**Introduction :**

Blood Relations Based Question are very common in all type of examination where you have been given relationship among few members of the family and based on given details you need to find out the ‘Unknown’ relation that exists satisfying the given criteria.

Questions depict relationships among the various members of a family in a roundabout chain.

The candidate is expected to find the relation of two particular persons mentioned in the question.

Generally, the question deals with a hierarchical structure which is based on seven generation three above & three below like this:

(Source –bankexamstoday )

**(This is the key to solve all type of Blood relation Problems )**

Also, You need to understand the common terms used while describing the family & blood relations.

Description | Relation |

Sister of father | Aunt |

Wife of uncle | Aunt |

Son of father or mother | Brother |

Brother of husband or wife | Brother-in-law |

Husband of sister/sister-in-law | Brother-in-law |

Son/daughter of uncle/aunt | Cousin |

Granddaughter of father/mother | Daughter or Niece |

Wife of son | Daughter-in-law |

Father’s father/mother only | Father |

Husband of mother | Father |

Son of grandfather/grandmother | Father/Uncle |

Father of wife/husband | Father-in-law |

Daughter of son/Daughter | Granddaughter |

Father of father or mother | Grandfather |

Husband of grandmother | Grandfather |

Father-in-law of father/mother | Grandfather |

Mother of father or mother | Grandmother |

Wife of grandfather | Grandmother |

Mother-in-law of father/mother | Grandmother |

Son of son/Daughter | Grandson |

Son’s/Daughter’s granddaughter | Great granddaughter |

Father of grandfather or grandmother | Great grandfather |

Mother of grandfather or grandmother | Great grandmother |

Son’s/Daughter’s grandson | Great Grandson |

Sister of mother | Maternal Aunt |

Brother of mother | Maternal Uncle |

Only daughter-in-law of father’s father/father’s mother | Mother |

Wife of father | Mother |

Daughter of father-in-law/mother-in-law of father | Mother/Aunt |

Mother of wife/husband | Mother-in-law |

Son of brother or sister | Nephew |

Daughter of brother/sister | Niece |

Father’s/Mother’s only son/daughter | Oneself |

Son of father | Oneself/Brother |

Father of daughter/son | Oneself/husband |

Mother of son/daughter | Oneself/Wife |

Children of same parents | Siblings |

Daughter of father or mother | Sister |

Sister of husband or wife | Sister-in-law |

Wife of brother/brother-in-law | Sister-in-law |

Grandson of father/mother | Son/Nephew |

Husband of daughter | Son-in-law |

Son of second wife of father | Step brother |

Second wife of father | Step mother |

Daughter of second wife of father | Step sister |

Brother of father | Uncle |

Husband of aunt | Uncle |

- First of all choose the two persons, between whom the relationship is to be established.
- Next, pinpoint the intermediate relationship i.e., such relationship through which long drawn relationship

can be established between the required persons. - Finally, conclude the relationship directly between the two persons as per the requirement of the question.
- From a particular name, we cannot ascertain the sex (gender) of that person. The name does not always

show the gender beyond the reasonable doubt. - Never make an assumption about the sex of given relation based on the name provided
- Always draw a pictorial diagram or Diagram based on Symbols to ascertain Family Tree Structure
- Representation of family tree structure is important as if you are able to draw valid pictorial you will be able to solve any kind of problem(We will see how to draw diagram step by step later in this blog post)

- Few Teachers suggest ” to relate the question to yourself e.g if a person’s name is given in the question and other relationships are related to him, try to put yourself on his place and relate yourself to him and this will help you in understanding the problem easily “.
- The above method only works if the problem is in simple nature and only involve few levels of Relationship

You can draw **tree diagrams** in the following fashion.

- Use vertical lines to represent parent-child relationships.
- Horizontal lines like <-> to denote marriages and dashed lines to represent sibling relationships. Apart from that, a sibling relationship can easily be established if they share the same root.
- You can also add gender differentiation to it by using a + sign for male and – sign for female.
- You can use (?) for the information that has not been provided to you.

**For Example **

⊕ │ ⊕ | Father-Son |

⊕ │ ϴ | Father-Daughter |

ϴ │ ⊕ | Mother-Son |

ϴ │ ϴ | Mother-Daughter |

As we have now understood the method to draw the diagram let’s move forth and practice some questions

Before that let’s see what type of Blood Relationship Questions are asked in various formats.

They are different in representation but substantially there is no difference between them.

**Mainly Questions on Blood Relations are of the following types:**

- Mixed-Up Relationship Descriptions
- Coded Relations/Symbolically Coded
- Puzzle-Based Question

(NET Exam Syllabus of Reasoning don’t provide exact information on what type of question can be asked but most of the time it has seen that Question asked are of a mixed nature )

However, if we consider the pattern of the question we should practise them separately-

Let’s Solve a few Examples!

The questions in this category are generally a dialogue/ conversation between two people and followed up with a question on the basis of the information provided in the conversation.

Given below are some examples.

D is the brother of B, M is the brother of B, K is the father of M and T is the wife of K. How is B related to T?

Pointing to a man in a photograph, a man said to a woman, “His mother is the only daughter of your father”.How is the woman related to the man in the photograph?

Above type of problem can be easily solved using pen and paper and start plotting the family tree diagram and the question will just fall into place.

Example –

*Abbas said to Chand, “Your mother’s husband’s sister is my aunt.” How is the lady related to Abbas? (1) Brother (2) Daughter (3) Sister (4) Aunt (5) None of these*

Solution:

Lady’s father’s sister is Lady’s aunt. But this sister is also Abbas’s aunt. Therefore Lady (Chand) is Abbas’s sister.

Hence, the answer is (3) Sister.

Read the information carefully and answer the question given below it.

- A family consists of 6 members P, Q , R, X, Y, Z.

2. Q is the son of R but R is not mother of Q.

3. P and R are married couple.

4. Y is the brother of R, X is the daughter of P.

5. Z is the brother of P.

**Questions :**

- Who is the brother in law of R?
- How many female members are there in the family?
- How is Q related to X?
- How is Y related to P?

In this type, relationships represented by codes and symbols like + , – , / , *. You have to analyze the required relation based on the given code. In this also you may need diagrammatic representation of problem to solve it. Use the same representation used in mixed blood relations.

In the coding equation better to solve the code from the last letter.

If P+Q means P is the husband of Q, P/Q means P is the sister of Q, P*Q means P is the son of Q. how is D related to A in D*B+C/A?

**Solution :**

C/A – C is the sister of Q.

B+C/A – B is brother in law of A (sister’s husband – brother in law.

D*B+C/A – D is the nephew of A (sister’s husband’s son means sister’s son i.e. nephew).

**So, the answer is Nephew.**

This type of Question is the mixture of other reasoning concepts like seating arrangement, direction problem, statement & conclusion and others.

So far, It has been not seen much questions were asked in the NET exam on these types but as NTA NET exam is online now and would be chances to have these types.

the most important aspect of this is there will be multiple questions based on the same set of instruction provided in one question; SO if you draw the incorrect family tree or pictorial Diagram chances are very high that you end of making mistake for all question.

The key aspect of solving these type of problem is *“Practise as Much as you can ” *

- A’s the only son sits second to the left of F’s daughter, who is not E. B’s daughter G is an immediate neighbour of F’s daughter.
- D’s mother sits opposite to G and sits is third to the left of C’s son. D’s sister and D’s mother are immediate neighbours of B’s sister, who is not sitting opposite any female.
- G’s father is B, who is the son of C. D’s sister F, sits opposite E’s grandfather C, who is the father of D.
- C is an immediate neighbour of D’s nephew, who is not the son of F.

**6. Who among the following sits opposite to H?**

a) C

b) E

c) A

d) D

e) G

**7. Who among the following is D’s mother?**

a) B

b) G

c) A

d) H

e) C

**8. If B’s daughter and D’s mother interchange their positions then who among the following sits third to the left F’s sister?**

a) B

b) A

c) H

d) F

e) None of these

**9. Four of the following five are alike in a certain way find the one who does not belong to the group?**

a) HB

b) FG

c) EB

d) CA

e) DH

**10. Who among the following sit third to the right of E?**

a) B

b) F

c) D

d) G

e) B

Answer : –

(Try Your Self – Below will Pictorial Diagram of Solution…. Check Answer from Diagram ….)

**Read More here – **

The number system or the numeral system is the system of identifying and expressing numbers. The number system presents a unique representation of each number and signifies the arithmetic and algebraic structure of the figures. It enables us to perform different arithmetic operations like addition, subtraction, and division.

The different kinds of number systems in mathematics are:-

- Binary
- Octal
- Decimal
- Hexadecimal

This article includes the whole concept of the number system with its kinds, conversions, and examples.

The number of radix or base ten is known as decimals. It’s the first number system in mathematics, where all the modern and ancient calculations are done. Other number systems based on this number is also derived from it. It’s generated using the combined use of digits ranging from zero to nine.

The number system uses digits like 0 and 1, which are the very common digits in the system, and thus it is used to express binary numbers. Whereas on the other side, 0 to 9 digits are used for different types of number systems. Let us discuss the different kinds of number systems.

The decimal number system includes a base of 10 since it practices ten digits from 0 to 9. The positions succeeding to the left of the decimal point express units, tens, hundreds, thousands, etc. The place value is described from right to left. The units have the position value as 100, tens have the position value as 101, hundreds as 102, thousands as 103, and carry on.

For example, the decimal number system 1747 comprises of the digit 7 in the units place, 4 in the tens place, 7 in the hundreds place, and 1 in the thousands position whose value can be addressed as

**1747**

**Explanation**:- The unit digit 7 with base 10 is multiplied by 10 with power 0.

The tens place digit 4 with base 10 is multiplied by 10 with power 1.

The hundredth place digit 7 with base 10 is multiplied by 10 with power 2.

The thousand place digit 1 with base 10 is multiplied by 10 with power 3.

Here is a description of it:

(1×10^{3}) + (7×10^{2}) + (4×10^{1}) + (7×10^{0})

=> (1×1000) + (7×100) + (4×10) + (7×1)

=> 1000 + 700 + 40 + 7

=> 1747

**10675 has place values as**

(1 × 10^{4}) + (0 × 10^{3}) + (6 × 10^{2}) + (7× 10^{1}) + (5 × 10^{0})

=> 1 × 10000 + 0 × 1000 + 6 × 100 + 7 × 10 + 5 × 1

=> 10000 + 0 + 600 + 70 + 5

=> 10675

The Binary number system has a base of 2. The number of digits existing here is two, i.e., 0 and 1. Mostly, the common base-2 is a radix of 2. The figures represented in this system are called binary numbers, which are 0 and 1.

For example, 100101 is binary. The binary number system is beneficial in electronic devices and computer systems since it can be quickly implemented using just two states, ON and OFF, i.e., 0 and 1.

Using the concept of 8421, he Decimal Numbers 0-9 are expressed in binary as:

- 0= 8421

[0000]

- 1= 8421

[0001]

- 2 = 8421

[0010]

- 3 = 8421

[0011]

- 4 = 8421

[0100]

- 5 = 8421

[0101]

- 6 = 8421

[0110]

- 7 = 8421

[0111]

- 8 = 8421

[1000]

- 9 = 8421

[1001]

We can describe 0 in binary representation as 0000 because the sum of 8,4,2,1 none can form a 0. Similarly, for 9, the representation is 1001 because one 8 and one 1 can sum up to forming 9 from the given sequence of 8421. You can transform any system into binary and vice versa.

The octal Number System has a base value of 8. It uses the number of digits from 0-7 for the conception of Octal Numbers. We can convert octal numbers to Decimal value by multiplying every digit with the place value and then summing the result. The octal numbers are beneficial for the description of UTF8 Numbers. The octal numbers are usually used in computer applications.

**Example: **Convert 217 (octal number representation) into decimal.

**Solution:**

217 = (2 × 8^{2}) + (1 × 8^{1}) + (7 × 8^{1})

=> (2 × 64) + (1 × 8) + (7 × 1)

=> 128 + 8 + 7

=> (143)_{10}

**Explanation**: The unit digit 7 with base 8 is multiplied by 8 with power 0.

The digit 1 with base 8 is multiplied by 8 with power 1.

The digit 2 with base 8 is multiplied by 8 with power 2.

The Hexadecimal Number System has a base value of 16. It uses the number of 16 digits i.e. from 0 to 15, to produce its numbers. The digits from 0 to 9 are taken just the same as the digits in the decimal number system except for the integers from 10 to 15 are represented as A to F i.e.

10 is expressed as A

11 = B

12 = C

13 = D

14 = E

15 = F

The hexadecimal Numbers are beneficial for managing memory address locations.

The number system conversion is a pretty simple task. Any of the number from any number system can be transformed into different number systems with the use of some techniques that are mentioned below:

The change of a number system means the transition from one base to different.

For decimal to binary, the two steps needed to perform the conversion are mentioned below:-

- Do the division process on the integer and the progressive quotient with the base of binary(2).
- Later, do the multiplication on the integer and the progressive quotient with the binary(base 2).

**Example: **Convert 19 with base 10 to binary:

Division by 2 | Quotient | Remainder |

19/2 | 9 | 1 |

9/2 | 4 | 1 |

4/2 | 2 | 0 |

2/2 | 1 | 0 |

And, the result goes from bottom to up, including the quotient of the last division. So, the result is (10011)_{2}.

For converting decimal to octal, the two steps needed to perform are mentioned below:

- Do the division process on the integer and the next quotient with the octal base (base 8).
- After this, do the multiplication process on the integer and the next quotient with the octal base (base 8).

**Example 1: **(160.25)_{10}

**Step 1:**

Divide 160 and its consecutive quotients with base 8.

Operation | Quotient | Remainder |

160/8 | 20 | 0 |

20/8 | 8 | 4 |

Operation | Answer | Carry |

0.25*8 | 0 | 2 |

As a result goes from bottom to up, including the quotient, at last, the answer will be (240.2)_{8}

For converting decimal to hexadecimal, the two steps needed to perform are mentioned below:

- Do the division process on the integer and the next quotient with the base of hexadecimal (16).
- Later, do the multiplication process on the integer and the continuous quotient with the hexadecimal base (16).

**Example 1: **(152)_{10}

**Step 1:**

Divide 152 and its continuous quotients with base 8.

Operation | Quotient | Remainder |

152/16 | 9 | 8 |

9/16 | 0 | 9 |

As a result goes from bottom to up, including the last quotient value, the answer will be (98)_{16}.

The three conversions feasible for binary numbers are binary to decimal, binary to octal, and binary to hexadecimal.

The method of converting binary number systems to decimals is quite easy. The method begins by multiplying every bit of binary number with its identical positional weights. Finally, add all the products.

**Example 1: **(11110.001)_{2}

Multiply every bit of (10110.001)_{2} with its corresponding positional weight, and in the last, add all the products of each bit with its weight.

**(11110.001)**** _{2 }**= (1×2

**=> **(1×16) + (1×8) + (1×4) + (1×2) + (0×1) + (0×1⁄2) + (0×1⁄4) + (1×1⁄8)

**=> **16 + 8 + 4 + 2 + 0 + 0 + 0 + 0.125

**=> **(30.125 )_{10}

The binary and octal base numbers are 2 and 8, respectively. In a binary number, the combination of three bits is similar to one octal digit. The two steps to convert a binary number into an octal number are mentioned below:

- You need to secure the pairs of three bits on both sides of the binary point. If anyone or two bits are left in a set of three bits pairs, we attach the demanded number of zeros on the last sides.
- Then, write the octal digits resembling every pair.

**Example 1: **(111111101011)_{2}

1. We create pairs of three bits on the binary point, as follows:

111 111 101 011

Next, write the octal digits which resemble every pair.

**(111110101011)**_{2}** = **(7753)_{8}

The binary and hexadecimal bases are 2 and 16, respectively. In a binary number system, the combination of four bits is similar to one hexadecimal digit. The two steps to change a binary number system into a hexadecimal number are mentioned below:

- Make the pairs of four-four bits on each side of the binary point. If anyone, two, or three bits are still left in a combination of four bits, append the demanded number of zeros on needed sides.
- Write the hexadecimal digits resembling every pair.

**Example 1: **(11110101111.0011)_{2}

1. Create pairs of four-four bits on each side of the binary point. Like,

111 1010 1111.0011

On the left side, the first pair only holds three bits. Present a total set of four bits, attach one zero on the left side.

0111 1010 1111.0011

2. Write the hexadecimal digits that resemble every pair.

**(011110101111.0011)**_{2}** = **(7AF.3)_{16}

The octal number can be converted into different number systems. The method of changing octal to decimal differs from the other process.

The method of changing octal to decimal is just like binary to decimal. The method begins by multiplying the numbers of octal with their identical positional weights. Then, add all products.

**Example 1: **(149.25)_{8}

**Step 1:**

Multiply every digit of 149.25 with its corresponding positional weight, and then add products of each bit with its weight.

**(149.25)8 **= (1×8^{2}) + (4×8^{1}) + (9×8^{0}) + (2×8^{-1}) + (5×8^{-2})

**(149.25)8 **= 64 + 32 + 9 + (2×1⁄8) + (5×1⁄64)

**(149.25)8 **= 64 + 32 + 9 + 0.25 + 0.078125

**(149.25)8 **= 105.328125

The conversion of a decimal number of the octal 149.25 is **105.328125**

The method of changing octal to binary is just the opposite method of binary to octal. Write the three-three bits of binary code for each octal number digit.

**Example 1: **(105.25)_{8}

Write the three-bit binary code for 1, 0,5 2, and 5.

**(108.25)**_{8}** **= (001 000 101.010 101)_{2}

The binary conversion of the octal number 105.25 is **(001000101.010101)**_{2}

To convert octal to hexadecimal, the two steps needed to do, are mentioned below:-

- Find the binary equivalent of
**25**. - Create the sets of four bits on each side of the binary point. If any one, two, or three bits are still left in a set of four bits combinations, Add the demanded number of zeros on the utmost sides. Write hexadecimal digits resembling every pair.

**Example 1: **(142.25)_{8}

**Step 1:**

**W**rite the three-bit binary code.

**(142.25)**_{8}** **= (001100010.010101)_{2}

The binary number of the octal number is **(001100010.010101)**_{2}

**Step 2:**

1. Create sets of four bits on each side of the binary point.

0 0110 0010.0101 01

On the left side, the first set has one digit only, and on the right side, the end set contains two-digit only. Create perfect pairs of four bits, append zeros on needed sides.

0000 0110 0010.0101 0100

2. Write the hexadecimal code, which resembles every pair.

**(0000 0110 0010.0101 0100)**_{2}** **= **(62.54)**_{16}

Hexadecimal numbers can easily be transformed into different number systems. The method of changing hexadecimal to decimal differs from others.

The method of changing hexadecimal to decimal is just like binary to decimal. The method begins by multiplying the numbers of hexadecimal digits with their similar positional weights. Then, add all products.

**Example 1: **(142A.25)_{16}

**Step 1:**

Multiply every number of **142A.25** with its corresponding positional weight, then add the products of every bit with its weight.

**(142A.25)**** _{16 }**= (1×16

**(142A.25)**** _{16 }**= (1×4096 )+ (4×256) +(2×16) + (10×1) + (2×16-1) + (5×16-2)

**(142A.25)**** _{16 }**= 4096 + 1024 + 32 + 10 + (2×1⁄16) + (5×1⁄256)

**(142A.25)**** _{16 }**= 5162 + 0.125 + 0.125

**(142A.25)**** _{16 }**= 5162.14453125

The decimal number of the hexadecimal number is **5162.14453125**

The method of changing hexadecimal to binary is the opposite method of binary to hexadecimal. Write the four-four bits binary code of every hexadecimal number.

**Example 1: **(142A.25)_{16}

Write the four-bit binary code.

(142A.25)_{16 }= (0001 0100 0010 1010.0010 0101)_{2}

The binary number of the hexadecimal number is **(1010000101010.00100101)**_{2}**.**

To convert hexadecimal to octal, the two steps needed to do, are mentioned below

- Find the binary equivalent of the hexadecimal digit.
- Then, create the sets of three-three bits on each side. If one or two bits are still left in a combination of three bits pairs. Add the expected amount of zeros on needed sides. Compose the octal digits resembling every pair.

**Example 1: **(AF.2B)_{16}

**Step 1:**

Use binary as a mediator.

Write the four-bit binary code.

The binary code of (AF.2B)_{16} is (10101111.00101011).

**Step 2:**

Create sets of three-three bits on each side of the binary point.

010 101 111.001 010 110

Write the octal code, which resembles every pair.

The octal number of the hexadecimal AF.2B is (257.126)_{8. }

Unit-I Teaching Aptitude Based Question

Unit-II Research Aptitude Based Question

Unit-III Comprehension Based Question

Unit-IV Communication Based Question

Unit-V Mathematical Reasoning and Aptitude Based Question

Unit-VI Logical Reasoning Based Question

Unit-VII Data Interpretation Based Question

Unit-VIII Information and Communication Technology (ICT) Based Question

Unit-IX People, Development and Environment Based Question

Unit-X Higher Education System Based Question

References

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- Number series [This Part ]
- letter series
- codes
- relationships
- classification

Questions on number series are prevalent in most of the exams. Almost 1-2 Questions comes in exam from this topic.

- These questions are based on numerical sequences that follow a logical rule/ pattern based on elementary arithmetic concepts.
- A particular series is given from which the pattern must be analysed. You are then asked to predict the next number in the sequence following the same rule
- There are some numbers are wrongly put into the series of number and you need to identify or correct them

- Number series questions are mostly numbers in the series are connected to each other. When you identify the connection, solving the question becomes easier for you.
- Identify the pattern asked in the question. Once you identify the pattern, solving the questions would be much easier.
- Once you have identified the pattern, apply it to the number before/ after the missing number in the series to get the answer.

- Try to analyse the given pattern such as prime numbers, perfect squares ,cubes, series of known numbers like Mathematics progression (AP/GP) etc.
- Next..if you are unable to find the familiar number :-
- Calculate difference B/W the given series elements
- Then observe the pattern in difference to see are they following any regular pattern or known numbers like said above.
- If the numbers are growing slowly its must be addition or subtraction series
- If the numbers are growing rapidly it might be a Square series or cube or multiplicative series.
- If the difference or sum don’t have any particular pattern it must be alternate number series.

- Now, You need to t signifies that the series follows a complex

pattern. Check for cases like multiplying the number and adding/subtracting a constant number from it to reach the pattern.

**Heads up!** There is no defined way to solve numbers series .

The Ultimate trick is to identify the numbers in the series and proceed accordingly.

*Question asked in UGC net exam in not of Bank PO or CAT level their level is much lower and its similar to asked in SSC Exam.*

- Mug Up Square root & Cube up to 30
- Remember Prime Numbers between 1-200
- Learn common Arithmetic & Geometric Progression series

The common patterns asked in number series topic are-

**Arithmetic Series** – This could be of two type. in which the next term is obtained by adding/subtracting a constant number to its previous term. **“common difference” is the key here**

Example: 4, 9, 14, 19, 24, 29, 34 [In the given series pattern is continued by adding 5 to the last number each time]

Further more this could be mixed with **Arithmetic** **Sequences** with the differences of consecutive numbers themselves form an arithmetic series.

Example: 1, 3, 6, 10, 15…..[ in the given series 3 – 1 = 2, 6 – 3 = 3, 10 – 6 = 4, 15 – 10 = 5….

Now, we get an arithmetic sequence 2, 3, 4, 5 ]

**Geometric Sequences** is **multiplying** by the same value each time.

Example – 1, 3, 9, 27, 81, 243, … [ The pattern is continued by multiplying by 3 each time…]

**Prime numbers-**

- Squares/ cubes-
- Pattern in differences-

**Pattern in alternate numbers-**

As the name of the series specifies, this type of series may consist of two series combined into a single series. The alternating terms of this series may form an independent series in itself.

Example: 3, 4, 8, 10, 13, 16 ? ?

As we can see, there are two series formed -> Series 1 : 3, 8, 13 with a common difference of 5

As we can see, there are two series formed -> Series 1 : 3, 8, 13 with a common difference of 5

-> Series 2 : 4, 10, 16 with a common difference of 6

So, next two terms of the series should be 18 & 22 respectively.

**Odd one out- **

**Complex Series**

**Cube roots and Square roots**

**Mixed Pattern **

**Warning!** Better check yourself, There could be multiple answer of number series asked based on logic applied by you or the Question setter.

**Few Reference Videos :-**

[Source – Number Series Tricks | Maths Tricks | Online Coaching For SBI – Provided by – adda247 ]

**Directions (1-10): What will come in place of the question mark (?) in the following number series ?**

** 1. 8 10 18 44 124 (?)**

(1) 344 (2) 366 (3) 354 (4) 356 (5) None of these

**2. 13 25 61 121 205 (?)**

(1) 323 (2) 326 (3) 324 (4) 313 (5) None of these

**3. 656 352 200 124 86 (?)**

(1) 67 (2) 59 (3) 62 (4) 57 (5) None of these

**4. 454 472 445 463 436 (?)**

(1) 436 (2) 456 (3) 454 (4) 434 (5) None of these

**5. 12 18 36 102 360 (?)**

(1) 1364 (2) 1386 (3) 1384 (4) 1376 (5) None of these

**6. 1 7 49 343 (?)**

(1) 16807 (2) 1227 (3) 2058 (4) 2401 (5) None of these

**7. 13 20 39 78 145 (?)**

(1) 234 (2) 244 (3) 236 (4) 248 (5) None of these

**8. 12 35 81 173 357 (?)**

(1) 725 (2) 715 (3) 726 (4) 736 (5) None of these

**9. 3 100 297 594 991 (?)**

(1) 1489 (2) 1479 (3) 1478 (4) 1498 (5) None of these

**10. 112 119 140 175 224 (?)**

(1) 277 (2) 276 (3) 287 (4) 266 (5) None of these

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