SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Surds and Indices

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In this chapter, we deals with questions based on index and surds of a number. Dealing with the topic candidate must have proper knowledge of basic concept and principle of surds and indices.

Surds
Any root of a rational number which cannot be exactly obtained is called a surd, e.g., √2, √6, √8, 3√4 etc.

Order of Surds
Let P be a rational number and m be a positive integer such that P^1/m = √P is irrational. Then, m√P is called surds of mth order.
e.g., 7½ = √7 = Surds of 2nd order.

Some Important and Basic Rules of Surds

Method of Arranging Surds in Increasing or Decreasing Order
Suppose given surds are p^1/a, q^1/b and r^1/c
First of all, take the LCM of a, b and c and use it to make the denominator of the powers the same. Then, easily we can find the required order.

Example The greatest among the numbers 3√2, 3√7, 6√5, 2√20 is
(a)3√2
(b)3√7
(c)6√5
(d)2√20

Operations on Surds
Addition and Subtraction
To add or subtract a surd, first make the possible factors of the terms, then add or subtract, i. e., Let x = √80 + 3√245 – √125
√80=√16 x 5=4√5; 3√245 =3√49×5=21√5; √125=√25×5=5√5 ,x=5√5

Example If √18225 = 135, then the value of √18225 + √182.25 + √1.8225 + √0.018225 is SSC (10 + 2) 2012
(a) 1.49985
(b) 14.9985
(c) 149.985
(d) 1499.85

Multiplication and Division
To multiply or divide the surds, we make the denominators of the powers same, then multiply or divide as usual –
i.e., Let x = √5 x 6√6 x 3√4

Indices
When a number ‘P’ is multiplied by itself ‘n’ times then the product is called nth power of ‘P and is written as Pⁿ. Here, P is called the base an ‘n’ is known as the index of the power. (Here, plural of index is called indices)

Some Important and Basic Rules of Indices

Essential Points

Reference Corner

1. If a^1/3 + b^1/3 + c^1/3 = 0, then a relation among a, b, c is SSC (10 + 2) 2014
(a) a + b + c = 3abc
(b) a³ + b³ + c³ = 0
(c) a + b + c=0
(d)(a + b+ c)³ =27abc
Answer:

2. If 3√a + 3√b = 3√c, then the simplest value of (a + b – c)³ + 27abc is ssc (10+2) 2014
(a) -3
(b) 0
(c) -1
(d) 3
Answer:

3. Which one of the following is true? SSC (10+2) 2014
(a) √5 + √3 > √6 +√2
(b) √5 + √3 < √6 +√2
(c) √5 + √3 = √6 +√2
(d)(√5 +√3)( √6 + √2)=1
Answer:

4. Let 3√a = 3√26 + 3√7 + 3√63 . Then, SSC (10+2) 2013
(a) a >729
(b)a = 729
(c) a <729 but a >216
(d)a<216
Answer:

5. The value of (x^b+c)^b-c (x^c+a)^c-a (x^a+b)^a-b 
(a)-1
(b)0
(c) 1
(d) 2
Answer:

6. If x = √3 + √2 and y = √3 – √2, then the value of 8xy (x² + y²) is SSC (10 + 2) 2013
(a) 16√6
(b)32
(c) 48√2
(d)80
Answer:

Practice Exercise

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Square Root and Cube Root

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Square
If a number is multiplied with itself, then the result of this multiplication is called the square of that number.
e.g., Square, of 5 = 5² = 5×5 = 25

Perfect Square
A natural number n is called a perfect square, if there exists a natural number m, such that n = m².
e.g., The numbers 1,4, 9, 16,… are square numbers.

Square Root
The square root of given number is that number whose square is equal to the given number. In general, we can say that, if a² = b, then square root of b is a. To represent the square root of a number, use the symbol ‘√’ on given number.

Methods to Find Square Root
The following methods are used to find the square root of any number

By Prime Factorization Method
The various steps involved in prime factorization method are
Step I Resolve the given number into prime factors.
Step II Make pairs of prime factors such that both the factors in each pair are equal.
Step III Take one factor from each pair.
Step IV Find the product of factors obtained in Step III, which is the required square root.

By Division Method
The steps involved in division method are
Step I In the given number, place bars over every pair of digits starting with the unit’s digit. Each pair and the remaining one digit (if any) on the extreme left is called a period.
Step II Think of the largest number whose square is less than or equal to the first period.
Step III Put the quotient above the period and write the product of divisor and quotient just below the first period. .
Step IV Subtract the product of divisor and quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.
Step V Now, the new divisor is obtained by adding the unit digit of the division to the divisor and annexing with a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend.
Step VI Repeat Steps II, III, IV and V till all the periods have been taken up.Now, the quotient, so obtained is the required square root of the given number.

Square Root of a Decimal Number
If the given number is in decimal form, then we separate the digits into periods of two to the right and left starting from the decimal point and then proceed normally. If the number of digit after the decimal are not even, then zero is put after the digits (extreme right) to make the digits even.

Square Root of a Fraction
If the given number is in fractional form, then find the square root of numerator and denominator separately and then write them in fractional form. Thus, the resultant fraction is the square root of the fraction.

Cube
If a number is multiplied two times with itself, then the result of this multiplication is called the cube of that number.
e.g., Cube of 4 = 4 x 4 x 4=4³

Cube Root
The cube root of a given number is the number whose cube is the given number.
In general, we Can say that a³ = b, then cube root of ‘b’ is ‘a’. Cube root of a number ‘a’ is denoted as 3√a.
Following method is used to find the cube root of given number

Prime Factorization Method
The various steps involved in prime factorization method are
Step I Resolve the given number into prime factors.
Step II Group the factors having three numbers in such a way that each number of the group is same.
Step III Take one factor from each group.
Step IV Find the product of the factors obtained in Step III which is the required cube root.

Example Find the cube root of 9261.
(a) 20
(b) 30
(c) 15
(d) 21

Essential Points

Reference Corner

1. 9x² + 25 – 30x can be expressed as the square of SSC (10+2) 2015
(a) 3x²-25
(b)3x+5
(c)-3x-5
(d)3x-5
Answer:
(d)9x² +25-30x
= (3x)² – 2 x(3) x (5) x + (5)² = (3x – 5)²
The required value is 3x – 5.

Practice Exercise

1.

(a) 3
(b) 4
(c) 1
(d) 2

2.

(a)5/9
(b)1-1/7
(c)4/7
(d)1-2/7

3.By what least number should 4320 be multiplied so as to obtain a number which is a perfect cube?
(a) 40
(b) 50
(c) 60
(d) 80

4.(3√1000 + 3√0.008 – 3√0.125) is equal to
(a) 9.7
(b) 9.97
(c) 9.997
(d) 9.9997

5.If √1+x/961 = 32/31, then the value of x is
(a) 63
(b) 61
(c) 65
(d) 64

6.The square root of 0.324 x 0.081 x 4.624/1.5625 x 0.0289 x 72.9 x 64 is
(a) 24
(b) 2.4
(c) 0.024
(d) 1.2

7.By what least number should 675 be multiplied so as to obtain a perfect cube number?
(a) 3
(b) 5
(c) 24
(d) 40

8.How many perfect squares lie between 120 and 300?
(a) 5
(b) 6
(c) 7
(d) 8

9.If (10.15)² = 103.0225, then the value of √1.030225 + √10302.25 is
(a) 1025.15
(b) 103.515
(c) 102.515
(d) 102.0515

10.Five times of a positive integer is equal to 3 less than twice the square of that number. The number is
(a) 3
(b) 13
(c) 23
(d) 33

11.The number whose square is equal to the difference of the squares of the numbers 68 and 32, is
(a) 36
(b) 48
(c) 60
(d) 64

12. The sum of digits of the smallest number, which when multiplied by 900, gives a perfect cube is
(a) 2
(b) 3
(c) 6
(d) 9

13. The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is
(a) 12
(b) 13
(c) 14
(d) 15

14.The smallest number added to 680621 to make the sum a perfect square is
(a) 4
(b) 5
(c) 6
(d) 8

15.

(a)7 1/12
(b)5 5/12
(c) 1 1/12
(d) 1 7/12

16.

(a)1
(b)2.5
(c)5
(d)25

17.

(a)5/6
(b)7 1/6
(c)7 1/3
(d)8 1/3

18. How many positive integers loss than 1000 are multiples of 11 whose square roots are whole numbers.
(a) 2
(b) 4
(c) 8
(d) 11

19. Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is
(a) 24
(b) 21
(c) 14
(d) 35

20. Find the largest number of 5-digit which is a perfect square?
(a) 99999
(b) 99764
(c) 99976
(d) 99856

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Number System

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In Hindu Arabic System, we use ten symbols 0,1,2, 3,4, 5,6, 7,8,9, which are called digits to represent any number. Out of these ten digits, 0 is called an insignificant digit whereas the others are called significant digit.
A group of digits representing a number is called a numeral. To write a number, we put digits from right to left at the places designated as unit, ten, hundred, thousand, ten thousand, lakh, ten lakh and so on.
Now, let us see how the number 5 1 287254 is represented.

It is read as “Five crore twelve lakh eighty seven thousand two hundred fifty four”.

Value of Numerals
1. Face Value Face value of a digit is the value of the digit itself irrespective of its place in the numeral.
e.g., In number 41232 => Face value of 3 is 3.
2. Place Value The place value of a digit is the place at which digit is present in the numeral
e.g., In number 41232 => Place value of 3 is 3 x 100 = 300.

Classification of Numbers

Natural Numbers All counting numbers, except zero (0) are called natural numbers denoted by N. e.g., 1, 2, 3,… etc.

Whole Numbers All natural numbers along with zero are called whole numbers denoted by W. e.g., 0, 1, 2, 3,… etc.

Even Numbers All counting numbers which are divisible by 2 are called even numbers, e.g., 2, 4, 6, 8,… etc.

Odd Numbers All counting numbers which are not divisible by 2 are called odd numbers, e.g., 1, 3, 5,… etc.

Prime Numbers A counting number is called prime number, if it has only two factors i.e., 1 and the number itself, e.g., 2, 3, 5, 7, 11, 13,… etc,

Co-prime Numbers Two natural numbers are said to be co-primes, if their highest common factor is 1. e.g., (9,2), (5,6), (11, 15), …etc. Co-prime numbers are also called as relatively prime numbers.

Composite Numbers A composite number is one which has other factors besides 1 and itself. Thus, it is a non-prime number, e.g., 4, 6, 9, 14, 15 etc.
Note 1 is neither prime nor composite.

Integers The collection of all whole numbers along with the negative numbers are called integers. The set of integers is denoted by Z or I. e.g., -4, -2, 0,-1, 3, 4,….
Here, -4, -2 are called negative integers and 1, 3,4 are called positive integers.
Example If p and q are two relatively prime positive integers such that p + q= 10, p < q, then the number of possible values of p is SSC (10+2) 2012
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(a) Two numbers are said to be co-prime, if their HCF is 1.
Co-prime numbers can be prime or not,
Now, p + g = 10, p< q
Possible values of p are, p = 3, q = 7
Possible values of p is 1 values.

Rational Numbers A number which can be expressed in the form of p/q, where p and q are integer and q ≠ 0 is q called rational number.

Irrational Numbers A number which cannot be expressed in the form of p/q, where p and q are integer and q ≠ 0. e.g., √2, √3, √7,… etc.

Real Numbers Real numbers comprises of both rational and irrational numbers, e.g., 7/9, √2, √5, π, 8/9,… etc.

Divisibility Test
A number is said to be
Divisible by 2 When its unit’s place digit is even or zero. Divisible by 3 When the sum of its digits is divisible by 3.
Divisible by 4 When the number formed by the last two digits is divisible by 4.
Divisible by 5 When its unit’s place digit is either 0 or 5.
Divisible by 6 When it is divisible by 2 and 3 both.
Divisible by 7 When difference between twice the digits at ones place and the number formed by other digits is either zero or multiple of 7.
e.g., 581 is divisible by 7 because 58-2×1 = 56
As, 56 is divisible by 7.
581 is divisible by 7.
Divisible by 8 When number formed by last three digits is divisible by 8.
Divisible by 9 When sum its digits is divisible by 9. Divisible by 10 When unit’s place digit is zero.
Divisible by 11 When the sum of digits at odd places and even places are equal or differ by a number divisible by 11.
Divisible by 12 When it is divisible by 3 and 4 both.

Important Divisibility Rules
• If a number is divisible by another number, then it is divisible by each of the factors of that number.
• If a number is divisible by two co-prime numbers, then it is divisible by their product also.
• If two given numbers are divisible by a number, then their sum and difference is also divisible by that number.
• (xⁿ – aⁿ) is divisible by (x – a) for all values of n.
• (xⁿ – aⁿ) is divisible by (x + a) for even values of n.
• (xⁿ + aⁿ) is divisible by (x + a) for odd values of n.

Division of Numbers
(Division Algorithm Lemma)
Let a and b be two integers such that b ≠ 0. On dividing a by b, q will be quotient and r will be the remainder, then the relationship between a, b, q and r is established as
a = bq + r
In general, we have .
Dividend = Divisor x Quotient + Remainder

Example 47 is added to the product of 71 and an unknown number. The new number is divisible by 7, giving the quotient 98. The unknown number is a multiple of ssc (10+2) 2011
(a) 2
(b) 5
(c) 7
(d) 3

Example A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be ssc (10+2)2010
(a) 1
(b)2
(c) 7
(d) 17

To Find the Unit’s Place Digit in the Product of Numbers
To find the unit’s place digit in the given product, first take unit’s place digits of each number. Find the product of these digits. If there is any ten place digit, then take unit’s place digit to continue the product. Then, the unit’s place digit in the last number is the required digit.
Simplification
The word simplification refers to a procedure useful for converting a lengthy expression into simplest form.
Rule for solving question on simplification is VBODMAS. You have to solve the expression by solving various operations in a particular sequence given by VBODMAS. It means
V-Underline portion i.e., bar
B-Brackets should be removed in the order (), {} and [ ], i. e., operations inside the bracket should be done first.
O-Of [whereever ‘of is given, the meaning is X or multiplication]
D- Division
M- Multiplication
A- Addition
S- Subtraction

Fraction
A number expressed in the form of a/b where a and b are integers and b ≠ 0, where a is known as numerator and b is known as denominator.

Types of Fraction
Proper Fraction When numerator is less than denominator, then fraction is called proper fraction.
Improper Fraction When numerator is greater than denominator, then fraction is called improper fraction.
Like Fraction A number of fractions having same denominator are called like fraction.
Unlike Fraction A number of fraction having different denominators are called unlike fraction.
Compound Fraction It is fraction of fraction.
e.g, ,1/4 of 5/7 of 7/9 etc
Complex Fraction In such fractions numerator or denominator both are fractions.
eg,

Mixed Fraction Those fractions which consists a whole number and a proper fraction are know as mixed fraction.
eg.,3 1/4,2 1/2 etc

Continued Fraction It contains an additional fraction in the numerator or in the denominator.
eg.,

Example The denominator of a fraction is 3 more than its numerator. If the numerator is increased by 7 and the denominator is decreased by 2, we obtain 2. The sum of numerator and denominator of the fraction is SSC (10 + 2) 2011
(a) 5
(b) 13
(c) 17
(d) 19

Example A number whose one-fifth part increased by 4 is equal to its one-fourth part diminished by 10, is SSC (10 + 2) 2011
(a) 260
(b) 280
(c) 240
(d) 270

Decimal Fraction In this type of fraction, denominator has power of 10. There is a special type of decimal fraction called ‘Recurring decimal fraction’.
Recurring Decimal Fraction This is the decimal fractions in which one or more decimal digits are repeated again and again.
e.g,

There are two types of recurring decimal fraction
1. Pure Recurring Decimal Fraction When all the figures in a decimal fractions are repeated after the decimal point, then the decimal fraction is called a pure recurring decimal fraction.

2. Mixed Recurring Decimal Fraction When some figures are not repeated while some of them are repeated in recurring decimal, then it is called mixed recurring decimal fraction.

Essential Points

• Sum of first n natural numbers = n(n + 1)/2
• Sum of first n odd numbers = n²
• Sum of first n even numbers = n(n + 1)
• Sum of square of first n natural numbers =n(n+1)(2n+1)/6
• Sum of cube of first n natural numbers =[n(n+1)/2]²
• (x^m – a^m) is divisible by (x – a) for all values of m.
• (x^m – a^m) is divisible by (x + a) for even values of m.
• (x^m + a^m) is divisible by (x + a) for odd values of m.
• Product of two numbers=HCF of numbers x LCM of the numbers.

Reference Corner

1. What is the value of 3/4 + 8/9?
(a) 57/27
(b) 11/13
(c) 59/36
(d) 11/9
Answer:

2. The difference between the greatest and the least four digit numbers that begins with 3 and ends with 5 is SSC (10 + 2) 2015
(a) 900
(b) 909
(c) 999
(d) 990
Answer:

3. The least value of n, such that (1 + 3 + 3² + … + 3ⁿ) exceeds 2000, is SSC (10 + 2) 2014
(a) 7
(b) 8
(c) 5
(d) 6
Answer:

4. The simplified value of (0.2)³ x 200 ÷ 2000 of (0.2)² is SSC (10 + 2) 2014
(a) 1/10
(b) 1
(c) 1/100
(d) 1/50
Answer:

5. The odd one out from the sequence of numbers 19, 23, 29, 37, 43, 46, 47 is SSC (10 + 2) 2014
(a) 37
(b) 19
(c) 23
(d) 46
Answer:

6. The next number of the sequence 1/2, 3/4, 5/8, 7/16, … is SSC (10 + 2) 2014
(a)9/24
(b)9/32
(c)10/24
(d)11/32
Answer:

7.The least number by which 20184 must be multiplied, so as to make the product a perfect square is SSC (10 + 2) 2014
(a)5
(b)6
(c)2
(d)3
Answer:

8. A teacher wants to arrange his students in an equal number of rows and columns. If there are 1369 students, the number of students in the last row are SSC (10 + 2) 2014
(a) 37
(b) 33
(c) 63
(d) 47
Answer:

9. The first term of an arithmetic progression is 22 and the last term is -11. If the sum is 66, the number of terms in the sequence are SSC (10+2) 2014
(a) 10
(b) 12
(c) 9
(d) 8
Answer:

10. In a division sum, the divisor is 3 times the quotient and 6 times the remainder. If the remainder is 2, then the dividend is SSC (10+2) 2013
(a) 36
(b) 28
(c) 50
(d) 48
Answer:

11. 1/7 + (999 692/693) is equal to SSC (10+2) 2013
(a) 99800
(b) 99900
(c) 1
(d) 99000
Answer:

12. The number of prime factors in 6³³³ x 7²²² x 8¹¹¹ is SSC (10 + 2) 2013
(a) 1111
(b) 1211
(c) 1221
(d) 1222
Answer:

Practice Exercise

1.Amit, while solving his Maths homework, took 12 as divisor instead of 21, in a question on division with zero remainder. The quotient obtained by him was 35. Find the correct quotient.
(a) 10
(b) 12
(c) 20
(d) 15

2.The sum of three consecutive odd numbers is 20 more than the first number among three. What is the middle number?
(a) 7
(b) 8
(c) 12
(d) 9

3.The sum of series 1 + 2+ 3+ 4+ …+ 998 + 999 + 1000
(a) 5050
(b) 500500
(c) 550000
(d) 55000

4.On dividing a certain number by 357, the remainder is 39. On dividing the same number by 17. What will be the remainder?
(a) 5
(b) 3
(c) 7
(d) 6

5.Each member of a kitty party contributed twice as many rupees as the total collection was Rs 3042. Find the number of members present in the party.
(a) 22
(b) 32
(c) 42
(d) 39

6. The difference between a number of two digit and the number obtained interchanging its digits is 63. What is the difference between its digits?
(a) 5
(b) 6
(c) 7
(d) 8

7. Sumit, Aditya and Sandeep cycling round a circle 1 km in circumference at they rate of 10, 20 and 40 m/min, respectively. If they all start together in the same direction, when will they again be together at the same place?
(a) After 50 min
(b) After 240 min
(c) After 800 min
(d) After 100 min

8. If the sum of the digits of a two digit number is 9 and the difference of those digits is 3, what is the product of the digits of the same number?
(a) 9
(b) 36
(c) 18
(d) 72

9. Out of fractions 5/7, 7/13, 4/7, 4/15 and 9/14 which is the second highest?
(a) 5/7
(b) 7/13
(c) 4/7
(d) 4/15

10. A number divided by 899 gives a remainder of 63. If the number is divided by 29, the remainder will be
(a) 2
(b) 5
(c) 13
(d) 28

11. The greatest number of five digit which when divided by 3, 5, 8, 12 have 2 as remainder
(a) 99999
(b) 99958
(c) 99960
(d) 99962

12. The sum of all natural numbers between 100 and 200 which are multiples of 3 is
(a) 5000
(b) 4950
(c) 4980
(d) 4900

13. Amar spends 1/3 of his income on food, 2/5 of his income on house rent and 1/5 of his income on clothes. If he still have Rs 400 left with him. Find Amar’s income,
(a) Rs 4000
(b) Rs 5000
(c) Rs 6000
(d) Rs 7000

14. A milkman has 75 L milk in one cane and 45 L in another. The maximum capacity of container which can measure mild of either container exact number of times, is
(a) 1 L
(b) 5 L
(c) 15 L
(d)25 L

Answers

Hints & Solutions

SSC CHSL Topic Wise Study Material – General Intelligence – Other Sub-Topics

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After analysing the previous papers, it is seemed that there are some topics which are frequently asked in examination except the topics which have been described earlier.

For the supplement to the students we are preparing a topic named sub-topics including all the remaining topics which have been asked in examinations.

Verbal General Intelligence
(i) Sitting Arrangement
(ii) Cube and Dice
(iii) Watch and Calendar

Non-Verbal General Intelligence
(i) Water and Mirror Images
(ii) Counting of Figures
(iii) Figure Formation

Verbal
(i) Sitting Arrangement

Sitting arrangement is the process of arranging the persons/objects based on the given information. Generally, information are arranged may be linear, circular, rectangular, square etc., on the basis of conditions provided.
There are three kinds of informations
(i) Definite Information When the place of any subject is definitely mentioned.
(ii) Comparative Information When the place of any subject is not mentioned definitely but in comparison to another subject is mentioned.
(iii) Negative Information A information, does not inform us anything exactly but it gives us a chance to eliminate a possibility.

Types There are two types of questions which are generally asked in various competitive exams.

1. Linear Arrangement In linear arrangement, the objects/persons are arranged in a straight line as per the information provided. Before solving this type of question, it is necessary to know the following facts

Example Six friends A,B,C,D,E and F are sitting in a row facing East. C is between A and E. B is just to the right of E’but left of D. F is not at the right end. How many persons are to the right of ‘E’? ssc (10+2) 2010
(a) 1
(b) 2
(c) 3
(d) 4

2. Circular/Square Arrangement In this type of arrangement, objects/ persons sits around a closed path facing towards or outside the centre on the basis of information provided. Before solving this type of question, it is necessary to know the following facts
In circle (Facing centre)

Example A,B,C,D,E and F are sitting in a circle facing towards centre. D is between F and B. A is second to the left of D and second to the right of E. Who is facing towards D? SSC (10+2) 2012
(a) C
(b) A
(c) E
(d) B

Reference Corner

Directions (Q.Nos. 1-3) Read the following information carefullly and answer the question that follow. SSC (10 + 2) 2014
(i) A, B, C, D, E, F and G are sitting in a circle facing at the centre and playing cards.
(ii) E is neighbor of A and D.
(iii) G is not between F and C.
(iv) F is to the immediate right of A.

1. Which of the following does not have the pair of persons sitting adjacent to each other?
(a) BA
(b) CB
(c) DE
(d) GD

2. Which of the following pairs has the second person sitting immediately to the right of the first?
(a) AB
(b) CB
(c) EA
(d) DG

3. What is the position of F?
(a) Third to the left of C
(b) Second to the right of C
(c) To the immediate left of A
(d) To the immediate right of A
SoL (Q.Nos. 1-3)
According to the question, the circular figure is as

1 (a) B and A are not adjacent to each other.
2. (c) A is sitting immediate right of E.
3. (d) F is immediate right of A.

Practice Exercise

1. A,P,R, X, S and Z are sitting in a row. S and Z are in the centre and A and P are at the ends. R is sitting on the left of A. Then, who is sitting on the right of P?
(a) A
(b) S
(c) X
(d)Z

2. Five persons are standing in a line. One of the two persons at the extreme ends is a professor and the other a businessman. An advocate is standing to the right of a student. An author is to the left to the businessman. The student is standing between the professor and the advocate. Courting from the left the advocate is at which place?
(a) 1st
(b) 2nd
(c) 3rd
(d) 5th

3. Five friends A,B,C,D and E are standing in a row facing South but not necessarily in the same order. Only B is between A and E, C is immediate right to E and D is immediate left to A. On the basis of above information, which of the following statements is definitely true?
(a) B is to the left of A
(b) D is third to the left of E
(c) B is to the right of E
(d) A is second to the left of C

4. Seven people A,B,C,D,E,F and G are standing in. a single file line, facing a booth. E is somewhere ahead of F. There is exactly one person standing between C and G. D is immediately behind A. F is behind both B and D. If D and C are fourth and fifth in line respectively, then which of the following must be true?
(a) A is first
(b) B is first
(c) F is sixth
(d) F is seventh

Directions (Q.Nos. 5-8) Read the following information carefully and answer the questions that follow.
(i) Eleven students A B, C, D, E, F, G, H, I, J and K are sitting in the first row of the class facing the teacher.
(ii) D, who is to the immediate left of F is second to the right of C.
(iii) A is second to the right of E, who is at one of the ends.
(iv) J is the immediate neighbour of A and B and third to the left of G.
(v) H is to the immediate left of D and third to the right of I.

5. Who is sitting in the middle of the row?
(a)B
(b)C
(c)G
(d)I

6. Which of the following groups of friends is sitting to the right of G?
(a) CHDE
(b)CHDF
(c) IBJA
(d) ICHDF

7. Which of the following statement is true in the context of the above sitting arrangement?
(a) There are three students sitting between D and G
(b) K is between A and J
(c) B is sitting between J and I
(d) G and C are neighbours sitting to the immediate right of H

8. If E and D, C and B, A and H and K and F interchange their positions, which of the following pairs of students is sitting at the ends?
(a) D and E
(b) E and F
(c) D and K
(d) K and F

Directions (Q.Nos. 9-13) Read the following information carefully and answer the questions that follow.
(i) A, B, C, D, E, F and G are sitting on a wall and all of them are facing East.
(ii) C is on the immediate right of D.
(iii) B is at an extreme end and has E as his neighbour.
(iv) G is between E and F.
(v) D is sitting third from the South end.

9. Who is sitting to the right of E?
(a) A
(b) C
(c) G
(d) F

10. Which of the following pairs of people are sitting at the extreme ends?
(a) AB
(b) AE
(c) CB
(d) FB

11. Name the person who should change place with C such that he gets the third place from the North end.
(a) E
(b) F
(c) G
(d)D

12. Immediately between which of the following pairs of people is D sitting?
(a) AC
(b) AF
(c) CE
(d) CF

13. Which of the conditions (i) to (v) given above is not required to find out the place in which A is sitting?
(a)(i)
(b)(ii)
(c)(iii)
(d)All are required

Answers

Hints & Solutions

(ii)Cube & Dice

A cube or dice is a regular polyhedron/ hexahedron having six identical square faces. Questions asked from this topic basically based on three dimensional figure, known as cube and dice. To solve these questions a candidate must have knowledge about the basic concepts of cube and dice.

Cube
A cube is three dimensional figure. Cube is a figure which has its length, width and height in equal form and has 8 corners, 6 surfaces and 12 edges.

Example A solid cube of 4 inches has been painted red, green and black on pair of opposite faces. It has been, then cut into one inch cubes. How many cubes have only four faces painted? SSC (10+2) 2010
(a) 0
(b) 4
(c) 8
(d) 16
Answer:
(a) None four faces painted when solid cube of 4 inches has been painted red, green and black pair of opposite ‘ faces and cut into one inch cubes.

Example A solid cube of 4 inches has been painted red, green and black on pair of opposite faces. It has been cut into one inch cubes. How many cubes have only one face painted? ssc (1o+2) 2011
(a) 4
(b) 8
(c) 16
(d) 24
Answer:

Some Important Facts
If a cube is painted on all of its surfaces with a colour and then divided into smaller cubes of equal size, then after separation, number ! ; of smaller cubes, so obtained will be calculated as under

Dice
A dice is three-dimensional figure with 6 surfaces. It may be in the form of a cube or in cuboid, After observing these figures, we have to find the opposite side of the dice.

There are two types of dice
1. Ordinary Dice In ordinary dice, the sum of opposite is not 7 but the sum of adjacent sides are 7.

2. Standard Dice In standard dice, the sum of opposite sides is 7. In other words, we can say that a dice which does not has 7 as total of two adjacent sides known as standard dice.

Example Which number is on the face opposite to 6 in the dice whose four views are given below? SSC (10 + 2) 2012

(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(a) From dice, 1, 2 and 3 numbers 2, 3, 4 and 5 are adjacent to number 6. Hence, number 1 is opposite to 6.

Reference Corner

1. Given below are the different positions of a dice. What shall come in the place of ‘X ’? SSC (10 + 2) 2014

(a) 3
(b) 5
(c) 2
(d) 1
Answer:

2.From the following two different appearances of dice, find out which colour is opposite to white ? SSC (10 + 2) 2014
(a) Blue
(b) Black
(c) Yellow
(d) Red
Answer:
(a) From both dices red and yellow faces are common. Hence, third colour blue is opposite to white.

Practice Exercise

Directions (Q.Nos. 1 and 2) Read the following information and answer the questions that follow.

A cube is coloured red on two opposite faces, blue on two adjacent faces and yellow on two remaining faces. It is then cut into two halves along the plane parallel to the red faces. One piece is then cut into four equal cubes and the other one into 32 equal cubes.

1. How many cubes will not have any coloured faces?
(a) 0
(b) 16
(c) 4
(d) 8

2. How many cubes will not have any red faces?
(a) 8
(b) 16
(c) 20
(d) 24

Directions (Q.Nos. 3-6) Read the following information and answer the questions that follow.

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so, obtained are now separated.

3. How many smaller cubes have no surface coloured?
(a) 24
(b) 16
(c) 8
(d) 10

4. How many smaller cubes will have atleast two surfaces painted with red colour?
(a) 4
(b) 18
(c) 32
(d) 24

5. How many smaller cubes have two surfaces painted with red colour?
(a) 24
(b) 8
(c) 12
(d) 20

6. How many smaller cubes have only three surfaces painted with red colour?
(a) 0
(b) 12
(c) 24
(d) 8

7. On the basis of two figures of dice you have to tell what number will be there on the opposite side of number 5?

(a)1
(b)3
(c)4
(d)5

8.Two positions of a dice are shown below when number 1 is on the top. What number will be there at the bottom?

(a)2
(b)3
(c)5
(d)Data inadequate

9.Two positions of a dice are shown below. When there are two dots at the bottom, the number of dots at the top will be

(a) 2
(b) 3
(c) 5
(d) 6

10.Four positions of a dice are given below

Identify the number at the bottom when the top is 3.
(a) 5
(b) 1
(c) 2
(d) 6

11.

Which number is at the opposite of number 5?
(a) 4
(b)6
(c) 1
(d)3

Answers

Hints & Solutions

(iii)Watch & Calendar

Question asked from this topic is based on watch and calendar. Question asked on watch in examination focus the angles of hands of watch and question asked on calendar in examination refers to the date and day on a prescribed given time period. To solve these questions a candidate must know the term of watch and calendar.

Watch
A watch is an instrument used for indicating and maintaining the time dial, hour hand, minute hand, second hand are its components. Dial of a watch is divided in 12 equal parts, each part is known as one hour and one hour is also divided in 5 equal parts, each such part is known as one minute. The Basic structure of a watch is as follows

The clock represents two things i.e minute and hour. The minute is a unit of time equal to 1/60 th of an hour or 60 s
i.e., 1 min =60 s. An hour is a unit of measurement for the time duration of 60 min or 3600 s. i.e.,
1 h =60 min =3600 s

1. See the Movement of Clock
(i) Clock’s long hand or minute hand covers 360° in 60 min.
So, we can say that angle traced by minute hand in 360°
one minute =360°/60 = 6 °

(ii) Clock’s short hand or hour hand covers 360° in 12 h.
So, we can say that angle traced by hour hand in one
hour = 360°/12° = 30°
In 60 min angle traced by hour hand is 30°
In 1 min angle traced by hour hand =30°/60° =1°/2
Relative angle between minute hand and hour hand
= 6° = 11°/2 = 5 1°/2
In other word, minute hand gains 5 1°/2 more than hour hand.

Example At what angle the hands of a clock are inclined at 3 h 40 min? SSC (10+2) 2012
(a) 150°
(b)120°
(c) 45°
(d)130°
Answer:
(d) From the formula, 11/2 min – 30 h
According to the question,
Here, min = 40, h = 3
So, required angle 11
= 11/2 x 40 – 30 x 3 = 220 – 90 = 130°
So, the hands of.a clock are inclined at 3 h 40 min at 130°.

2. Coincidence of Hour Hand and Minute Hand
Coincidence means at what time hour hand and minute hand overlap each other.
At 12 o’clock minute hand and hour hand overlap each other.
So, to coincide again, minute hand to cover 360° to cover 360°, it takes = 360°/55
=3600/55=720/11
=65 5/11 min
[45 min hand gains 5.5° over hour hand]

3. Incorrectness of a Clock
A clock is said to be incorrect, if it doesn’t show actual time, So, either it gains time or loses time due to incorrectness

Gaining Time
When coincidence of minute hand and hour hand takes
less than 65 5/11 min, then clock is said too fast.

Losing Time
When coincidence of minute and hour hand takes more than 65 5/11 min, then clock is said to slow.

Example A clock is set right at 1 pm. If it gains 1 min an hour, what is the true time when the clock indicates. 6 pm the same day?
(a) 40 5/11 min past 5 pm
(b) 55 5/61 min past 5 pm
(c) 45 5/11 min past 5 pm
(d) 56 5/61 min past 5 pm
Answer:

Calendar
Calendar measures a day, a month and an year. In other words we can say that calendar is the measurement of a year.
If clock decides our 24 h daily routine, then calendar decides our 365 days of a year. Geographically clocks work on rotation of Earth whereas calendar works on revolution of Earth around Sun. A year has 365 days and 6 h.
So, after every 4 yr these extra 6 h converts into a day which is called a leap year. In questions, asked on the basis of calendar mainly based on odd days concept.
So, first of all understand what a odd days is and how we count this.
Here, in a year of 365 days, there is 1 odd day.
As, 365/52=7-Quotient,Remainder-1 day
As, a year contains 52 weeks.
But for a leap year, odd days = 2
As, a leap year has 365 days.

Odd Days
We are supposed to find the day of the week on a given date. For this, we use the concept of ‘odd days’. In a given period, the number of days more than the complete weeks are called odd days.

Leap Year
1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year and no other century is a leap year.
• A leap year has 366 days.

For An Ordinary Year
The year which is not a leap year is called an ordinary year. An ordinary year has 365 days.
Example If 18th February, 2005 falls on Friday, then what will be the day on 18th February, 2007? SSC (10 + 2) 2011
(a) Sunday
(b) Wednesday
(c) Tuesday
(d) Monday
Answer:
(a) According to the question,
18th February, 2005 = Friday
So, 18th February, 2006 = Friday + 1 day = Saturday
So, 18th February, 2007 = Saturday + 1 = Sunday
[2005, 2006, and 2007 are ordinary years]

Reference Corner

1.If January 1 is a Friday, what is the first day of the month of March in a leap year? SSC (10+2) 2013
(a) Tuesday
(b) Wednesday
(c) Thursday
(d) Friday
Answer:
(a) Total number of days from January 1 to March 1
= 31 + 29 + 1 = 61 days
February in a leap years = 29 days) =61 ÷ 7
= 8 weeks and 5 odd days
So, the fifth day from Friday = Tuesday

2.If the day before yesterday was Wednesday, when will Sunday be? SSC (10 + 2) 2013
(a) Today
(b) Tomorrow
(c) Day after tomorrow
(d) Two days after tomorrow
Answer:
(c) If the day before yesterday was Wednesday, then today will be Friday and the day after tomorrow will be Sunday.

Practice Exercise

1. How many times are the hands of a clock at right angles in a day?
(a) 22
(b) 44
(c) 11
(d) 24

2. How many times do the hands of, a clock point towards each other in a day?
(a) 11
(b) 48
(c) 24
(d) 22

3. At what time between 9 and 10 o’clock will the hands of a watch be together?
(a) 35 min past 9
(b) 49 1/11 min past 9
(c) 55 2/11 min past 9
(d) 45 1/11 min past 9

4. At what angle the hands of a clock are inclined at 30 min past 6?
(a) 45°
(b)15°
(c) 30°
(d)20°

5. What is the angle between the two hands of a clock, when the clock shows 5 h 30 min?
(a) 45°
(b) 30°
(c)60°
(d)15°

6. If the second day of a month is a Friday, which of the following would be the last day of the next month which has 31 days?
(a) Sunday
(b) Monday
(c) Tuesday
(d) Data inadequate

7. If 30th January, 2003 was Thursday, what was the day on 2nd March, 2003?
(a) Tuesday
(b) Thursday
(c) Saturday
(d) Sunday

8. Reaching the place of meeting 20 min before 8 : 50 h Suresh found himself 30 min earlier, than the man who came 40 min late. What was the scheduled time of the meeting?
(a) 8 : 00
(b) 8 : 05
(c) 8 : 10
(d) 8 : 20

9. The priest told the devotee, ‘The temple bell is rung at regular intervals of 45 min. The last bell was rung 5 min ago. The next bell is due to be rung at 7 : 45 am”. At what time did the priest give this information to the devotee?
(a) 7 : 40 am
(b) 7 : 05 am
(c) 7 : 00 am
(d) 6 : 55 am

10. If 18th February, 2005 falls on Friday, then what will be the day on 18th February, 2007?
(a) Sunday
(b) Monday
(c) Tuesday
(d) Wednesday

11. How many days will there be from 26th January, 2004 to 15th May, 2004 (both days included)?
(a) 110
(b) 111
(c) 112
(d) 113

12. Seema remembers that her father’s birthday was certainly after eighth but before thirteenth of December. Her sister Nirmala remembers that their father’s birthday was definitely after ninth but before fourteenth of December. On which date of December was their father’s birthday?
(a) 10th
(b) 11th
(c) 12th
(d) Data inadequate

13. Kishan remembers that his brother Dev’s birthday falls after 20th May but before 28th May, while Garima remembers that Dev’s birthday falls before 22nd May but after 12th May. On what date Dev’s birthday falls?
(a) 20th May
(b) 21st May
(c) 22nd May
(d) Cannot be determined

14. Ayush leaves his house at 20 min to seven in the morning, reaches Kapil’s house in 25 min, they finish their breakfast in another 15 min and leave for their office which takes another 35 min. At what time do they leave Kapil’s house to reach their office?
(a) 7 : 40 am
(b) 7 : 20 am
(c) 7 : 45 am
(d) 8 : 15 am

15. If 3rd December, 2000 was Sunday, what day was 3rd January, 2001?
(a) Tuesday
(b) Wednesday
(c) Thursday
(d) Friday

Answers

Hints & Solutions

Non-Verbal
(i) Water & Mirror Images

Question asked from this topic refers to the water and mirror image of an object. The question asked in examination mainly divided in two parts, in first part there is a figure which is knows as question figure and in second part there are four figures, from that four figures one belongs to the water or mirror image of the question figure, known as answer figure.

Mirror Image
The figure obtained by putting a mirror in front of the real figure is known as mirror image or we can say that the reflection of an object into a mirror is called mirror image.
In the mirror image of an object the lower and upper parts are constant while LHS and RHS get interchanged, means left part of an object becomes right part and right part becomes the left part. Left hand side w Right hand side

Example Which of the answer figure is exactly the mirror image of the given figure, when the mirror is held on the line AB? ssc (10+2) 2011

Water Image
The reflection of an object into the water is called its water image. It is obtained by inverting an object vertically. The water image of the figure looks like the mirror image of the figure when the mirror is placed horizontally at the bottom of the question figure. The candidate is required to determine how the image of an object would look like in water when it is placed near a water source.

Example Find the water image of the object given in the question figure denoted by (A), out of the figures given in the answer choices, (a), (b), (c) and (d).

Reference Corner

1. Find out the mirror image of the given figure. SSC (10+2)2014

Answer:
(d)

2. If a mirror is placed on the line MN, then which of the answer words is the right image of the given word? SSC (10+2) 2013

Answer:
(a)

Practice Exercise

Directions (Q. NOS. 1-6) In each of the following questions, choose the correct mirror image of the figure given from amongst the four alternatives (a), (b), (c) and (d) given along with it.

Directions (Q.NOS. 7-9) In each of the following questions. Questions figure is followed by four other figures a, b, c, and d. Showing the possible water images of question figure. Choose the correct water image of the question figure out of given four alternatives.

Directions (Q. NOS. 10-12) In each of the following questions, four alternative are given, which follow the word number marked as question. You have to select one alternative, which exactly matches with the mirror image of the word/number in the question.

Directions (Q. NOS. 13-15) In each of the following questions, a word/group of letters or numbers or both is followed by four alternatives a, b, c and d showing possible water image of that word/group of letters or numbers or both. One, out of these four alternatives, is the exact water image of that word/group of letters or numbers or both. Chooses from the alternatives is the correct water image of that word/group of letters or numbers or both.

Answers

(ii) Counting of Figures

Counting of figures is the realisation of simple geometrical plane figures from a complex figure. It is designed to test the analytical ability and logical approach of a candidate. The figures which are asked for counting can be a straight line, triangle, square, rectangle, polygon etc.
To find the accurate answer for these question, firstly, a candidate needs to find the required figures formed by individual section of the given figure, then the figure formed by combination of two figure and so on.
Such type of questions are designed to test the analytical and logical approach of a candidate.

Example How many triangles are there in the given question figure? ssc(1o+2) 2012

(a) 6
(b)7
(c) 8
(d) 9
Answer:

Reference Corner

1. How many rectangles are there in the given figure?

(a)6
(b)7
(c)8
(d)9
Answer:

Practice Exercise

1. How many squares are there in the figure given below?

(a) 4
(b) 5
(c) 6
(d) 7

2. How many triangles are there in the following figures?

(a) 16
(b) 12
(c) 10
(d) 8

3. Total number of squares in the following figures are ?

(a) 6
(b) 8
(c) 5
(d) 10

4. How many triangles are there in the following figure?

(a)29
(b)27
(c)23
(d)30

5.What is the number of straight lines in the following figure?

(a)11
(b)14
(c)16
(d)17

6. How many triangles are there in the following figure?

(a) 6
(b) 10
(c) 8
(d) 12

7. How many triangles are there in the following figure?

(a) 18
(b) 28
(c) 20
(d) 24

8. How many triangles are there in the following figure?

(a)16
(b)15
(c)9
(d)7

9.How many circles are there in this figure ?

(a)21
(b)19
(c)18
(d)17

Answers

Hints & Solutions

(iii) Figure Formation

The process of formation of a defined geometrical figure with the use of pieces of different design is known as formation of figure.
Formation of figures deals with the problems related to the formation of geometrical figures like triangle, square, circle, etc., by joining some pieces out of a group of pieces of different designs. Some questions are asked in which the question figure contains some figures which can be joined together to obtain one of the alternative answer figures and one has to find out the correct alternative. Besides this, there are questions in which one question figure is given and we have to find out the correct answer figure in which all the pieces which are required to form the question figure are present.
In such questions, a question figure is given followed by four answer choices. The candidate is required to select the correct figure out of the given answer choice figures.
For better understanding, example is given below

Example Find the figure given in the answer choices, that can form the questions figure.

Reference Corner

Directions (Q.Nos.1 and 2) In each of the following questions, find out which of the answer figures (a), (b), (c) and (d) can be formed from the pieces given in figure (X).

1.

Practice Exercise

Directions (Q. NOS.1 -8) In each of the following questions, find out which of the answer figures (a), (b), (c) and (d) can be formed

Answers

SSC CHSL Topic Wise Study Material – General Intelligence – Social Intelligence

SSC CHSL Study MaterialSSC CHSL Previous PapersSSC CHSL Practice Workbook

Blood relations means any relation between two or more persons which is acquired by them by the virtue of their birth.
Blood relationship is defined as the social relationship among the members of the family.The relationship can be divided into two main categories.
(1) Maternal
(2) Paternal
Relations on the mother’s side are called maternal, while the relations on the father’s side are called paternal.
To solve these types of questions, one needs to know all the human relationship.

Some Important Blood Relations

Generally, the questions based on blood relation deal with the hierarchical structure of the family (i.e., seven generations of the family) which is generally three generation above and three generation below the current generation.

Different relationships between the family members of different generations are given below

For differentiating a male and a female, we use (+) symbol for ‘male’ and (-) symbol for ‘female’.
Types of questions covered in this chapter are as follows:
• Blood Relations Based on Conversation.
• Blood Relations Based on Puzzle.
• Symbolically Coded Blood Relationship.

Blood Relations Based on Conversation.
In this type, a person gives information to another person either about a particular person in a photograph or a person present in front of him. Using this information, it is required to establish a relationship between a given person and the person in the photograph/the person about which the information is provided.
Example Pointing to a girl in a bus, a man tells his friend, “She is the daughter of the only son of my father’s wife”. How is the girl related to the man? ssc (to+2) 2011
(a) Cousin
(b) Daughter
(c) Mother
(d) Sister

Blood Relations Based on Puzzle
In this type, more than one information in the form of some puzzle is given and based on the information, it is required to deduce the relation between the two individuals which it asked.
Example Kannan is the brother of Kumar. Lakshmi is the daughter of Kumar. Kalai is sister of Kannan and Govind is the brother of Lakshmi. Who is the uncle of Govind? ssc (1o+2) 2012
(a) Kumar
(b) Kalai
(c) Lakshmi
(d) Kannan

Symbolically Coded Blood Relationship
In this type, certain symbols and codes such as +, -,x, ÷, $, ©, @ etc, are used to represent the information in coded form and it is required to decode the information with the help of symbols to be used for making family diagram and then find out the relationship between the persons asked in the question.
Directions Read the following information carefully and answer the question that follows.
(i) ‘A + B’ means ‘A is the son of B’.
(ii) ‘A – B’ means ‘A is the wife of B’.
(iii) ‘A x B’ means ‘A is the brother of B’.
(iv) ‘A ÷ B’ means ‘A is the mother of B’.
(v) ‘A = B’ means ‘A is the sister of B’.

Example What does ‘P x R ÷ Q’ mean?
(a) P is the nephew of Q
(b) P is the daughter of Q
(c) P is the brother of Q
(d) P is the niece of Q

Example What does T = R ÷ Q mean?
(a) P is the aunt of Q
(b) Q is the uncle of P
(c) P is the sister of Q
(d) Q is the niece of P

Reference Corner

1. Deepak has a brother named Aditya. Deepak is the son of Kuldeep. Bunty is Kuldeep’s father. How is Aditya related to Bunty? SSC (10+2) 2017
(a) Uncle
(b) Brother
(c) Grandson
(d) Grandfather
Answer:

2. Karan has a brother Prem and sister Neesha. Karan’s wife is Naj and has a-daughter Naksha. Naksha got married with Neesha’s son Akbar and has a baby girl Riya. What is relation between Naksha and Neesha? SSC (10+2) 2015
(a) Mother and daughter
(b) Sister
(c) Niece and aunt
(d) Mother and granddaughter
Answer:

3. A is B’s sister. C is B’s mother. D is C’s father. E is D’s mother. Then, how is A related to D? SSC (10+2) 2014
(a) Daughter
(b) Granddaughter
(c) Grandmother
(d) Grandfather
Answer:

Practice Exercise

1.D’s father’s mother’s son’s wife is related to D as
(a) Grandmother
(b) Mother
(c) Aunt
(d) Cannot be determined

2.P’s father’s father is the husband of Q’s mother’s mother. How is P related to Q?
(a) Cousin
(b) Sister
(c) Brother
(d) Cannot be determined

3.A, B and C are sisters, D is the brother of E and E is the daughter of B. How is A related to D?
(a) Sister
(b) Cousin
(c) Niece
(d) Aunt

4.Read the information and answer the question
I. F is the brother of A.
II. C is the daughter of A.
III. K is the sister of F.
IV. G is the brother of C.
Who is the uncle of G?
(a) A
(b) C
(c) F
(d) K

5.Pointing to Neeraj, Kavita said, “His mother’s brother is the father of my son Pramod.”How is Neeraj related to Kavita?
(a) Niece
(b) Nephew
(c) Sister-in-law
(d) None of these

6.Pointing towards a female in the picture, Arti said “She is the mother of Preeti, whose father is my son.” How is Arti related to that female in the picture?
(a) Aunt
(b) Mother
(c) Data inadequate
(d) None of these

7.Pointing towards a person, a man said to a woman, “His mother is the only daughter of your father.” How is the woman related to that person?
(a) Daughter
(b) Sister
(c) Mother
(d) Wife

8.Pragya is the niece of Abhi. Abhi’s mother is Neha, Komal is Neha’s mother. Komal’s husband is Narayan. Rakhee is the mother-in-law of Narayan. How is Pragya related to Narayan?
(a) Daughter
(b) Great granddaughter
(c) Grand niece
(d) Great grandson’s daughter

9.If ‘A $ B’ means ‘A is the father of B’, ‘A ★ B’ means ‘A is the mother of B’, ‘A @ B’ means ‘ A is the wife of B’, then which of the following means ‘M’ is the grandmother of N?
(a) M ★ T $ N @ R
(b) M ★ T $ R @ N
(c) M ★ R $ T @ N
(d) M ★ R @ T @ N

Directions (Q. NOS. 10 and 11) Read the following information carefully and answer the questions that follow.
(i) ‘P x Q’ means ‘P is mother of Q’.
(ii) ‘P + Q’ means ‘P is sister of Q’.
(iii) T + Q’ means ‘P is brother of Q’.
(iv) ‘P – Q’ means ‘P is father of Q’.

10.Which of the following means ‘K is son of R’?
(a)RxK
(b)R-K
(c) K + T x R
(d) R – J÷K + M

11.Which of the following means ‘M is paternal uncle of T?
(a) M + J – T
(b) M + J x T
(c) M ÷J – T
(d) M + J + T

Directions (Q. Nos. 12-14) Read the following information carefully and answer the questions that follow.
(i) ‘A + B’ means ‘A is father of B’.
(ii) ‘A x B’ means ’A is daughter of B’.
(iii) ‘A ÷ B’ means ‘A is brother of B’.
(iv) ‘A – B’ means ‘A is wife of B’.

12. In ‘ L – M+ K ÷ F ’, how is ‘F’ related to ‘L’?
(a) Son
(b) Daughter
(c) Nephew
(d) Cannot be determined

13. Which of the following expressions means ‘J’ is son of ‘D’?
(a)D + L x H ÷ J
(b)J ÷ P x D
(c) J ÷ P – D
(d) T – D + J

14. In ‘H+ K x R ’, how if ‘R’ related to ‘H*?
(a) Husband
(b) Brother
(c) Wife
(d) Mother

Directions (Q. NOS. 15-19) Read the following information carefully and answer the questions that follow.

All the six members of a family A, B, C, D, E and F are travelling together. B is the son of C but C is not the mother of B, A and C are a married couple. E is the brother of C, D is the daughter of A, F is the brother of B.

15. How many male members are there in the family?
(a) 1
(b) 2
(c) 3
(d) 4

16. Who is the mother of B?
(a)D
(b) F
(c) E
(d) A

17. How many children does A have?
(a) One
(b) Two
(c) Three
(d) Four

18. Who is the wife of E?
(a) A
(b) F
(c) B
(d) Cannot be determined

19. Which of the following is a pair of females?
(a) AE
(b) BD
(c) DF
(d) AD

Answers

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