20 Cool Facts about Maths

1. The word “hundred” comes from the old Norse term, “hundrath”, which actually means 120 and not 100.

2. In a room of 23 people there’s a 50% chance that two people have the same birthday.

3. Most mathematical symbols weren’t invented until the 16th century. Before that, equations were written in words.

4. “Forty” is the only number that is spelt with letters arranged in alphabetical order.

5. Conversely, “one” is the only number that is spelt with letters arranged in descending order.

6. From 0 to 1000, the only number that has the letter “a” in it is “one thousand”.

7. ‘Four’ is the only number in the English language that is spelt with the same number of letters as the number itself.

8. Every odd number has an “e” in it.

9. The reason Americans call mathematics “math”, is because they argue that “mathematics” functions as a singular noun so ‘math’ should be singular too.

10. Markings on animal bones indicate that humans have been doing maths since around 30,000BC.

11. “Eleven plus two” is an anagram of “twelve plus one” which is pretty fitting as the answer to both equations is 13.

12. Also, there are 13 letters in both “eleven plus two” and “twelve plus one”.

13. Zero is not represented in Roman numerals.

14. The word “mathematics” only appears in one Shakespearean play, “The Taming of the Shrew”.

15. -40 °C is equal to -40 °F.

16. In France, a pie chart is sometimes referred to as a “camembert”.

17. The symbol for division (i.e.÷) is called an obelus.

18. 2 and 5 are the only prime numbers that end in 2 or 5.

19. A ‘jiffy’ is an actual unit of time. It means 1/100th of a second.

20. If you shuffle a deck of cards properly, it’s more than likely that the exact order of the cards you get has never been seen before in the whole history of the universe.

 

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Objective Questions 2

1- A line which cuts a pair of parallel lines is called

(A) tangent

(B) chord

(C) traversal

(D) intersector

 

2-An angle whose value is ____, is called complete angle.

(A) 180°

(B) 240°

(C) 360°

(D) none of the above

 

3-The areas of two similar triangles are 81 sq. cm and 49 sq. cm. Find the ratio of their corresponding heights.

(A) 9:7

(B) 7:9

(C) 6:5

(D) 81:49

 

4-Consider ΔABD such that angle ADB = 20° and C is a point on BD such that AB=AC and CD=CA. Then the measure of angle ABC is

(A) 30°

(B) 40°

(C) 45°

(D) 60°

 

5-If the length and breadth of a rectangle are increased by a% and b% respectively, then the area will be increased by

(A) (a-b+2ab/100)%

(B) (a+b+2ab/100)%

(C) (a+b+ab/100)%

(D) (a-b+ab/100)%

 

 

6-A, B and C can complete a piece of work in 14, 6 and 12 days respectively. Working together, they will complete the work in

(A) 19/9 days

(B) 27 days

(C) 28/9 days

(D) 25/8 days

 

7-If Px = Qy = Rz  and Q/P = R/Q, then 2z/(x+z) = ?

(A) y/z

(B) y/x

(C) x/y

(D) z/y

 

8-A shopkeeper purchases 15 mangoes for Rs. 10 and sells them at 10 mangoes for Rs. 15. Thus, he earns a profit of

(A) 50%

(B) 75%

(C) 80%

(D) 125%

 

9-   4950/6 + 112 x 1.75 = ? x 2

(A) 510.5

(B) 505.2

(C) 515.5

(D) none of the above

 

10-If a certain sum of money can become 5 times of its principal in 10 years, then the rate of interest is

(A) 20%

(B) 30%

(C) 40%

(D) 50%

 

11-An amount of Rs. 10,000 becomes Rs. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest?

(A) 25%

(B) 20%

(C) 40%

(D) 30%

 

ANSWERS:

1-(C), 2-(C), 3-(A), 4-(B), 5-(C), 6-(C), 7-(B), 8-(D), 9-(A), 10-(C), 11-(C)

12-What will come in the place of question mark (?) in the following series?

2, 5, 7, 12, 19, 31, 50, ?

(A) 81

(B) 74

(C) 69

(D) none of the above

 

13-In an equilateral triangle has the height of 12 cm then what is the area of the triangle?

(A) 42√3 c.c.

(B) 48√3 c.c.

(C) 24√3 c.c.

(D) 34√3 c.c.

 

14-The monthly income and monthly expenditure ratio of A and B are 5:6 and 4:5 respectively. If both of them can have Rs. 500 as monthly savings, then what is the income of A?

(A) Rs. 3,000

(B) Rs, 500

(C) Rs. 5,000

(D) Rs. 2,500

 

15-Find out the least number which when multiplied by 45, the result becomes a perfect square.

(A) 9

(B) 15

(C) 5

(D) None of the above

 

16-   (175)2 – (75)2 = ?

(A) 5000

(B) 20000

(C) 25000

(D) None of the above

17-If a = (√3+1)/(√3-1) and b = (√3-1)/(√3+1) then (a²+ab+b²)/(a²-ab+b²) = ?

(A) 15/11

(B) 17/11

(C) 19/11

(D) 1

 

18- If the fractions 3/5, 2/3, ¼, 5/7 and 6/11 are arranged in ascending order of their values, then which one will be the fourth

(A) 3/5

(B) 1/4

(C) 5/7

(D) 2/3

 

19- 1 hectare = ?

(A) 1000 m²

(B) 10000 m²

(C) 100000 m²

(D) None of the above

 

20-The sum of two numbers is 24 and the sum of their squares is 386, then one number is

(A) 17

(B) 19

(C) 9

(D) 11

 

21- A wheel rotates 15 times each minute. How many degrees will it rotate in 12 seconds of time?

(A) 360°

(B) 720°

(C) 1080°

(D) None of the above

 

22-If f(n) = n^5 – n, n ϵ N, then f(n) is divisible by

(A) 25

(B) 30

(C) 35

(D) 32

 

ANSWERS:

12-(A), 13-(C), 14-(D), 15-(C), 16-(C), 17-(D), 18-(D), 19-(B), 20-(B), 21-(C), 22-(B)

23-If “+” means “-“, “-“ means “x” means “/” and “/” means “+”, then

2 – 50 + 40 x 10 / 4 = ?

(A) 104

(B) 100

(C) 98

(D) 110

 

24-In the below series, which number comes next?

1, 3, 7, 15, 31, 63, ?

(A) 120

(B) 126

(C) 127

(D) 94

 

25-A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

(A) 230 m

(B) 240 m

(C) 260 m

(D) 270 m

 

26-The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

(A) 15

(B) 16

(C) 18

(D) 25

 

27-By what least number, 432/625 be divided to get a perfect cube?

(A) 4/5

(B) 6/5

(C) 5/6

(D) 2/5

 

28-The difference between two positive numbers is 3 and the sum of their squares is 369. Then the sum of the numbers is

 

(A) 33

(B) 20

(C) 81

(D) 27

 

29-A reduction of 20% in the price of sugar enables a purchaser to obtain 3 kg more for Rs. 120. The original price of sugar per kg is

(A) Rs. 15

(B) Rs. 12

(C) Rs. 8

(D) Rs. 10

 

30-The average of the first five multiples of 3 is

(A) 3

(B) 9

(C) 12

(D) 15

 

31-A reduction in the price of apples enables a person to purchase 3 apples for Re. 1 instead of Rs. 1.25. The percent reduction in price is

(A) 20%

(B) 25%

(C) 30%

(D) 35%

 

32-If a+b:b+c:c+a = 6:7:8 and a+b+c = 14, then value of ‘c’ is

(A) 6

(B) 7

(C) 8

(D) 14

 

33-If two numbers are in the ratio of 5:8 and if 9 is added to each, the ratio becomes 8:11. Find the sum of the numbers.

(A) 39

(B) 49

(C) 64

(D) 19

 

ANSWERS:

23-(B), 24-(C), 25-(D), 26-(B), 27-(D), 28-(D), 29-(D), 30-(B), 31-(A), 32-(A), 33-(A)

34-If √5 = 2.24 and √6 = 2.45, then the value of (√2/√3)+(√5/√6)=

 

(A) 1.37

(B) 1.57

(C) 1.73

(D) 1.75

 

35-(16)0.16x(16)0.04x(2)0.2 is equal to

(A) 1

(B) 2

(C) 4

(D) 16

 

36-If 257.5 x 52.5 / 1251.5 = 5x, then the value of ‘x’ is

(A) 16

(B) 17.5

(C) 8.5

(D) 13

 

37-The value of [(1/5)/(1/5) of 1/5]/[(1/5) of (1/5) / (1/5)] is

(A) 1

(B) 25

(C) 1/25

(D) 125

 

38-A fraction is such that if the numerator is multiplied by 3 and denominator is reduced by 3, we get 18/11, but if the numerator is increased by 8 and the denominator is doubled, we get 2/5. Then the fraction is

(A) 8/15

(B) 12/25

(C) 11/21

(D) 9/28

 

39-If two numbers are in the ratio of 5:8 and 9 is added to each, the ratio becomes 8:11. Find the sum of the numbers.

(A) 39

(B) 49

(C) 64

(D) 19

 

40-On selling a pen for Rs. 18, a man loses 1/10 of its cost price. The cost price of the pen is

(A) Rs. 16.20

(B) Rs. 19.80

(C) Rs. 20

(D) Rs. 25

 

 

41-Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is

(A) 15

(B) 16

(C) 18

(D) 25

 

42-56 men can complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work?

(A) 18

(B) 32

(C) 98

(D) 48

 

43-A train running at 36 km/h takes 10 s to pass a telegraph pole. How long would it take to cross a platform 110m long?

(A) 24 s

(B) 31 s

(C) 21 s

(D) 33 s

 

44-The perimeter of a rectangle is 28 m, whereas its area is 48 m2. What is the length of its diagonal?

(A) 5 m

(B) 10 m

(C) 12 m

(D) 12.5 m

 

45-The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. The area of the rectangle is

(A) 16 cm2

(B) 14 cm2

(C) 12 cm2

(D) 10 cm2

 

46-A hall, 20 m long and 15 m broad, is surrounded by a verandah of uniform width of 2.5 m. The cost of flooring the verandah at Rs. 3.50 per square metre is

(A) Rs. 500

(B) Rs. 600

(C) Rs. 700

(D) Rs. 800

 

ANSWERS:

34-(C), 35-(B), 36-(D), 37-(A), 38-(B), 39-(A), 40-(C), 41-(B), 42-(B), 43-(C), 44-(B), 45-(C), 46-(C)

1.   If a solid, cone of base radius ‘r’ and height ‘h’ is placed over a solid cylinder having same base radius ‘r’ and height – ‘h’ as that of the cone, then the curved surface area of the shape is  Is it true?

         (a) No

(b) Yes

         (c) May be

(d) Cannot be determined

2.   A cylinder and a cone are of the same base radius and same height. Find the ratio of the volumes of the cylinder of that of the cone.

         (a) 1 : 3

(b) 1 : 2

(c) 3 : 1

(d) 2 : 1

3.   In the figure, the shape of a solid copper piece (made of two pieces) with dimensions as shown. The face ABCDEFA has uniform cross section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece.

         (a) 840 cm

(b) 880 cm3

(c) 876 cm3

(d) 890 cm3

4.   A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

         (a) 465

(b) 912

(c) 769

(d) 858

5.   What is the area of a semi–circle of radius 5 cm?

         (a) 78.57 cm

(b) 71.42 cm

(c) 63.18 cm

(d) 79.86 cm

Answers

Objective Questions

Question 1. The average of first 50 natural numbers is …………. .  A. 25.30  B. 25.5  C. 25.00  D. 12.25 Question 2. A fraction which bears the same ratio to 1/27 as 3/11 bear to 5/9 is equal to ……….. .  A. 1/55  B. 55  C. 3/11  D. 1/11 Question 3. The number of 3-digit numbers divisible by 6, is ………….. .  A. 149  B. 166  C. 150  D. 151 Question 4. What is 1004 divided by 2?  A. 52  B. 502  C. 520  D. 5002 Question 5. A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?  A. 78  B. 136  C. 156  D. 196 Question 6. 125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content be raised to 25%?  A. 15/2 gallons.  B. 17/2 gallons.  C. 19/2 gallons.  D. 81/3 gallons. Question 7. 106 × 106 – 94 × 94 = ?  A. 2004  B. 2400  C. 1904  D. 1906 Question 8. Which of the following numbers gives 240 when added to its own square?  A. 15  B. 16  C. 18  D. 20 Question 9. Evaluation of 83 × 82 × 8-5 is …………. .  A. 1  B. 0  C. 8  D. None of these. Question 10. The simplest form of 1.5 : 2.5 is …………… .  A. 6 : 10  B. 15 : 25  C. 0.75 : 1.25  D. 3 : 5

Permutation And Combination

Questions for practice:

(Choose correct one)

1. Out of 7 consonants and 4 vowels, how many words

of 3 consonants and 2 vowels can be formed?

A. 24400.                  B. 21300

C. 210                        D. 25200

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2. In a group of 6 boys and 4 girls, four children are to

be selected. In how many different ways can they be

selected such that at least one boy should be there?

A. 159.                          B. 209

C. 201.                          D. 212

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3. From a group of 7 men and 6 women, five persons

are to be selected to form a committee so that at least 3

men are there in the committee. In how many ways can

it be done?

A. 624                             B. 702

C. 756.                            D. 812

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4. In how many different ways can the letters of the

word 'OPTICAL' be arranged so that the vowels always

come together?

A. 610                             B. 720

C. 825                             D. 920

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5. In how many different ways can the letters of the

word 'CORPORATION' be arranged so that the vowels

always come together?

A. 47200                          B. 48000

C. 42000                          D. 50400

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6. In how many ways can a group of 5 men and 2

women be made out of a total of 7 men and 3 women?

A. 1                             B. 126

C. 63                           D. 64

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7. In how many different ways can the letters of the

word 'MATHEMATICS' be arranged such that the

vowels must always come together?

A. 9800                             B. 100020

C. 120960                         D. 140020

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8. There are 8 men and 10 women and you need to

form a committee of 5 men and 6 women. In how many

ways can the committee be formed?

A. 10420                             B. 11

C. 11760                             D. None of these

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9. How many 3-letter words with or without meaning,

can be formed out of the letters of the word,

'LOGARITHMS', if repetition of letters is not allowed?

A. 720                                            B. 420

C. None of these                          D. 5040

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10. In how many different ways can the letters of the

word 'LEADING' be arranged such that the vowels

should always come together?

A. None of these.                          B. 720

C. 420                                              D. 122

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11. A coin is tossed 3 times. Find out the number of

possible outcomes.

A. None of these                          B. 8

C. 2                                                 D. 1

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12. In how many different ways can the letters of the

word 'DETAIL' be arranged such that the vowels must

occupy only the odd positions?

A. None of these                          B. 64

C. 120                                            D. 36

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13. A bag contains 2 white balls, 3 black balls and 4 red

balls. In how many ways can 3 balls be drawn from the

bag, if at least one black ball is to be included in the

draw?

A. 64                                                 B. 128

C. 32                                                 D. None of these

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14. In how many different ways can the letters of the

word 'JUDGE' be arranged such that the vowels always

come together?

A. None of these                          B. 48

C. 32                                               D. 64

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15. In how many ways can the letters of the word

'LEADER' be arranged?

A. None of these                          B. 120

C. 360                                             D. 720

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16. How many words can be formed by using all letters

of the word 'BIHAR'?

A. 720                                                  B. 24

C. 120                                                  D. 60

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17. How many arrangements can be made out of the

letters of the word 'ENGINEERING' ?

A. 924000                                           B. 277200

C. None of these                                D. 182000

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18. How many 3 digit numbers can be formed from the

digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and

none of the digits is repeated?

A. 20                                             B. 16

C. 8                                                D. 24

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19. How many words with or without meaning, can be

formed by using all the letters of the word, 'DELHI'

using each letter exactly once?

A. 720                                             B. 24

C. None of these                           D. 120

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20. What is the value of P(100,2) ?

A. 9801 B. 12000

C. 5600 D. 9900

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21. In how many different ways can the letters of the

word 'RUMOUR' be arranged?

A. None of these                                             B. 128

C. 360                                                               D. 180

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22. There are 6 periods in each working day of a school.

In how many ways can one organize 5 subjects such

that each subject is allowed at least one period?

A. 3200                                             B. None of these

C. 1800                                             D. 3600

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23. How many 6 digit telephone numbers can be

formed if each number starts with 35 and no digit

appears more than once?

A. 720                                             B. 360

C. 1420                                           D. 1680

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24. An event manager has ten patterns of chairs and

eight patterns of tables. In how many ways can he

make a pair of table and chair?

A. 100                                             B. 80

C. 110                                             D. 64

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25. 25 buses are running between two places P and Q. In

how many ways can a person go from P to Q and return

by a different bus?

A. None of these                                     B. 600

C. 576                                                       D. 625

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26. A box contains 4 red, 3 white and 2 blue balls. Three

balls are drawn at random. Find out the number of

ways of selecting the balls of different colours?

A. 62                                             B. 48

C. 12                                             D. 24

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27. A question paper has two parts P and Q, each

containing 10 questions. If a student needs to choose 8

from part P and 4 from part Q, in how many ways can

he do that?

A. None of these                                     B. 6020

C. 1200                                                     D. 9450

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28. In how many different ways can 5 girls and 5 boys

form a circle such that the boys and the girls alternate?

A. 2880                                             B. 1400

C. 1200                                             D. 3212

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29. Find out the number of ways in which 6 rings of

different types can be worn in 3 fingers?

A. 120                                             B. 720

C. 125                                             D. 729

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30. In how many ways can 5 man draw water from 5

taps if no tap can be used more than once?

A. None of these                                       B. 720

C. 60                                                            D. 120

.