of the empty space and in that series two ‘b’ The ‘c’ letter is used in between, so at the beginning of the series, the letter ‘c’ will be used in the space between two ‘b’, thus the chain formed

ab c baabc_aabcb_abcb_

ab __ c__ baabc b aabcb_abcb_

Again the letter b and a are used on both sides of the next empty space, and the letter ‘a’ is used between b and a right behind the chain. Hence the series will be low

ab c baabc b aabcb b aabcb a abcb_

Again the ‘abcb’ letter is used behind the next empty space and just behind the chain we see that the letter ‘a’ is used after abcb, this series type chain will be lower

ab c ba / abc b a / abcb a / abcb a

Therefore, the intended reply will be ‘cbaa’ according to the option.

** 2. **(c) The given series will be organized as follows

a a bb / aa b b / aa b b / aab b / aab

Therefore, the answer to the option will be ‘abbb’.

** 3. **(d) The given series will be organized as follows

aaa / b bb / a aa / b b b / aaa / b bb

Therefore, according to the alternative, the intended answer will be ‘babb’.

** 4. **(d) The given series will be organized as follows

t sr / s tr / t sr / s t r / t sr / st r

Therefore, the desired answer according to the option will be ‘tstttr’.

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