text:
Edugross

# Class 6 Maths MCQ

###### Chapter 1 – Knowing Our Numbers Class 6 MCQs Questions with Answers

Question 1.
The greatest of the numbers
123, 27, 650, 2342, 40000 is
(a) 40000
(b) 2342
(c) 27
(d) 650

Question 2.
The greatest of the numbers
1000, 10000, 10, 1000000, 100000 is
(a) 1000000
(b) 100000
(c) 10000
(d) 1000

Question 3.
The smallest of the numbers
1000, 50000, 111, 3222, 225 is
(a) 111
(b) 225
(c) 1000
(d) 3222

Question 4.
The smallest of the numbers
2325, 2352, 2235, 2253, 2523, 2532 is
(a) 2235
(b) 2253
(c) 2325
(d) 2532

Question 5.
Using the digits 1, 2, 3, 4 without repetition, the greatest 4-digit number that can be made is
(a) 4321
(b) 4312
(c) 4213
(d) 4231

Question 6.
Using the digits 1, 5, 7, 2 without repetition, the greatest 4-digit number that can be made is
(a) 7521
(b) 7512
(c) 7215
(d) 7251

Question 7.
Using the digits 3, 5, 7, 0 without repetition the greatest 4-digit number that can be made is
(a) 7530
(b) 7503
(c) 7350
(d) 7305

Question 8.
The smallest 4-digit number that can be made using the digits 1,8,5,3 without repetition is
(a) 1583
(b) 1538
(c) 1385
(d) 1358

Question 9.
The smallest 4-digit number that can be made using the digits 5,3,6,4 without repetition is
(a) 3546
(b) 3564
(c) 3456
(d) 3465

Question 10.
The smallest 4-digit number that can be made using the digits 6, 5, 0, 4 without repetition is
(a) 4560
(b) 4056
(c) 4065
(d) 4506

Question 11.
Make the greatest 4-digit number by using any one digit of 2. 6. 5 twice.
(a) 6652
(b) 6625
(c) 6256
(d) 6265

Question 12.
Make the greatest 4-digit number by using any one digit of 0, 3, 6 twice.
(a) 6630
(b) 6603
(c) 6360
(d) 6306

Question 13.
Make the smallest 4-digit number by using any one digit of 4,3,2 twice.
(a) 2234
(b) 2243
(c) 2432
(d) 2324

Question 14.
Make the smallest 4-digit number by using any one digit of 7, 0, 6 twice.
(a) 6007
(b) 6070
(c) 6700
(d) None of these

Question 15.
Take two digits, say 1 and 2. Make the greatest 4-digit number using both the digits equal number of times.
(a) 1122
(b) 2112
(c) 2121
(d) 2211

Question 16.
Take two digits, say 3 and 4. Make the smallest 4-digit number using both the digits equal number of times.
(a) 3344
(b) 4433
(c) 4343
(d) 4334

Question 17.
Take two digits 0 and 1. Make the greatest 4-digit number using both the digits equal number of times.
(a) 1100
(b) 1001
(c) 1010
(d) None of these

Question 18.
Take two digits, 0 and 1. Make the smallest 4-digit number using both the digits equal number of times.
(a) 1001
(b) 1010
(c) 1100
(d) None of these

Question 19.
Make the greatest 4-digit number using any four different digits with the condition that 5 is at ones place.
(a) 9875
(b) 9857
(c) 9758
(d) 9785

Question 20.
Make the smallest four-digit number using any four different digits such that 5 is at ones place,
(a) 1025
(b) 1205
(c) 1250
(d) None of these

Question 21.
Arrange the following numbers in ascending
order: 132,2000,7500,525.
(а) 7500,2000,525,132
(b) 132,525,2000,7500
(c) 132,525,7500,2000
(d) 7500,2000,132,525

Question 22.
Arrange the following numbers in descending
order: 4000,8500,50600,7235.
(а) 50600,8500,7235,4000
(b) 50600,8500,4000,7235
(c) 50600,7235,8500,4000
(d) 50600,7235,4000,8500

Question 23.
The greatest 2-digit number is
(a) 98
(b) 99
(c) 79
(d) 89

Question 24.
The smallest 2-digit number is
(a) 31
(b) 21
(c) 11
(d) 10

Question 25.
The greatest 3-digit number is
(a) 991
(b) 997
(c) 999
(d) 998

Question 26.
The smallest 3-digit number is
(a) 100
(b) 101
(c) 111
(d) none of these

Question 27.
The greatest 4-digit number is
(a) 8888
(b) 6789
(c) 9876
(d) 9999

Question 28.
The smallest 4-digit number is
(a) 1001
(b) 1000
(c) 1111
(d) 9999

Question 29.
Which of the following numbers comes next to 999?
(a) 100
(b) 998
(c) 1000
(d) None of these

Question 30.
Which of the following numbers comes just before 1000?
(a) 999
(b) 1001
(c) 990
(d) 909

Question 31.
Which of the following numbers is equal to 1 lakh?
(a) 100000
(b) 10000
(c) 1000
(d) 100

Question 32.
Which of the following numbers is equal to 1 crore ?
(a) 10000000
(b) 1000000
(c) 100000
(d) 10000

Question 33.
1 million = how many lakh?
(a) 10
(b) 100
(c) 1000
(d) 10000

Question 34.
1 crore = how many million?
(a) 10000
(b) 1000
(c) 100
(d) 10

Question 35.
1 billion = how many million?
(a) 10
(b) 100
(c) 1000
(d) 10000

Question 36.
1 lakh = how many ten thousand?
(a) 1
(b) 10
(c) 100
(d) 1000

Question 37.
1 million = how many hundred thousand?
(a) 10
(b) 100
(c) 1
(d) None of these

Question 38.
1 crore = how many ten lakhs?
(a) 100
(b) 1
(c) 10
(d) None of these

Question 39.
Insert comma suitably in 67810138 by using International System.
(a) 67,810,138
(b) 67,81,01,38
(c) 6,78,10,138
(d) 678,10,138

Question 40.
1 centimetre =? millimetres
(a) 10
(b) 100
(c) 1000
(d) none of these

Question 41.
1 metre =? centimetres
(a) 10
(b) 100
(c) 1000
(d) none of these

Question 42.
1 metre =? millimetres
(a) 10
(b) 100
(c) 1000
(d) none of these

Question 43.
1 Kilometre =? metres
(a) 1000
(b) 10
(c) 100
(d) none of these

Question 44.
1 km = ? mm
(a) 10,00,000
(b) 1,00,000
(c) 10,000
(d) 1000

Question 45.
49 to the nearest tens is
(a) 50
(b) 40
(c) 45
(d) 55

Question 46.
123 to the nearest tens is
(a) 130
(b) 120
(c) 125
(d) 123

Question 47.
Which of the following rounding off is correct?
(a) 841 → 800
(b) 286 → 200
(c) 9870 → 9800
(d) 87 → 80

Question 48.
In Roman numerals L stands for
(a) 100
(b) 50
(c) 70
(d) 90

Question 49.
In Roman numerals C stands for
(a) 10
(b) 100
(c) 1000
(d) 1

Question 50.
In Raman numerals D stands for
(a) 100
(b) 1000
(c) 500
(d) 10

Question 51.
In Raman numerals M stands for
(a) 1000
(b) 100
(c) 10
(d) none of these

Question 52.
60 in Roman numerals is
(a) LX
(b) LXX
(c) LXXX
(d) XL

Question 53.
80 in Roman numerals is
(a) LXXX
(b) LXX
(c) LX
(d) XXXL

Question 54.
90 in Roman numerals is
(a) XL
(d) XC
(c) CX
(d) LX

Question 55.
I made an expenditure of ₹ 2725 in November, 2009 and of ₹ 2275 in December, 2009. What is the total expenditure made by me in November, 2009 and December, 2009 together?
(a) ₹ 2000
(b) ₹ 3000
(c) ₹ 4000
(d) ₹ 5000

Hint:
Total expenditure = 2725 + 2275 = 5000

Question 56.
The difference between the greatest number of 4-digit and the smallest number of 5-digit is
(a) 1
(b) 10
(c) 100
(d) 11

Hint:
Difference = 10,000 – 9999 = 1

Question 57.
The monthly salary of Apala is ₹ 20975 and that of Meenu is ₹ 15875. The difference of their monthly salaries is
(a) ₹ 6000
(b) ₹ 4900
(c) ₹ 5000
(d) ₹ 5100

Hint:
Difference = 20975 – 15875 = 5100

Question 58.
To stitch a trouser 1 m 25 cm cloth is required. Out of 10 m cloth, how many trousers can be stitched?
(a) 2
(b) 4
(c) 6
(d) 8

Hint:
1 m 25 cm = 125 cm
10m = 1000cm
1000 ÷ 125 = 8

Question 59.
Manish multiplied 100 by 89 instead of multiplying by 79. How much was his answer greater than the correct answer?
(a) 100
(b) 1000
(c) 10000
(d) None of these

Hint:
100 × 89 = 8900
100 × 79 = 7900
8900 – 7900 = 1000

Question 60.
Sangeeta types 25 pages per day. How many pages will she type in the month of November ?
(a) 900
(b) 800
(c) 700
(d) 750

Hint:
Number of days in
November, 2009 = 30
25 × 30 = 750

###### Chapter 2 – Whole Numbers Class 6 MCQs Questions with Answers

Question 1.
The successor of 99 is
(a) 99
(b) 98
(c) 100
(d) none of these

Question 2.
The predecessor of 100 is
(a) 101
(b) 100
(c) 99
(d) none of these

Question 3.
The successor of 27 is
(a) 26
(b) 25
(c) 24
(d) 28

Question 4.
The predecessor of 36 is
(a) 34
(b) 35
(c) 33
(d) 37

Question 5.
The natural number that has no predecessor is
(a) 1
(b) 10
(c) 100
(d) 1000

Question 6.
The difference between the successor of a number and the number it self is
(a) 0
(b) – 1
(c) 1
(d) none of these

Question 7.
The difference between the predecessor of a number and the number it self is
(a) 1
(b) -1
(c) 2
(d) -2

Question 8.
The difference between the successor and the predecessor of a number is
(a) 1
(b) 2
(c) -1
(d) -2

Question 9.
To find the predecessor of a number, we have to subtract from the number itself.
(a) 1
(b) 2
(c) 3
(d) 4

Question 10.
To find the successor of a number, we have to add the number itself.
(a) 4
(b) 3
(c) 2
(d) 1

Question 11.
The smallest whole number is
(a) 0
(b) 1
(c) -1
(d) none of these

Question 12.
Which of the following statement is true?
(а) All natural numbers are also whole numbers.
(b) All whole numbers are also natural numbers.
(c) There is no smallest whole number.
(d) The greatest whole number is 100

Question 13.
Which of the following is true?
(a) 210 > 201
(b) 210 < 201
(c) 210 = 201
(d) none of these

Question 14.
Which of the following statement is true?
(a) 1 is the smallest natural number.
(b) 50 is the predecessor of 49.
(c) 1 is the smallest whole number.
(d) 599 is the successor of 600

Question 15.
Which of the following statement is true?
(a) The whole number 0 has no predecessor.
(b) There are 10 whole numbers between 11 to 21.
(c) The successor of a two digit number is always a two digit number.
(d) The predecessor of a two digit number is never a single digit number

Question 16.
How many natural numbers are there between 1 and 10?
(a) 6
(b) 7
(c) 8
(d) 9

Question 17.
Find 27 ÷ (9 ÷ 3).
(a) 3
(b) 6
(c) 9
(d) 27

Question 18.
Find (24 ÷ 4) – 2.
(a) 1
(b) 3
(c) 4
(d) 2

Question 19.
Which of the following will not represent zero?
(a) 0 + 1
(b) 0 × 0
(c) $$\frac { 0 }{ 2 }$$
(d) $$\frac { 2-2 }{ 2 }$$

Question 20.
1 ÷ 0 =
(a) 1
(b) 0
(c) 2
(d) not defined

Question 21.
‘Whole numbers are closed under addition and multiplication.’ This property is known as
(a) closure property
(b) commutativity of addition and multiplication
(c) associativity of addition and multiplication
(d) distributivity of multiplication over addition

Question 22.
‘3 + 5 = 5 + 3’
The above is known as
(a) closure property
(c) commutativity of multiplication
(d) none of these

Question 23.
‘3 × 5 = 5 × 3’
The above is known as
(a) closure property
(c) commutativity of multiplication
(d) none of these

Question 24.
‘(1 + 2) + 3 = 1 + (2 + 3)’
The above is known as
(c) commutativity of multiplication
(d) associativity of multiplication

Question 25.
‘(2 × 3) × 4 = 2 × (3 × 4)’
The above is known as
(c) commutativity of multiplication
(d) associativity of multiplication

Question 26.
‘2 × (3 + 4) = (2 × 3) + (2 × 4)’
The above is known as
(a) distributivity of multiplication over addition
(c) associativity of multiplication
(d) none of these

Question 27.
I purchased 10 litres of milk in the morning and 5 litres of milk in the evening. If the milk costs ₹ 30 per litre, how much money will I have to pay to the milkman?
(a) ₹ 450
(b) ₹ 300
(c) ₹ 150
(d) none of these

Hint:
Required money = (10 + 5) 30 =10 × 30 + 5 × 30 = 300 + 150 = 450.

Question 28.
Which of the following is true?
(a) The number 2 can be arranged as a line.
(b) The number 2 can be arranged as a square.
(c) The number 2 can be arranged as a triangle.
(d) The number 2 can be arranged as a rectangle

Question 29.
The number 5 can be arranged as a
(a) line
(b) rectangle
(c) square
(d) triangle

Question 30.
The number 6 cannot be shown as a
(a) square
(b) line
(c) rectangle
(d) triangle

Question 31.
The number 10 cannot be shown as a
(a) square
(b) rectangle
(c) line
(d) triangle

Question 32.
Which of the following numbers can be shown as square?
(a) 11
(b) 12
(c) 13
(d) 16

Question 33.
First triangular number is
(a) 3
(b) 6
(c) 10
(d) 15

Question 34.
Which of the following numbers cannot be shown by two rectangles?
(a) 12
(b) 16
(c) 18
(d) 15

Question 35.
Which of the following numbers is not a triangular number?
(a) 3
(b) 6
(c) 10
(d) 9

Question 36.
Which of the following numbers cannot be arranged as a rectangle?
(a) 4
(b) 6
(c) 8
(d) 7

###### Chapter 3 – Playing with Numbers Class 6 MCQs Questions with Answers

Question 1.
Which of the following numbers is not a factor of 68?
(a) 2
(b) 4
(c) 17
(d) 6

Question 2.
Which of tfie following numbers is not a factor of 36?
(a) 2
(b) 4
(c) 18
(d) 8

Question 3.
Which of the following numbers is not a factor of 24?
(a) 2
(b) 3
(c) 4
(d) 5

Question 4.
Which of the following numbers is not a factor of 15?
(a) 1
(b) 3
(c) 4
(d) 5

Question 5.
Which of the following number is not a factor of 21?
(a) 1
(b) 3
(c) 6
(d) 7

Question 6.
Which of the following number is not a multiple of 27?
(a) 1
(b) 3
(c) 9
(d) 6

Question 7.
Which of the following numbers is not a factor of 12?
(a) 4
(b) 2
(c) 3
(d) 8

Question 8.
Which of the following numbers is not a factor of 20?
(a) 2
(b) 4
(c) 5
(d) 6

Question 9.
Which of the following number is not a factor of 18?
(a) 2
(b) 3
(c) 6
(d) 8

Question 10.
Which of the following number is not a multiple of 6?
(a) 12
(b) 21
(c) 24
(d) 36

Question 11.
Which of the following number is not a multiple of 5?
(a) 15
(b) 20
(c) 30
(d) 33

Question 12.
Which of the following number is not a multiple of 9?
(a) 18
(b) 36
(c) 81
(d) 75

Question 13.
The smallest prime number is
(a) 1
(b) 2
(c) 3
(d) 4

Question 14.
The smallest composite number is
(a) 1
(b) 2
(c) 3
(d) 4

Question 15.
The prime number which is even, is
(a) 2
(b) 3
(c) 5
(d) 13

Question 16.
1 is
(a) a prime number
(b) a composite number
(c) neither prime nor composite
(d) an even number

Question 17.
The smallest odd number is
(a) 1
(b) 2
(c) 3
(d) 4

Question 18.
The smallest even number is
(a) 1
(b) 2
(c) 3
(d) 4

Question 19.
The least prime number between 1 and 10 is
(a) 2
(b) 5
(c) 3
(d) 7

Question 20.
The greatest prime number between 1 and 10 is
(a) 7
(b) 5
(c) 3
(d) 2

Question 21.
Which of the following numbers is prime?
(a) 21
(b) 12
(c) 17
(d) 39

Question 22.
Which of the following numbers is composite?
(a) 19
(b) 23
(c) 6
(d) 29

Question 23.
Which of the following statements is true?
(a) The product of two even numbers is always even.
(b) The sum of three odd numbers is even.
(c) All prime numbers are odd.
(d) Prime numbers do not have any factors.

Question 24.
Which of the following statements is false?
(a) All even numbers are composite numbers.
(b) If an even number is divided by 2, the quotient may be odd or even.
(c) The sum of two odd numbers and one even number is even.
(d) Sum of two prime numbers is not always even.

Question 25.
128 is divisible by
(a) 2
(b) 3
(c) 5
(d) 10

Question 26.
275 is divisible by
(a) 5
(b) 3
(c) 6
(d) 8

Question 27.
116 is divisible by
(a) 2
(b) 3
(c) 6
(d) 8

Question 28.
200 is divisible by
(a) 8
(b) 3
(c) 6
(d) 11

Question 29.
1331 is divisible by
(a) 11
(b) 2
(c) 3
(d) 5

Question 30.
1000 is divisible by
(a) 10
(b) 6
(c) 3
(d) 11

Question 31.
The greatest common factor of 8 and 20 is
(a) 2
(b) 1
(c) 4
(d) 8

Question 32.
The common factor of 9 and 15 is
(a) 3
(b) 6
(c) 9
(d) 15

Question 33.
The common factor of 4 and 15 is
(a) 1
(b) 2
(c) 3
(d) 5

Question 34.
Which of the following pairs of number are not co-prime?
(a) 7,15
(b) 12,49
(c) 18,23
(d) 12,21

Question 35.
Which of the following pairs of number are co-prime?
(a) 30,415
(b) 17, 68
(c) 16, 81
(d) 15, 100

Question 36.
The greatest common factor of 4, 8 and 12 is
(a) 2
(b) 1
(c) 4
(d) 8

Question 37.
The greatest common factor of 5, 15 and 25 is
(a) 1
(b) 5
(c) 10
(d) 15

Question 38.
The common factor of 3, 4 and 9 is
(a) 1
(b) 3
(c) 4
(d) 2

Question 39.
The greatest common factor of 75,60 and 210 is
(a) 1
(b) 3
(c) 5
(d) 15

Question 40.
The smallest common factor of 4, 12 and 16 is
(a) 1
(b) 2
(c) 4
(d) 8

Question 41.
The HCF of 8 and 12 is
(a) 1
(b) 2
(c) 3
(d) 4

Question 42.
The HCF of 24 and 36 is
(a) 3
(b) 6
(c) 12
(d) 24

Question 43.
The HCF of 27 and 63 is
(a) 3
(b) 6
(c) 9
(d) 18

Question 44.
The HCF of 36 and 84 is
(a) 3
(b) 4
(c) 6
(d) 12

Question 45.
The HCF of 30 and 42 is
(a) 2
(b) 3
(c) 5
(d) 6

Question 46.
The LCM of 5 and 20 is
(a) 5
(b) 10
(c) 15
(d) 20

Question 47.
The LCM of 6 and 18 is
(a) 6
(b) 12
(c) 18
(d) 36

Question 48.
The LCM of 12 and 48 is
(a) 6
(b) 12
(c) 24
(d) 48

Question 49.
The LCM of 9 and 45 is
(a) 3
(b) 9
(c) 5
(d) 45

Question 50.
The LCM of 5 and 6 is
(a) 10
(b) 20
(c) 30
(d) 60

###### Chapter 4 – Basic Geometrical Ideas Class 6 MCQs Questions with Answers

Question 1.
How many points are enough to fix a line?
(a) 1
(b) 2
(c) 3
(d) 4

Question 2.
Two intersecting lines intersect in
(a) 1 point
(b) 2 points
(c) 3 points
(d) 4 points

Question 3.
How many lines can pass through one given point?
(a) 1
(b) 2
(c) 4
(d) Countless

Question 4.
How many lines can pass through two given points?
(a) Only one
(b) 2
(c) 4
(d) Countless

Question 5.
How many vertices are there in the following figure?

(a) 5
(b) 3
(c) 2
(d) 4

Question 6.
How many sides are there in the following figure?

(a) 5
(b) 4
(c) 2
(d) 3

Question 7.
How many diagonals are there in the follow-ing figure?

(a) 4
(b) 5
(c) 2
(d) 3

Question 8.
How many vertices are there in a triangle?
(a) 1
(b) 2
(c) 3
(d) 4

Question 9.
How many sides are there in a triangle?
(a) 1
(b) 2
(c) 3
(d) 4

Question 10.
How many angles are there in a triangle?
(a) 1
(b) 2
(c) 3
(d) 4

Question 11.
How many vertices are there in a quadrilat¬eral?
(a) 1
(b) 2
(c) 3
(d) 4

Question 12.
How many sides are there in a quadrilateral?
(a) 1
(b) 2
(c) 3
(d) 4

Question 13.
How many angles are there in a quadrilateral?
(a) 1
(b) 2
(c) 3
(d) 4

Question 14.
(a) 1
(b) 2
(c) 3
(d) 4

Question 15.
How many pairs of opposite angles are there in a quadrilateral?
(a) 1
(b) 2
(c) 3
(d) 4

Question 16.
How many pairs of opposite sides are there in a quadrilateral?
(a) 1
(b) 2
(c) 3
(d) 4

Question 17.
(a) 1
(b) 2
(c) 3
(d) 4

Question 18.
Which of the following statements is false?
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.
(c) Every diameter of a circle is also a chord.
(d) Every chord of a circle is also a diameter.

###### Chapter 5 – Understanding Elementary Shapes Class 6 MCQs Questions with Answers

Question 1.
The angle measure for one complete revolution is
(a) 180°
(b) 360°
(c) 90°
(d) none of these.

Question 2.
The angle measure for half a revolution is
(a) 90°
(b) 180°
(c) 360°
(d) none of these.

Question 3.
The angle measure for one-fourth revolution is
(a) 90°
(b) 360°
(c) 180°
(d) none of these.

Question 4.
Through what angle measure does the hour hand of a clock turn through, when it goes from 3 to 9?
(a) 90°
(b) 360°
(c) 180°
(d) none of these.

Question 5.
Through what angle measure does the hour hand of a clock turn through, when it goes from 5 to 8?
(a) 90°
(b) 180°
(c) 360°
(d) none of these.

Question 6.
Through what angle measure does the hour hand of a clock turn through, when it goes from 12 to 9?
(a) 270°
(b) 180°
(c) 360°
(d) 90°.

Question 7.
Through what angle does the hour hand of a clock turn through, when it goes from 2 to 11?
(a) 270°
(b) 90°
(c) 360°
(d) 180°.

Question 8.
Through what angle does the hour hand of a clock turn through, when it goes from 6 to 3?
(a) 90°
(b) 180°
(c) 270°
(d) 360°.

Question 9.
What part of a revolution have you turned through if you stand facing north and turn clockwise to face west?
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 3 }{ 4 }$$
(d) none of these.

Question 10.
What part of a revolution have you turned through if you stand facing east and turn clockwise to face west?
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 3 }{ 4 }$$
(d) none of these.

Question 11.
What part of a revolution have you turned through, if you stand facing north and turn clockwise to face east?
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 3 }{ 4 }$$
(d) none of these

Question 12.
Find the number of right angles turned through by the hour hand of a clock when it goes from 12 to 3.
(a) 1
(b) 2
(c) 3
(d) 4.

Question 13.
Find the number of right angles turned through by the hour hand of a clock when it goes from 4 to 10.
(a) 1
(b) 2
(c) 3
(d) 4.

Question 14.
Find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 12.
(a) 1
(b) 2
(c) 3
(d) 4.

Question 15.
How many right angles do you make if you start facing north and turn clockwise to south?
(a) 1
(b) 2
(c) 3
(d) 4.

Question 16.
How many right angles do you make if you start facing east and turn clockwise to south?
(a) 1
(b) 2
(c) 3
(d) 4.

Question 17.
How many right angles do you make if you start facing south and turn clockwise to east?
(a) 1
(b) 2
(c) 3
(d) 4.

Question 18.
How many right angles do you make if you start facing east and turn clockwise to east?
(a) 1
(b) 2
(c) 3
(d) 4.

Question 19.
The measure of a right angle is
(a) 45°
(b) 90°
(c) 60°
(d) 180°.

Question 20.
The measure of a straight angle is
(a) 90°
(b) 45°
(c) 180°
(d) 60°.

Question 21.
The measure of an acute angle is
(a) < 90°
(b) > 90°
(c) = 90°
(d) none of these.

Question 22.
The measure of an obtuse angle is
(a) < 90°
(b) > 90° and < 180°
(c) = 90°
(d) none of these.

Question 23.
The measure of a reflex angle is
(a) 180°
(b) < 180°
(c) > 180°
(d) < 90°.

Question 24.
Which of the following angles is the measure of an acute angle?
(a) 30°
(b) 90°
(c) 120°
(d) 210°.

Question 25.
Which of the following angles is the measure of an obtuse angle?
(a) 120°
(b) 90°
(c) 60°
(d) 240°.

Question 26.
Which of the following angles is the measure of a reflex angle?
(a) 90°
(b) 180°
(c) 120°
(d) 270°.

Question 27.
A triangle having three unequal sides is called a
(a) scalene triangle
(b) isosceles triangle
(c) equilateral triangle
(d) right triangle.

Question 28.
A triangle having two equal sides is called
(a) a scalene triangle
(b) an isosceles triangle
(c) an equilateral triangle
(d) a right-angled triangle.

Question 29.
A triangle having three equal sides is called
(а) a scalene triangle
(b) an isosceles triangle
(c) an equilateral triangle
(d) a right triangle.

Question 30.
Which of the following statement is true?
(a) The opposite sides of a trapezium are par-allel.
(b) All the sides of a parallelogram are of equal in length.
(c) The diagonals of a square are perpendicular to each other.
(d) All the angles of a rectangle are not equal.

Question 31.
The following shape is of a

(a) cone
(b) cylinder
(c) sphere
(d) pyramid.

Question 32.
The shape is of

(a) cylinder
(b) cone
(c) sphere
(d) cuboid.

Question 33.

The shape is of
(a) cone
(b) cylinder
(c) cuboid
(d) sphere

Question 34.
The shape is of

(a) cuboid
(b) cylinder
(c) cone
(d) sphere

Question 35.
The shape is of

(a) cone
(b) cylinder
(c) sphere
(d) Pyramid

Question 36.
The shape is of

(a) triangular prism
(b) pyramid
(c) cuboid
(d) cylinder.

Question 37.
The number of faces of the shape is

(a) 2
(b) 4
(c) 5
(d) 3

Question 38.
The number of edges of the shape is

(a) 4
(b) 8
(c) 10
(d) 12

Question 39.
The number of corners of the shape is

(a) 8
(b) 6
(c) 5
(d) 3

Question 40.
The number of faces of the shape is

(a) 2
(b) 3
(c) 4
(d) 5

Question 41.
The number of edges of the shape is

(a) 6
(b) 8
(c) 9
(d) 4

Question 42.
The number of comers of the shape is

(a) 1
(b) 2
(c) 4
(d) 6

Question 43.
The number of faces of the shape is

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

Question 44.
The number of edges of the shape is

(a) 3
(b) 6
(c) 4
(d) 15

Question 45.
The number of vertices of the shape is

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

Question 46.
The number of faces of the shape is

(a) 2
(b) 4
(c) 3
(d) 6

Question 47.
The number of edges of the shape is

(a) 12
(b) 6
(c) 9
(d) 8

Question 48.
The number of vertices of the shape is

(a) 4
(b) 6
(c) 5
(d) 8

Question 49.
The number of vertices of a sphere is
(a) 0
(b) 1
(c) 2
(d) none of these.

Question 50.
The number of comers of a cylinder is
(a) 0
(b) 1
(c) 2
(d) none of these.

###### Chapter 6 – Integers Class 6 MCQs Questions with Answers

Question 1.
The succeeding number of the number 0 is
(a) –1
(b) 0
(c) 1
(d) 11.

Question 2.
The succeeding number of the number – 1 is
(a) –1
(b) 1
(c) 0
(d) -11.

Question 3.
The succeeding number of the number – 4 is
(a) -1
(b) -2
(c) -3
(d) -4

Question 4.
The succeeding number of the number 9 is
(a) 9
(b) 8
(c) 10
(d) 11.

Question 5.
The preceding number of the number 1 is
(a) 1
(b) -1
(c) 2
(d) 0.

Question 6.
The preceding number of the number 0 is
(a) 1
(b) -1
(c) 0
(d) none of these.

Question 7.
The preceding number of the number 2 is
(a) 3
(b) 1
(c) 0
(d) 4

Question 8.
The preceding number of the number 6 is
(a) 2
(b) 3
(c) 4
(d) 5

Question 9.
An integer between –3 and –1 is
(a) –3
(b) –1
(c) –2
(d) 0

Question 10.
Which of the following is true?
(a) 0 < –8
(b) 0 > –8
(c) 4 < –4
(d) 0 > 6.

Question 11.
Which of the following is false?
(a) -1 < –2
(b) 79 < 89
(c) –1 < 1
(d) 1 > 0.

Question 12.
Which of the following statements is true?
(a) Every positive integer is larger than every negative integer.
(b) Zero is greater than every positive integer.
(c) Zero is smaller than every negative integer.
(d) Farther a number from zero to the right, smaller is its value.

Question 13.
Which of the following statements, is false?
(a) Zero is neither a negative integer nor a positive integer.
(b) Zero is less than every positive integer.
(c) Zero is larger than every negative integer.
(d) Farther a number from zero on the left, larger is its value.

Question 14.
Which of the following statements, is true?
(a) Greatest negative integer is – 1.
(b) – 10 is to the right of – 8 on a number line.
(c) – 50 is to the left of – 100 on a number line.
(d) – 11 is larger than – 10.

Question 15.
(+1) + (+2) = ?
(a) +1
(b) +2
(c) +3
(d) –3

Question 16.
(-1) + (-2) = ?
(a) –1
(b) –2
(c) –3
(d) + 3

Question 17.
(- 2) + (+ 3) = ?
(a) – 2
(b) + 3
(c) + 1
(d) –1

Question 18.
(- 4) + (+ 3) = ?
(a) –1
(b) 1
(c) 0
(d) + 2.

Question 19.
(- 1) + (- 1) = ?
(a) – 1
(b) – 2
(c) 2
(d) 0

Question 20.
(- 1) + (+ 1 ) = ?
(a) –1
(b) +1
(c) 0
(d) none of these.

Question 21.
(-2) – (- 1) = ?
(a) –1
(d) 1
(c) 0
(d) –2

Question 22.
(-1) – (-2) = ?
(a) –1
(b) 1
(c) 0
(d) none of these.

Question 23.
(- 1) + ? = 0
(a) +1
(b) –1
(c) 0
(d) none of these.

Question 24.
10 + ? = 0
(a) –1
(b) –10
(c) 0
(d) 1

Question 25.
9 + (- 9) = ?
(a) 9
(b) -9
(c) 1
(d) 0

Question 26.
(- 1) + ? = – 2
(a) 1
(b) –1
(c) 0
(d) 2

Question 27.
? – 5 = –5
(a) 0
(b) 5
(c) -5
(d) 1

Question 28.
? – 4 = – 2
(a) 1
(b) 2
(c) 3
(d) 4.

Question 29.
2 – (- 1) – 2 – (- 3) =
(a) 0
(b) 1
(c) 2
(d) 3

Question 30.
2 – (- 1) – (- 2)
(a) 3
(b) 4
(c) 2
(d) 5

###### Chapter 7 – Fractions Class 6 MCQs Questions with Answers

Question 1.
The fraction representing the shaded portion is

(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 3 }{ 4 }$$
(c) $$\frac { 1 }{ 2 }$$
(d) $$\frac { 1 }{ 8 }$$

Question 2.
The fraction representing the shaded portion is

(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 1 }{ 3 }$$
(d) $$\frac { 1 }{ 8 }$$

Question 3.
The fraction representing the shaded portion is

(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 3 }{ 4 }$$
(d) none of these

Question 4.
The fraction representing the shaded portion is

(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 1 }{ 8 }$$
(d) none of these

Question 5.
The fraction representing the shaded portion is

(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 4 }$$
(c) $$\frac { 1 }{ 3 }$$
(d) $$\frac { 1 }{ 6 }$$

Question 6.
What fraction of ₹ 1 is 50 paise?
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 4 }$$
(c) $$\frac { 1 }{ 8 }$$
(d) $$\frac { 1 }{ 10 }$$

Question 7.
What fraction of ₹ 1 is 25 paise?
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 4 }$$
(c) $$\frac { 1 }{ 8 }$$
(d) $$\frac { 1 }{ 10 }$$

Question 8.
What fraction of an hour is 30 minutes?
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 1 }{ 3 }$$
(d) $$\frac { 1 }{ 5 }$$

Question 9.
What fraction of a day is 12 hours?
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 4 }$$
(c) $$\frac { 1 }{ 3 }$$
(d) $$\frac { 1 }{ 6 }$$

Question 10.
Which of the following is a proper fraction?
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 5 }{ 4 }$$
(c) $$\frac { 3 }{ 2 }$$
(d) $$\frac { 9 }{ 2 }$$

Question 11.
Which of the following is a proper fraction?
(a) $$\frac { 0 }{ 1 }$$
(b) $$\frac { 5 }{ 2 }$$
(c) $$\frac { 7 }{ 4 }$$
(d) $$\frac { 11 }{ 3 }$$

Question 12.
Which of the following is a proper fraction whose numerator is 1 and denominator is 3?
(a) $$\frac { 1 }{ 3 }$$
(b) $$\frac { 1 }{ 6 }$$
(c) $$\frac { 1 }{ 9 }$$
(d) $$\frac { 1 }{ 12 }$$

Question 13.
Which of the following is an improper fraction?
(a) $$\frac { 2 }{ 3 }$$
(b) $$\frac { 3 }{ 4 }$$
(c) $$\frac { 4 }{ 5 }$$
(d) $$\frac { 5 }{ 4 }$$

Question 14.
Which of the following is an improper fraction?
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 3 }{ 8 }$$
(c) $$\frac { 11 }{ 3 }$$
(d) $$\frac { 2 }{ 5 }$$

Question 15.
Express $$\frac { 5 }{ 2 }$$ as a mixed fraction.
(a) 1 $$\frac { 1 }{ 2 }$$
(b) 2 $$\frac { 1 }{ 2 }$$
(c) 3 $$\frac { 1 }{ 2 }$$
(d) 4 $$\frac { 1 }{ 2 }$$

Question 16.
Express $$\frac { 9 }{ 4 }$$ as a mixed fraction.
(a) 2 $$\frac { 1 }{ 4 }$$
(b) 3 $$\frac { 1 }{ 4 }$$
(c) 4 $$\frac { 1 }{ 4 }$$
(d) 5 $$\frac { 1 }{ 4 }$$

Question 17.
Express the mixed fraction 1$$\frac { 1 }{ 2 }$$ as an improper fraction.
(a) $$\frac { 2 }{ 3 }$$
(b) $$\frac { 3 }{ 2 }$$
(c) $$\frac { 3 }{ 4 }$$
(d) none of these

Question 18.
Express the mixed fraction 2 $$\frac { 3 }{ 4 }$$ as an improper fraction.
(a) $$\frac { 11 }{ 4 }$$
(b) $$\frac { 4 }{ 11 }$$
(c) $$\frac { 9 }{ 11 }$$
(d) $$\frac { 7 }{ 11 }$$

Question 19.
The simplest form of $$\frac { 12 }{ 20 }$$ is
(a) $$\frac { 1 }{ 5 }$$
(b) $$\frac { 2 }{ 5 }$$
(c) $$\frac { 3 }{ 5 }$$
(d) $$\frac { 4 }{ 5 }$$

Question 20.
The simplest form of $$\frac { 45 }{ 20 }$$ is
(a) $$\frac { 9 }{ 4 }$$
(b) $$\frac { 4 }{ 9 }$$
(c) $$\frac { 9 }{ 8 }$$
(d) $$\frac { 2 }{ 9 }$$

Question 21.
Which of the following fractions is not equivalent to $$\frac { 1 }{ 3 }$$ ?
(a) $$\frac { 5 }{ 15 }$$
(b) $$\frac { 6 }{ 18 }$$
(c) $$\frac { 4 }{ 12 }$$
(d) $$\frac { 7 }{ 20 }$$

Question 22.
Which of the following fractions is equivalent to $$\frac { 3 }{ 4 }$$?
(a) $$\frac { 6 }{ 11 }$$
(b) $$\frac { 9 }{ 10 }$$
(c) $$\frac { 15 }{ 20 }$$
(d) $$\frac { 21 }{ 25 }$$

Question 23.
The equivalent fraction of $$\frac { 2 }{ 5 }$$ with numerator 4 is
(a) $$\frac { 4 }{ 10 }$$
(b) $$\frac { 4 }{ 12 }$$
(c) $$\frac { 4 }{ 16 }$$
(d) $$\frac { 4 }{ 20 }$$

Question 24.
The equivalent fraction of $$\frac { 20 }{ 36 }$$ with denominator 9 is
(a) $$\frac { 4 }{ 9 }$$
(b) $$\frac { 5 }{ 9 }$$
(c) $$\frac { 7 }{ 9 }$$
(d) $$\frac { 8 }{ 9 }$$

Question 25.
Which of the following pairs of fractions are equivalent?
(a) $$\frac { 1 }{ 2 }$$ , $$\frac { 2 }{ 4 }$$
(b) $$\frac { 1 }{ 3 }$$ , $$\frac { 3 }{ 7 }$$
(c) $$\frac { 2 }{ 5 }$$ , $$\frac { 4 }{ 9 }$$
(d) $$\frac { 4 }{ 7 }$$ , $$\frac { 8 }{ 13 }$$

Question 26.
Which of the following pairs of fractions are not equivalent?
(a) $$\frac { 1 }{ 2 }$$ , $$\frac { 2 }{ 3 }$$
(b) $$\frac { 4 }{ 5 }$$ , $$\frac { 12 }{ 15 }$$
(c) $$\frac { 6 }{ 7 }$$ , $$\frac { 12 }{ 14 }$$
(d) $$\frac { 4 }{ 9 }$$ , $$\frac { 36 }{ 81 }$$

Question 27.
Which of the following pairs of fractions are like fractions?
(a) $$\frac { 1 }{ 5 }$$ , $$\frac { 4 }{ 5 }$$
(b) $$\frac { 2 }{ 3 }$$ , $$\frac { 3 }{ 4 }$$
(c) $$\frac { 4 }{ 5 }$$ , $$\frac { 5 }{ 6 }$$
(d) $$\frac { 5 }{ 6 }$$ , $$\frac { 6 }{ 7 }$$

Question 28.
Which of the following pairs of fractions are unlike fractions?
(a) $$\frac { 2 }{ 3 }$$ , $$\frac { 3 }{ 5 }$$
(b) $$\frac { 1 }{ 7 }$$ , $$\frac { 6 }{ 7 }$$
(c) $$\frac { 2 }{ 9 }$$ , $$\frac { 5 }{ 9 }$$
(d) $$\frac { 4 }{ 13 }$$ , $$\frac { 12 }{ 13 }$$

Question 29.
Apala typed 50 pages of a book containing 100 pages. Meenu typed 25 pages of the same book. Who typed more?
(a) Apala
(b) Meenu
(c) Both (a) and (b)
(d) none of these

Question 30.
$$\frac { 1 }{ 3 }$$ + $$\frac { 2 }{ 3 }$$ =
(a) 1
(b) 2
(c) 3
(d) none of these

Question 31.
$$\frac { 1 }{ 3 }$$ + $$\frac { 1 }{ 3 }$$ + $$\frac { 1 }{ 3 }$$ =
(a) 1
(b) 2
(c) 3
(d) none of these

Question 32.
$$\frac { 1 }{ 4 }$$ + $$\frac { 1 }{ 4 }$$ + $$\frac { 1 }{ 4 }$$ + $$\frac { 1 }{ 4 }$$ =
(a) 1
(b) 2
(c) 4
(d) 8

Question 33.
$$\frac { 5 }{ 4 }$$ – $$\frac { 1 }{ 4 }$$ =
(a) 1
(b) 4
(c) 5
(d) none of these

Question 34.
$$\frac { 8 }{ 10 }$$ – $$\frac { 3 }{ 10 }$$ =
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 5 }$$
(c) $$\frac { 1 }{ 10 }$$
(d) none of these

Question 35.
1 – $$\frac { 1 }{ 2 }$$ =
(a) $$\frac { 1 }{ 2 }$$
(b) 1
(c) – $$\frac { 1 }{ 2 }$$
(d) $$\frac { 1 }{ 4 }$$

Question 36.
$$\frac { 0 }{ 1 }$$ + $$\frac { 0 }{ 1 }$$ =
(a) 0
(b) 1
(c) -1
(d) 2

Question 37.
$$\frac { 8 }{ 15 }$$ – ? = $$\frac { 7 }{ 15 }$$
(a) $$\frac { 1 }{ 15 }$$
(b) $$\frac { 2 }{ 15 }$$
(c) $$\frac { 4 }{ 15 }$$
(d) $$\frac { 7 }{ 15 }$$

Question 38.
? – $$\frac { 1 }{ 4 }$$ = $$\frac { 1 }{ 4 }$$
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 3 }{ 4 }$$
(d) $$\frac { 5 }{ 4 }$$

Question 39.
? + $$\frac { 2 }{ 7 }$$ = $$\frac { 5 }{ 7 }$$
(a) $$\frac { 1 }{ 7 }$$
(b) $$\frac { 2 }{ 7 }$$
(c) $$\frac { 3 }{ 7 }$$
(d) $$\frac { 4 }{ 7 }$$

Question 40.
$$\frac { 25 }{ 7 }$$ – $$\frac { 15 }{ 5 }$$ =
(a) 1
(b) 2
(c) 5
(d) 3

Question 41.
$$\frac { 1 }{ 2 }$$ – $$\frac { 1 }{ 4 }$$ =
(a) $$\frac { 1 }{ 4 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 1 }{ 8 }$$
(d) $$\frac { 1 }{ 3 }$$

Question 42.
1 $$\frac { 1 }{ 2 }$$ + 2 $$\frac { 1 }{ 2 }$$ =
(a) 1
(b) 2
(c) 3
(d) 4

Question 43.
Apala bought 21/2 kg of potatoes whereas Meenu bought 11/2 kg of potatoes. Find the total amount of potatoes purchased by Apala and Meenu both.
(a) 1 kg
(b) 2 kg
(c) 3 kg
(d) 4 kg

Question 44.
A teacher finished $$\frac { 3 }{ 4 }$$ of his course. How much course is left?
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 4 }$$
(c) $$\frac { 1 }{ 6 }$$
(d) $$\frac { 1 }{ 3 }$$

Question 45.
Mamsh read $$\frac { 5 }{ 6 }$$ part of a book. Preeti read $$\frac { 1 }{ 6 }$$ part of that book. What more part was read by Manish?
(a) $$\frac { 2 }{ 3 }$$
(b) $$\frac { 1 }{ 6 }$$
(c) $$\frac { 5 }{ 6 }$$
(d) none of these

###### Chapter 8 – Decimals Class 6 MCQs Questions with Answers

Question 1.
3 – tenths =
(a) 0.3
(b) 0.03
(c) 0.003
(d) 0.0003.

Question 2.
Two tens and 2-tenths =
(a) 20.2
(b) 2.02
(c) 202
(d) none of these.

Question 3.
One hundred and 1 – one =
(a) 101
(b) 1.01
(c) 10.1
(d) 0.101.

Question 4.
Twelve point one =
(a) 12.1
(b) 12.01
(c) 1.21
(d) 0.121.

Question 5.
$$\frac { 2 }{ 10 }$$ =
(a) 0.2
(b) 0.02
(c) 0.002
(d) 0.0002

Question 6.
$$\frac { 12 }{ 10 }$$ =
(a) 0.12
(b) 1.2
(c) 1.02
(d) 1.002

Question 7.
$$\frac { 22 }{ 10 }$$ =
(a) 0.22
(b) 2.2
(c) 2.02
(d) 2.002

Question 8.
1 + $$\frac { 1 }{ 10 }$$ =
(a) 0.11
(b) 1.1
(c) 1.01
(d) 1.001

Question 9.
$$\frac { 5 }{ 2 }$$ =
(a) 0.5
(b) 0.2
(c) 2.5
(d) 0.25

Question 10.
$$\frac { 3 }{ 5 }$$ =
(a) 0.6
(b) 0.006
(c) 0.0006
(d) 0.06

Question 11.
2 $$\frac { 1 }{ 10 }$$ =
(a) 2.1
(b) 2.01
(c) 2.001
(d) 2.0002

Question 12.
$$\frac { 16 }{ 5 }$$ =
(a) 0.32
(b) 3.2
(c) 3.02
(d) 3.002

Question 13.
0.4 =
(a) $$\frac { 1 }{ 5 }$$
(b) $$\frac { 2 }{ 5 }$$
(c) $$\frac { 3 }{ 5 }$$
(d) $$\frac { 4 }{ 5 }$$

Question 14.
1.5 =
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 5 }{ 2 }$$
(c) $$\frac { 3 }{ 2 }$$
(d) $$\frac { 7 }{ 2 }$$

Question 15.
3.2 =
(a) $$\frac { 16 }{ 5 }$$
(b) $$\frac { 8 }{ 5 }$$
(c) $$\frac { 32 }{ 5 }$$
(d) $$\frac { 24 }{ 5 }$$

Question 16.
1.0 =
(a) $$\frac { 1 }{ 1 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { 2 }{ 4 }$$
(d) $$\frac { 3 }{ 9 }$$

Question 17.
1 mm=
(a) 0.1 cm
(b) 0.01 cm
(c) 0.001 cm
(d) 0.0001 cm.

Question 18.
10mm =
(a) 1.0 cm
(b) 0.1cm
(c) 0.01 cm
(d) 0.001 cm.

Question 19.
2 cm 2 mm =
(a) 2.2 cm
(b) 0.22 cm
(c) 2.1 cm
(d) 1.2 cm.

Question 20.
111 mm =
(a) 11.1 cm
(b) 1.11cm
(c) 0.111 cm
(d) 0.0111 cm.

Question 21.
Between which two whole numbers on the number line does the number 0.5 lie?
(a) 0 and 1
(b) 1 and 2
(c) 2 and 3
(d) – 1 and 0.

Question 22.
Between which two whole numbers on the number line does the number 3.3 lie?
(a) 0 and 1
(b) 1 and 2
(c) 2 and 3
(d) 3 and 4.

Question 23.
Between which two whole numbers on the number line does the number 5.3 lie?
(a) 1 and 2
(b) 2 and 3
(c) 3 and 4
(d) 5 and 6

Question 24.
0.02 =
(a) $$\frac { 1 }{ 25 }$$
(b) $$\frac { 1 }{ 50 }$$
(c) $$\frac { 1 }{ 100 }$$
(d) $$\frac { 1 }{ 10 }$$

Question 25.
1.44 =
(a) $$\frac { 36 }{ 25 }$$
(b) $$\frac { 72 }{ 25 }$$
(c) $$\frac { 36 }{ 50 }$$
(d) $$\frac { 72 }{ 100 }$$

Question 26.
10 + 2 + $$\frac { 1 }{ 10 }$$ + $$\frac { 2 }{ 100 }$$ =
(a) 12.12
(b) 12.21
(c) 11.11
(d) 21.12

Question 27.
111 + $$\frac { 1 }{ 100 }$$ =
(a) 111.01
(b) 111.1
(c) 111.001
(d) 111.0001

Question 28.
$$\frac { 2 }{ 10 }$$ + $$\frac { 3 }{ 100 }$$ + $$\frac { 4 }{ 1000 }$$ =
(a) 0.234
(b) 2.34
(c) 23.4
(d) 234

Question 29.
12 + $$\frac { 2 }{ 10 }$$ + $$\frac { 4 }{ 1000 }$$ =
(a) 12.204
(b) 12.204
(c) 12.402
(d) 12.240

Question 30.
0.005 =
(a) $$\frac { 1 }{ 2 }$$
(b) $$\frac { 1 }{ 20 }$$
(c) $$\frac { 1 }{ 200 }$$
(d) $$\frac { 1 }{ 2000 }$$

Question 31.
0.625 =
(a) $$\frac { 1 }{ 8 }$$
(b) $$\frac { 2 }{ 8 }$$
(c) $$\frac { 3 }{ 8 }$$
(d) $$\frac { 5 }{ 8 }$$

Question 32.
10 paise =
(a) 0.1 rupee
(b) 0.01 rupee
(c) 0.001 rupee
(d) 0.0001 rupee.

Question 33.
8cm =
(a) 0.8 m
(b) 0.08 m
(c) 0.008 m
(d) 0.0008 m.

Question 34.
40 mm=
(a) 4 cm
(b) 8 cm
(c) 0.4 cm
(d) 0.04 cm.

Question 35.
5m =
(a) 0.5 km
(b) 0.05 km
(c) 0.005 km
(d) 0.0005 km.

Question 36.
55 m=
(a) 0.055 km
(b) 0.35 km
(c) 0.0055 km
(d) 5.5 km.

Question 37.
5g =
(a) 0.005 kg
(b) 0.05 kg
(c) 0.5 kg
(d) none of these.

Question 38.
5 kg 5 g =
(a) 5.005 kg
(b) 5.05 kg
(c) 5.5 kg
(d) 0.55 kg.

Question 39.
12 kg 20 g =
(a) 12.02 kg
(b) 12.2 kg
(c) 12.002 kg
(d) 12.0002 kg.

Question 40.
1 kg 500 g =
(a) 1.5 kg
(b) 1.05 kg
(c) 1.005 kg
(d) 1.0005 kg.

###### Chapter 9 – Data Handling Class 6 MCQs Questions with Answers

Question 1.
The maximum marks obtained by any student is
(a) 95
(b) 78
(c) 75
(d) 25.

Question 2.
The minimum marks obtained by any student is
(a) 95
(b) 78
(c) 75
(d) 25.

Question 3.
How many students got the same marks?
(a) 2
(b) 3
(c) 4
(d) 5.

Hint:
62, 62

Question 4.
The difference between the maximum and mini¬mum marks obtained is
(a) 60
(b) 50
(c) 70
(d) 80.

Hint:
95 – 25 = 70

Question 5.
How many students got 75 or more marks?
(a) 1
(b) 2
(c) 3
(d) 4

Hint:
95, 78, 75

Question 6.
How many students got marks below 60?
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
55, 36, 42, 25

Question 7.
How many students got marks between 60 and 75?
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
62,62,73

Observe the following table and answer the related questions:

Question 8.
Which blood group is the most common?
(a) A
(b) B
(c) O
(d) AB.

Question 9.
Which blood group is the rarest?
(a) AE
(b) B
(c) A
(d) O.

Question 10.
What is the total number of students?
(a) 30
(b) 15
(c) 20
(d) 10.

Question 11.
The maximum frequency is
(a) 12
(b) 9
(c) 6
(d) 3.

Question 12.
The minimum frequency is
(a) 3
(b) 6
(c) 9
(d) 12

Question 13.
The difference between maximum and mini-mum frequency is
(a) 3
(b) 6
(c) 9
(d) 12.

Hint:
12 – 3 = 9

Question 14.
The ratio of the frequencies of blood groups AB and B is
(a) 1:2
(b) 1:3
(c) 2:3
(d) 3:4.

Hint:
3 : 6 = 1 : 2

Question 15.
The ratio of the frequencies of blood groups B and O is
(a) 1:3
(b) 2:3
(c) 3 :4
(d) 1:2.

Hint:
6 : 12 = 1 : 2

Observe the following pictograph and answer the related questions :

Question 16.
On which day were the maximum number of students present?
(a) Monday
(b) Thursday
(c) Tuesday
(d) Saturday.

Question 17.
On which day were the minimum number of students present?
(a) Friday
(b) Saturday
(c) Thursday
(d) Wednesday.

Question 18.
The number of students present on Friday is
(a) 10
(b) 20
(c) 40
(d) 50.

Question 19.
On how many days were more than 20 students present?
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
Monday, Tuesday, Wednesday, Thursday

Question 20.
On how many days were less than 20 students present?
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
Friday

Observe the following bar graph and answer the related questions:

Question 21.
Which political party won the maximum number of seats?
(a) A
(b) B
(c) C
(d) D.

Question 22.
Which political party won the minimum number of seats?
(a) A
(b) B
(c) D
(d) E.

Question 23.
Which two political parties won the same number of seats?
(a) C, D
(b) C, E
(c) D, E
(d) B, D.

Hint:
C → 20, D → 20

Question 24.
What is the difference between the maximum and minimum numbers of seats won?
(a) 10
(b) 20
(c) 30
(d) 40.

Hint:
40 – 10 = 30

Question 25.
How many parties won more than 20 seats?
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
A,B

Question 26.
How many parties won less than 60 seats?
(a) 2
(b) 3
(c) 5
(d) 4.

Hint:
A, B, C, D, E

Question 27.
What is the total number of seats won by party C and party D?
(a) 10
(b) 20
(c) 30
(d) 40.

Hint:
20 + 20 = 40

Observe the following bar graph and answer the related questions:

Question 28.
In which class is the number of student’s maxi¬mum?
(a) VI
(b) VIII
(c) IX
(d) X.

Question 29.
In which class/classes is the number of students minimum?
(a) IX, X
(b) VIII
(c) VI
(d) VII.

Question 30.
In which classes is the number of students are same?
(a) IX,X
(b) VI,VII
(c) VIII,IX
(d) VI,X.

Hint:
IX → 400
X → 400

Question 31.
In which class is the number of students 500?
(i) VIII
(ii) VII
(c) IX
(d) X.

Hint:
500 → VIII

Question 32.
What is the difference between the maximum and the minimum number of students?
(a) 100
(b) 200
(c) 300
(d) 400.

Hint:
700 – 400 = 300

Question 33.
In how many classes is the number of students are same?
(a) 2
(b) 3
(c) 4
(d) 5.

Hint:
IX, X

Question 34.
What is the difference between the number of students of class VI and class VII?
(a) 100
(b) 200
(c) 300
(d) 400.

Hint:
700 – 600 = 100

Question 35.
What is the total number of students?
(a) 2600
(b) 2000
(c) 3600
(d) 1600.

Hint:
700 + 600 + 500 + 400 + 400 = 2600

Question 36.
What is the ratio of the number of students of class X and class IX ?
(a) 1:1
(b) 1:2
(c) 2:1
(d) 1:4.

Hint:
400 : 400 = 1 : 1

###### Chapter 10 – Mensuration Class 6 MCQs Questions with Answers

Question 1.
Perimeter of a rectangle =
(c) 2 × (Length + Breadth)
(d) 2 × (Length × Breadth)

Question 2.
Perimeter of a square =
(a) 4 × Length of a side
(b) 2 × Length of a side
(c) 3 × Length of a side
(d) 6 × Length of a side

Question 3.
Perimeter of an equilateral triangle
(a) 2 × Length of a side
(b) 3 × Length of a side
(c) 4 × Length of a side
(d) 6 x Length of a side

Question 4.
Area of a rectangle =
(c) 2 × (Length + Breadth)
(d) 2 × (Length × Breadth)

Question 5.
Area of a square =
(a) side × side
(b) 4 × Length of a side
(c) 2 × Length of a side
(d) 6 × Length of a side

Question 6.
Perimeter of a regular pentagon =
(a) 4 × Length of a side
(b) 3 × Length of a side
(c) 6 × Length of a side
(d) 5 × Length of a side

Question 7.
Perimeter of a regular hexagon =
(a) 3 × Length of a side
(b) 4 × Length of a side
(c) 5 × Length of a side
(d) 6 × Length of a side

Question 8.
Apala went to a park 20 m long and 10 m wide. She took one complete round of it. The distance covered by her is
(a) 30 m
(b) 60 m
(c) 20 m
(d) 10 m

Hint:
Distance covered = 2(20 + 10) = 60 m

Question 9.
The perimeter of the figure is

(a) 12 m
(b) 14 m
(c) 24 m
(d) 7 m

Hint:
Perimeter = 2(4 + 3) = 14 m

Question 10.
The perimeter of the figure is

(a) 8 m
(b) 16 m
(c) 4 m
(d) none of these.

Hint:
Perimeter = 4 × 2 = 8 m

Question 11.
A page is 25 cm long and 20 cm wide. Find the perimeter of this page.
(a) 90 cm
(b) 45 cm
(c) 500 cm
(d) 5 cm

Hint:
Perimeter = 2(25 + 20) = 90 cm

Question 12.
The perimeter of the figure is

(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm

Hint:
Perimeter = 4(1 + 2 + 2) = 20 cm

Question 13.
The perimeter of the figure is

(a) 20 cm
(b) 10 cm
(c) 24 cm
(d) 15 cm

Hint:
Perimeter = 4 + 3 + 2 + 2 + 3 + 6 = 20 cm

Question 14.
Meenu wants to put a lace border all around a rectangle table cover 2 m long and 1 m wide. Find the length of the lace required by Meenu.
(a) 3 m
(b) 4 m
(c) 5 m
(d) 6 m

Hint:
Length of the lace = 2(2 + 1) = 6 m

Question 15.
Find the perimeter of a rectangle whose length and breadth are 9 cm and 1 cm respectively,
(a) 10 cm
(b) 20 cm
(c) 30 cm
(d) 40 cm

Hint:
Perimeter = 2(9 + 1) = 20 cm

Question 16.
An athlete takes 10 rounds of a rectangular park, 40 m long and 30 m wide. Find the total distance covered by him.
(a) 1400 m
(b) 700 m
(c) 70 m
(d) 2800 m

Hint:
Total distance covered = 10 × 2 × (40 + 30) = 1400 m

Question 17.
Find the cost of fencing a rectangular park of length 10 m and breadth 5 m at the rate of? 10 per metre.
(a) ₹ 300
(b) ₹ 600
(c) ₹ 150
(d) ₹ 1200

Hint:
Cost= 10 × 2 × (10 + 5) = ₹ 300

Question 18.
The perimeter of a square of side 1 m is
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 m

Hint:
Perimeter = 4 × 1 =4 m

Question 19.
The perimeter of an equilateral triangle of side 1 m is
(a) 1 m
(b) 2 m
(c) 3 m
(d) 6 m

Hint:
Perimeter = 3 × 1 = 3 m

Question 20.
The perimeter of a regular pentagon of side 1 m is
(a) 5 m
(b) 10 m
(c) 15 m
(d) 20 m

Hint:
Perimeter = 5 × 1 = 5 m

Question 21.
The perimeter of a regular hexagon of side 1 m is
(a) 3 m
(b) 2 m
(c) 4 m
(d) 6 m

Hint:
Perimeter = 6 × 1 = 6 m

Question 22.
Find the distance travelled by Sangeeta if she takes 5 rounds of a square park of side 10 m.
(a) 200 m
(b) 100 m
(c) 400 m
(d) 800 m

Hint:
Distance = 5 × 4 × 10 = 200 m

Question 23.
The perimeter of an equilateral triangle is 9 m. Find the length of the side.
(a) 1 m
(b) 2 m
(c) 3 m
(d) 9 m

Hint:
Length of side = $$\frac { 9 }{ 3 }$$ = 3 m

Question 24.
The perimeter of a square is 8 m. Find the length of the side.
(a) 1 m
(b) 2 m
(c) 4 m
(d) 8 m

Hint:
Length of side = $$\frac { 8 }{ 4 }$$ = 2 m

Question 25.
The perimeter of a regular pentagon is 10 m. Find the length of the side.
(a) 1 m
(b) 2 m
(c) 5 m
(d) 10 m

Hint:
Length of side = $$\frac { 10 }{ 5 }$$ = 2 m

Question 26.
The perimeter of a regular hexagon is 12 m. Find the length of the side.
(a) 2 m
(b) 3 m
(c) 4 m
(d) 6 m

Hint:
Length of side = $$\frac { 12 }{ 6 }$$ = 2 m

Question 27.
The perimeter of the figure is

(a) 12 cm
(b) 7 cm
(c) 6 cm
(d) 24 cm

Hint:
Perimeter = 4 + 3 + 3 + 2 = 12 cm

Question 28.
The perimeter of the figure is

(a) 15 cm
(b) 30 cm
(c) 7.5 cm
(d) 20 cm

Hint:
Perimeter = 4 + 3 + 5 + 3 = 15 cm

Question 29.
The perimeter of the figure is

(a) 8 cm
(b) 12 cm
(c) 15 cm
(d) 16 cm

Hint:
Perimeter = 5 + 3 – 5 – 3 = 16 cm

Question 30.
The perimeter of the figure is

(a) 10 cm
(b) 20 cm
(c) 15 cm
(d) 50 cm

Hint:
Perimeter = 5 × 2 = 10 cm

Question 31.
The perimeter of a triangle of sides 2 cm, 3 cm and 4 cm is
(a) 9 cm
(b) 18 cm
(c) 27 cm
(d) 36 cm

Hint:
Perimeter = 2 – 3 – 4 = 9 cm

Question 32.
Two sides of a triangle are 5 cm and 4 cm. The perimeter of the triangle is 12 cm. The third side has length
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 6 cm

Hint:
Third side = 12 – (5 + 4) = 3 cm

Question 33.
A rectangular piece of land measures 0.5 km by 0.25 km. Each side is to be fenced with 4 rounds of wire. What is the length of the wire needed?
(a) 2 km
(b) 3 km
(c) 4 km
(d) 6 km

Hint:
Length of wire = 4 × 2 × (0.5 + 0.25) = 6 km.

Question 34.
The area of a rectangle of length 2 cm and breadth 1 cm is
(a) 1 cm2
(b) 2 cm2
(c) 4 cm2
(d) 8 cm2

Hint:
Area = 2 × 1 = 2 cm2

Question 35.
The area of a square of side 1 cm is
(a) 1 cm2
(b) 4 cm2
(c) 9 cm2
(d) 16 cm2

Hint:
Area = 1 × 1 = 1 cm2

Question 36.
The area of a rectangular sheet of paper is 20 cm2. Its length is 5 cm. Find its width.
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

Hint:
Width = $$\frac { 20 }{ 5 }$$ = 4 cm

Question 37.
The perimeter of a rectangular piece of card board is 6 m. Its breadth is 1 m. Find its length.
(a) 1 m
(b) 2 m
(c) 3 m
(d) 6 m

Hint:
Length = $$\frac { 6 }{ 2 }$$ – 1 = 2 m

Question 38.
The area of the figure is

(a) 1 sq. unit
(b) 5 sq. unit
(c) 4 sq. unit
(d) 6 sq. unit

Hint:
Area = 5 × 1 × 1 = 5

Question 39.
The area of the figure in (sq. unit) is

(a) 1
(b) 5
(c) 4
(d) 6

Hint:
Area = 2 × 1 + 2 × 1 + 1 × 1 =5

Question 40.
The area of the figure is

(a) 5 sq. unit
(b) 9 sq. unit
(c) 7 sq. unit
(d) 8 sq. unit

Hint:
Area = 3 × $$\frac { 1 }{ 2 }$$ + 1 × 2 + 3 × $$\frac { 1 }{ 2 }$$ = 5.

###### Chapter 11 – Algebra Class 6 MCQs Questions with Answers

Question 1.
The rule, which gives the number of matchsticks required to make the matchstick pattern L, is
(a) 2 n
(b) 3 n
(c) 4n
(d) 5 n

Question 2.
The rule, which gives the number of matchsticks required to make the matchstick pattern C, is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 3.
The rule, which gives the number of matchsticks required to make the matchstick pattern F, is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 4.
The rule, which gives the number of matchsticks required to make the matchstick pattern U, is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 5.
The rule, which gives the number of matchsticks required to make the matchstick pattern V, is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 6.
The rule, which gives the number of matchsticks required to make the matchstick pattern A, is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 7.
The rule, which gives the number of matchsticks required to make the matchstick pattern [], is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 8.
The rule, which gives the number of matchsticks required to make the matchstick pattern ≅, is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 9.
The rule, which gives the number of matchsticks required to make the matchstick pattern E. is
(a) 2 n
(b) 3 n
(c) 4 n
(d) 5 n

Question 10.
The rule, which gives the number of matchsticks required to make the matchstick pattern A, is
(a) 3 n
(b) An
(c) 5 n
(d) 6 n

Question 11.
The rule, which gives the number of matchsticks required to make the matchstick pattern A, is
(a) 3 n
(b) 4 n
(c) 5 n
(d) 6 n

Question 12.
The rule, which gives the number of matchsticks required to make the matchstick pattern S, is
(a) 3 l
(b) 4 n
(c) 5 n
(d) 6 n

Question 13.
The side of a square is l. Its perimeter is
(a) 3l
(b) 2l
(c) 4l
(d) 6l

Question 14.
14. The side of an equilateral triangle is l. Its perimeter is
(a) l
(b) 2l
(c) 3l
(d) 6l

Question 15.
The side of a regular pentagon is l. Its perimeter is
(a) 3l
(b) 6l
(c) 4l
(d) 5l

Question 16.
The side of a regular hexagon is l. Its perimeter is
(a) l
(b) 2l
(c) 3l
(d) 6l

Question 17.
The length of an edge of a cube is l. The total length of its edges is
(a) 3l
(b) 4l
(c) 6l
(d) 12l

Question 18.
The radius of a circle is r. Its diameter is
(a) 2r
(b) 4r
(c) 3r
(d) 6r

Question 19.
Which of the following is an expression with numbers only?
(a) x + 1
(b) 2x
(c) 1 – x
(d) 3

Question 20.
Which of the following is an expression with numbers only?
(a) 2(4 – 3) + 5 × 6
(b) 2 × 3 – 4x
(c) 4 × 5 – 10 × 2 – 25 + x
(d) $$\frac { x }{ 8 }$$

Question 21.
Which of the following is not an expression with numbers only?
(a) 2 × (3 + 4)
(b) (2 + 3) × 4
(c) 2 × 3 + 4 × 5
(d) 2x + 1

Question 22.
The expression for ‘1 added top’ is
(a) P + 1
(b) p – 1
(c) 1 – p
(d) – 1 – P

Question 23.
The expression for ‘ 1 subtracted from p’ is
(a) p – 1
(b) p + 1
(c) 1 – p
(d) – 1 – p

Question 24.
The expression for ‘p multiplied by 2’ is
(a) p + 2
(b) P – 2
(c) $$\frac { p }{ 2 }$$
(d) 2p

Question 25.
The expression for ‘p divided by 2’ is
(a) $$\frac { p }{ 2 }$$
(b) 2p
(c) P + 2
(d) p – 2

Question 26.
The expression for ‘ 1 subtracted from -p’ is
(a) -P-1
(b) p – 1
(c) 1 – p
(d) 1 + p

Question 27.
The expression for ‘ 1 added to -p’ is
(a) – p + 1
(b) – p – 1
(c) p + 1
(d) p – 1

Question 28.
The expression for ‘p multiplied by – 2’ is
(a) -2p
(b) – $$\frac { p }{ 2 }$$
(c) p – 2
(d) – p – 2

Question 29.
The expression for ‘ -p multiplied by 2’ is
(a) -2p
(b) – $$\frac { p }{ 2 }$$
(c) p – 2
(d) – p – 2

Question 30.
The expression for’ -p divided by 2’ is
(a) – $$\frac { p }{ 2 }$$
(b) -2p
(c) -p + 2
(d) – p – 2

Question 31.
The expression for ‘ 1 added to 2p’ is
(a) 2p + 1
(b) 2p – 1
(c) 1 – 2p
(d) – 1 – 2p

Question 32.
The expression for ‘ 1 subtracted from 2p’ is
(a) 2p – 1
(b) 2p + 1
(c) 1 – 2p
(d) -2p -1

Question 33.
The expression for added’ is ‘ 2 times x to which 1 is
(a) 2x + 1
(b) x + 2
(c) 1 – 2x
(d) 2x – 1

Question 34.
The expression for ‘2 times x from which 1 is subtracted’ is
(a) 2x – 1
(b) 2x + 1
(c) x – 2
(d) x + 2

Question 35.
The expression for ‘x is divided by 2 and the result is added to 1’ is
(a) 1 + $$\frac { x }{ 2 }$$
(b) 1 – $$\frac { x }{ 2 }$$
(c) 2 + x
(d) 2 – x

Question 36.
The expression for ‘x is divided by – 2 and the result is added to 1’ is
(a) 1 – $$\frac { x }{ 2 }$$
(b) 1 + $$\frac { x }{ 2 }$$
(c) $$\frac { x }{ 2 }$$ – 1
(d) – 1 – $$\frac { x }{ 2 }$$

Question 37.
If Apala’s present age is x years, what will be her age in years after 20 years from now?
(a) x + 20
(b) x – 20
(c) $$\frac { x }{ 20 }$$
(d) 20x

Question 38.
If Meenu’s present age is x years, what was her age in years, 10 years back?
(a) x – 10
(b) 10 – x
(c) – x – 10
(d) 10x

Question 39.
If the age of Hari Kishan is two times the age of Manish (which is x years), then the age of Hari Kishan, in years, is
(a) $$\frac { x }{ 2 }$$
(b) 2x
(c) x + 2
(d) x – 2

Question 40.
The salary of Hari Kishan is two times the salary of Manish (which in Rs. x), then the salary of Hari Kishan, in rupees, is
(a) 2x
(b) $$\frac { x }{ 2 }$$
(c) x + 2
(d) x – 2

Question 41.
Which of the following is an equation in a variable?
(a) $$\frac { 10 }{ 2 }$$ = 5
(b) 2 × 3 + 2 × 1 = 8
(c) 2 × 4 = 8
(d) 3p = 12

Question 42.
Which of the following is an equation in a variable?
(a) 2 < 10
(b) 3 > 12
(c) x – 1 =0
(d) 2 + 3 = 3 + 2

Question 43.
Solve: p + 1 = 2
(a) 1
(b) 2
(c) -1
(d) -2

Hint:
p + 1 = 2 ⇒ p = 2 – 1 = 1

Question 44.
Solve : m – 2 = 3
(a) 2
(b) 3
(c) 5
(d) 1

Hint:
m – 2 = 3 ⇒ m = 3 + 2 = 5

Question 45.
Solve: $$\frac { y }{ 3 }$$ = 5
(a) 3
(b) 5
(c) 2
(d) 15

Hint:
$$\frac { y }{ 3 }$$ = 5 ⇒ y = 5 × 3 = 15

Question 46.
Solve: 3z = 9
(a) 1
(b) 2
(c) 3
(d) 4

Hint:
3z = 9 ⇒ z = $$\frac { 9 }{ 3 }$$ = 3

Question 47.
Solve: $$\frac { 1 }{ 2 }$$ + 5 = 7
(a) 1
(b) 2
(c) 3
(d) 4

Hint:
$$\frac { 1 }{ 2 }$$ + 5 = 7
⇒ $$\frac { 1 }{ 2 }$$ = 7 – 5 = 2 ⇒ l = 2 × 2 = 4

Question 48.
Solve: 7u = 21
(a) 1
(b) 2
(c) 3
(d) 4

Hint:
7u = 21 ⇒ u = $$\frac { 21 }{ 7 }$$ = 3

Question 49.
Solve: k – 3 = 3
(a) 3
(b) -3
(c) 0
(d) 6

Hint:
k – 3 = 3 ⇒ k = 3 + 3 = 6

Question 50.
Solve: r + 5 = 5
(a) 0
(b) 1
(c) 5
(d) -5

Hint:
r + 5 = 5
⇒ r = 5 – 5 = 0

###### Chapter 12 – Ratio and Proportion Class 6 MCQs Questions with Answers

Question 1.
The cost of a pen is ₹ 10. The cost of a penci 1 is ₹ 2. How many times of the cost of a pencil is the cost of a pen?
(a) 5 times
(b) 2 times
(c) 10 times
(d) none of these

Hint:
10 = 5 × 2

Question 2.
The monthly salary of Hari Kishan is ₹ 80000. The monthly salary of Manish is ₹ 40000. How many times of the salary of Manish is the salary of Hari Kishan?
(a) 2 times
(b) 4 times
(c) 3 times
(d) 8 times

Hint:
80000 = 2 × 40000

Question 3.
There are 30 boys and 20 girls in a class. The ratio of the number of girls to the number of boys is
(a) 2:3
(b) 3:2
(c) 2:5
(d) 3:5

Hint:
$$\frac { 20 }{ 30 }$$ = $$\frac { 2 }{ 3 }$$ = 2 : 3

Question 4.
There are 25 boys and 25 girls in a class. The ratio of the number of boys to the total number of students is
(a) 1:2
(b) 1 : 3
(c) 2:3
(d) 3:2

Hint:
$$\frac{25}{25+25}$$ = $$\frac { 25 }{ 50 }$$ = $$\frac { 1 }{ 2 }$$ = 1 : 2

Question 5.
The height of Apala is 150 cm. The height of Pari is 120 cm. The ratio of the height of Apala to the height of Pari is
(a) 4:5
(b) 5:4
(c) 5:2
(d) 4:1

Hint:
$$\frac { 150 }{ 120 }$$ = $$\frac { 15 }{ 12 }$$ = $$\frac { 5 }{ 4 }$$ = 5 : 4

Question 6.
The cost of a car is ₹ 3,00,000. The cost of a motorbike is ₹ 50,000. The ratio of the cost of motorbike to the cost of car is
(a) 1:6
(b) 1:5
(c) 1:4
(d) 1:3

Hint:
$$\frac { 50,000 }{ 3,00,000 }$$ = $$\frac { 1 }{ 6 }$$ = 1 : 6

Question 7.
The speed of Shubham is 6 km per hour. The speed of Yash is 2 km per hour. The ratio of the speed of Shubham to the speed of Yash is
(a) 2:3
(b) 3:1
(c) 1:3
(d) 3:2

Hint:
$$\frac { 6 }{ 2 }$$ = $$\frac { 3 }{ 1 }$$ = 3 : 1

Question 8.
The length and breadth of a rectangular park are 50 m and 40 m respectively. Find the ratio of the length to the breadth of the park.
(a) 4:5
(b) 4:1
(c) 5:1
(d) 5:4

Hint:
$$\frac { 50 }{ 40 }$$ = $$\frac { 5 }{ 4 }$$ = 5 : 4

Question 9.
The ratio 40 cm to 1 m is
(a) 2:5
(b) 3:5
(c) 4:5
(d) 5:2

Hint:
1 m = 100 cm
$$\frac { 40 }{ 100 }$$ = $$\frac { 2 }{ 5 }$$ = 2 : 5

Question 10.
In a family, there are 8 males and 4 females. The ratio of the number of females to the number of males is
(a) 1:2
(b) 1:4
(c) 1:8
(d) 2:1

Hint:
$$\frac { 4 }{ 8 }$$ = $$\frac { 1 }{ 2 }$$ = 1 : 2

Question 11.
Which of the following ratios is equivalent to 2:3?
(a) 4:8
(b) 4:9
(c) 6:9
(d) 6:12

Hint:
2 : 3 = $$\frac { 2 }{ 3 }$$ = $$\frac{2 \times 3}{3 \times 3}$$ = $$\frac { 6 }{ 9 }$$ = 6 : 9

Question 12.
Which of the following ratios is not equiva-lent to 10:5?
(a) 1:2
(b) 2:1
(c) 20:10
(d) 30:15

Hint:
10 : 5 = $$\frac { 10 }{ 5 }$$ = $$\frac{10 \div 5}{5 \div 5}$$ = $$\frac { 2 }{ 1 }$$ = 2 : 1
20 ÷ 10 = $$\frac { 20 }{ 10 }$$ = $$\frac{20 \div 10}{10 \div 10}$$ = $$\frac { 2 }{ 1 }$$ = 2 : 1
30 ÷ 15 = $$\frac { 30 }{ 15 }$$ = $$\frac{30 \div 15}{15 \div 15}$$ = $$\frac { 2 }{ 1 }$$ = 2 : 1

Question 13.
Find the ratio of number of circles and number of squares inside the following rectangle:
(a) 3:1
(b) 2:1
(c) 2:3
(d) 3:2

Hint:
12 : 8 = $$\frac { 12 }{ 8 }$$ = $$\frac{12 \div 4}{8 \div 4}$$ = $$\frac { 3 }{ 2 }$$ = 3 : 2

Question 14.
There are 20 teachers in a school of 500 students. The ratio of the number of teachers to the number of students is
(a) 1:20
(d) 1:50
(c) 1:25
(d) 25:1

Hint:
20 : 500 = $$\frac { 20 }{ 500 }$$ = $$\frac { 1 }{ 25 }$$ = 1 : 25

Question 15.
The ratio of 25 minutes to 1 hour is
(a) 7:5
(b) 5:12
(c) 12:5
(d) 5:7

Hint:
1 hour = 60 minutes
25 : 60 = $$\frac { 25 }{ 60 }$$ = $$\frac { 5 }{ 12 }$$ = 5 : 12

Question 16.
Out of 30 students in a class, 20 like cricket and 10 like Hockey. The ratio of the number of students liking Hockey to the total number of students is
(a) 3:1
(b) 1:3
(c) 2:3
(d) 1:2

Hint:
10 : 30 = $$\frac { 10 }{ 30 }$$ = $$\frac { 1 }{ 3 }$$ = 1 : 3

Question 17.
The cost of 1 dozen bananas is ₹ 30. The cost of 6 oranges is ₹ 18. The ratio of the cost of a i banana to the cost of an orange is
(a) 3:2
(b) 2:3
(c) 6:5
(d) 5:6

Hint:
30 : 2 × 18 = $$\frac{30}{2 \times 18}=\frac{30}{36}=\frac{5}{6}$$ = $$\frac { 5 }{ 6 }$$ = 5 : 6

Question 18.
The present age of Hari Kishan is 60 years. The present age of Manish is 30 years. The ratio of the age of Manish to the age of Hari Kishan 10 years ago was
(a) 2:5
(b) 5:2
(c) 2:3
(d) 3:2

Hint:
30 – 10 : 60 – 10 = 20 : 50
= $$\frac { 20 }{ 50 }$$ = $$\frac { 2 }{ 5 }$$ = 2 : 5

Question 19.
100 students appeared in annual examination. 60 students passed. The ratio of the number of students who failed to the total number of students is
(a) 5:2
(b) 2:5
(c) 2:3
(d) 3:2

Hint:
100 – 60 = 40
40 : 100 = $$\frac { 40 }{ 100 }$$ = $$\frac{40 \div 20}{100 \div 20}$$ = $$\frac { 2 }{ 5 }$$ = 2 : 5

Question 20.
₹ 100 are divided between Sangeeta and Manish in the ratio 4:1. Find the amount Sangeeta gets.
(a) ₹ 80
(b) ₹ 20
(c) ₹ 60
(b) ₹ 50

Hint:
$$\frac{4}{4+1}$$ × 100 = $$\frac { 4 }{ 5 }$$ × 100 = 4 × 20 = 80

Question 21.
Which of the following are in proportion?
(a) 2, 3, 20, 30
(b) 3, 4, 15, 18
(c) 1, 3, 11, 22
(d) 2, 5, 40, 80

Hint:
2 : 3 = 20 : 30

Question 22.
Which of the following is true?
(a) 15:40 :: 10:30
(b) 16:48 :: 25:75
(c) 40:60 :: 30:40
(d) 20:100 :: 30:120

Hint:
16 : 48 = $$\frac { 16 }{ 48 }$$ = $$\frac{16 \div 16}{48 \div 16}$$ = $$\frac { 1 }{ 3 }$$ = 1 : 3
25 : 75 = $$\frac { 25 }{ 75 }$$ = $$\frac{25 \div 25}{75 \div 25}$$ = $$\frac { 1 }{ 3 }$$ = 1 : 3

Question 23.
Which of the following is false?
(a) 25 g : 30 g :: 40 kg : 48 kg
(b) 81 : 91 :: 24 h : 27 h
(c) 32 m : 40 m :: 6 minutes : 12 minutes
(d) 25 km : 60 km :: ₹ 10 : ₹ 24

Hint:
32 m : 40 m = $$\frac { 32 }{ 40 }$$ = $$\frac{32 \div 8}{40 \div 8}$$ = $$\frac { 4 }{ 5 }$$ = 4 : 5
6 minutes : 12 minutes = $$\frac { 6 }{ 12 }$$ = $$\frac{6 \div 6}{12 \div 6}$$
= $$\frac { 1 }{ 2 }$$ = 1 : 2
4 : 5 ≠ 1 : 2

Question 24.
Which of the following statement is not true?
(a) 4 : 7 = 5 : 9
(b) ₹ 5 : ₹ 25 = 12g : 60g
(c) 30 : 80 = 6 : 16
(d) 12 : 36 = 14 : 42

Hint:
4 : 7 = $$\frac { 4 }{ 7 }$$
5 : 9 = $$\frac { 5 }{ 9 }$$
$$\frac { 4 }{ 7 }$$ ≠ $$\frac { 5 }{ 9 }$$

Question 25.
A car requires 5 litres of petrol to cover 80 km. How many litres of petrol are required to cover 32 km?
(a) 1
(b) 2
(c) 3
(d) 4

Hint:
$$\frac { 5 }{ 80 }$$ × 32 = 2

Question 26.
The cost of 10 notebooks is ₹ 100. The cost of 1 notebook is
(a) ₹ 10
(b) ₹ 100
(c) ₹ 20
(d) ₹ 5

Hint:
$$\frac { 100 }{ 10 }$$ = 10

Question 27.
The cost of 1 dozen pens is ₹ 24. Find the cost of 30 pens.
(a) ₹ 40
(b) ₹ 45
(c) ₹ 30
(d) ₹ 60

Hint:
1 dozen = 12
$$\frac { 24 }{ 12 }$$ × 30 = 60

Question 28.
The cost of 3 envelopes is ₹ 15. The cost of 10 envelopes is
(a) ₹ 20
(b) ₹ 30
(c) ₹ 45
(d) ₹ 50

Hint:
$$\frac { 15 }{ 3 }$$ × 10 = 50

Question 29.
The cost of 5 kg of tomatoes is ₹ 100. The cost of 2 kg of tomatoes is
(a) ₹ 20
(b) ₹ 40
(c) ₹ 30
(d) ₹ 50

Hint:
$$\frac { 100 }{ 5 }$$ × 2 = 40

Question 30.
The weight of 50 books is 10 kg. The weight of 25 books is
(a) 5 kg
(b) 8 kg
(c) 6 kg
(d) 4 kg

Hint:
$$\frac { 10 }{ 50 }$$ × 25 = 5

Question 31.
The cost of 20 m of cloth is ₹ 400. The cost of 15 m of cloth is
(a) ₹ 100
(b) ₹ 200
(c) ₹ 300
(d) ₹ 360

Hint:
$$\frac { 400 }{ 20 }$$ × 15 = 300

Question 32.
The salary of a month of an employee is ₹ 4000. The annual salary of the employee is
(a) ₹ 48000
(b) ₹ 24000
(c) ₹ 12000
(d) ₹ 8000

Hint:
1 year = 12 months
4000 × 12 = 48000

Question 33.
An aeroplane covers a distance of 5000 km in 5 hours. How much distance will it cover in 2 hours?
(a) 1000 km
(b) 2000 km
(c) 3000 km
(b) 4000 km

Hint:
$$\frac { 5000 }{ 5 }$$ × 2 = 2000

Question 34.
The fare for 5 tickets from Kosi Kalan to Mathura is ₹ 150. The fare for 3 tickets is
(a) ₹ 90
(b) ₹ 60
(c) ₹ 75
(d) ₹ 45

Hint:
$$\frac { 150 }{ 5 }$$ × 3 = 90

Question 35.
150 kg of oil can be filled in 10 containers. To fill 750 kg of oil, how many containers will be required?
(a) 10
(b) 20
(c) 40
(d) 50

Hint:
$$\frac { 10 }{ 150 }$$ × 750 = 50

Question 36.
The cost of 8 almirahs is ₹ 8000. The cost of 1 almirah is
(a) ₹ 1000
(b) ₹ 2000
(c) ₹ 4000
(d) ₹ 6000

Hint:
$$\frac { 8000 }{ 8 }$$ = 1000

###### Chapter 13 – Symmetry Class 6 MCQs Questions with Answers

Question 1.
How many lines of symmetry does the figure have?

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

Question 2.
How many lines of symmetry does the figure have?

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

Question 3.
How many lines of symmetry does the figure have?

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

Question 4.
How many lines of symmetry does the figure have?

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

Question 5.
How many lines of symmetry does the figure have ?

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

Question 6.
How many lines of symmetry does the figure have ?

(a) 1
(b) 2
(c) 3
(d) no line of symmetry

Question 7.
How many lines of symmetry does the figure have?

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

Question 8.
How many lines of symmetry does the figure have?

(a) 0
(b) 1
(c) 2
(d) Countless

Question 9.
How many lines of symmetry does the figure have?

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

Question 10.
How many lines of symmetry does a regular hexagon have?
(a) 1
(b) 3
(c) 4
(d) 6

Question 11.
Which of the following letters has horizontal line of symmetry?
(a) C
(b) A
(c) J
(d) L

Question 12.
Which of the following letters has horizontal line of symmetry?
(a) Z
(b) V
(c) U
(d) E

Question 13.
Which of the following letters has horizontal line of symmetry?
(a) S
(b) W
(c) D
(d) Y

Question 14.
Which of the following letters has vertical line of symmetry?
(a) R
(b) C
(c) B
(d) T

Question 15.
Which of the following letters has vertical line of symmetry?
(a) N
(b) K
(c) B
(d) M

Question 16.
Which of the following letters has vertical line of symmetry?
(a) J
(b) D
(c) E
(d) O

Question 17.
Which of the following letters has no line of symmetry?
(a) P
(b) O
(c) H
(d) X


text:
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Definite integral of trig function

AP.CALC:
FUN‑6 (EU)
,
FUN‑6.B (LO)
,
FUN‑6.C (LO)

## Video transcript

- [Voiceover] Let's see if we can evaluate the definite integral from 11 pi over two to six pi of nine sine of x dx. So the first thing, let's see if we can take the antiderivative of nine sine of x, and we could use some of our integration properties to simplify this a little bit. So this is going to be equal to, this is the same thing as nine times the integral from 11 pi over two to six pi of sine of x dx. And what's the anitderivative of sine of x? Well we know, from our derivatives, that the derivative with respect to x of cosine of x is equal to negative sine of x, negative sine of x. So can we construct this in some way so this is a negative sine of x? What if I multiplied, on the inside, what if I multiplied it by negative one? Well I can't just multiply in only one place by negative one, I need to multiply by negative one twice so I'm not changing its value. So what if I said negative nine times negative sine of x? Well this is still gonna be nine sine of x. If you took negative nine times negative sine of x, it is nine sine of x, and I did it this way because now negative sine of x, it matches the derivative of cosine of x. So we could say that this is all going to be equal to, it's all going to be equal to, you have your negative nine out front, negative nine times, times, I'll put it in brackets, negative nine times, the antiderivative of negative sine of x, well that is just going to be cosine of x, cosine of x, and we're going to evaluate it at its bounds. We're going to evaluate it at six pi, let me do that in a color I haven't used yet, we're gonna do that at six pi, and we're also going to do that at 11 pi over two, 11 pi over two, so this is going to be equal to, this is equal to negative nine times, I'm going to create some space here, so actually that's probably more space than I need, it's going to be cosine of six pi, cosine of six pi, minus cosine of 11 pi over two, cosine of 11 pi over two. Well what is cosine of six pi going to be? Well, cosine of any multiple of two pi is going to be equal to one. You could view six pi as, we're going around the unit circle three times. So this is the same thing as cosine of two pi, or the same thing as cosine of zero, so that is going to be equal to one. If that seems unfamiliar to you I encourage you to review the unit circle definition of cosine. And what is cosine of 11 pi over two? Let's see, let's subtract some, let's subtract some multiple of two pi here to put it in values that we can understand better. So this is, so let me write it here, cosine of 11 pi over 2, that is the same thing as, let's see, if we were to subtract, this is the same thing as cosine of 11 pi over two minus, this is the same thing as five and one half pi, right? Yeah, so this is, so we could view this as, we could subtract, let's subtract four pi, which is going to be, we could write that as eight pi over two. In fact, no, let's subtract five, no, let's subtract four pi, which is eight pi over 2. So once again, I'm just subtracting a multiple of two pi, which isn't gonna change the value of cosine, and so this is going to be equal to cosine of 3 pi over 2. And if we imagine the unit circle, and let me draw the unit circle here. So it's my y axis, my x axis, and then I have the unit circle, so, whoops. So the unit circle just like that. So if we start at, this is zero, then you go to pi over two, then you go to pi, then you go to three pi over two, so that's this point on the unit circle, so the cosine is the x coordinate, so this is going to be zero. This is zero so this is zero, and so we get one minus zero, so everything in the brackets evaluates out to one, and so we are left with, so let me do that, so all of this is equal to one. And so you have negative nine times one, which of course is just negative nine, is what this definite integral evaluates to.
AP® is a registered trademark of the College Board, which has not reviewed this resource.

format: plain


text:
# residues of tangent and cotangent

We will determine the residues of the tangent and the cotangent at their poles, which by the http://planetmath.org/node/9074parent entry are simple (http://planetmath.org/SimplePole).

By the rule in the entry coefficients of Laurent series, in a simple pole$z=a$  of $f$ one has

 $\mbox{Res}(f;\,a)\;=\;\lim_{z\to a}(z\!-\!a)f(z).$
• We get first

 $\displaystyle\mbox{Res}(\cot;\,0)\;=\;\lim_{z\to 0}z\cot{z}\;=\;\lim_{z\to 0}% \frac{\cos{z}}{\frac{\sin{z}}{z}}\;=\;\frac{1}{1}\;=\;1.$ (1)
• All the poles of cotangent are  $n\pi$  with  $n\in\mathbb{Z}$.  Since $\pi$ is the period of cotangent, we could infer that the residues in all poles are the same as (1).  We may also calculate (with the change of variable  $z\!-\!n\pi=w$) directly

 $\mbox{Res}(\cot;\,n\pi)\;=\;\lim_{z\to n\pi}(z\!-\!n\pi)\cot{z}\;=\;\lim_{w\to 0% }w\cot(w\!+\!n\pi)\;=\;\lim_{w\to 0}w\cot{w}\;=\;1.$
• In the parent entry (http://planetmath.org/ComplexTangentAndCotangent), the complement formula for the tangent function is derived.  Using it, we can find the residues of tangent at its poles $\displaystyle\frac{\pi}{2}+n\pi$, which are .  For example,

 $\mbox{Res}(\tan;\,\frac{\pi}{2})\;=\;\lim_{z\to\frac{\pi}{2}}\left(z\!-\!\frac% {\pi}{2}\right)\cot\left(\frac{\pi}{2}\!-\!z\right)\;=\;\lim_{w\to 0}w\cot(-w)% \;=\;-\mbox{Res}(\cot;\,0)\;=\;-1.$

Similarly as above, the residues in other poles are $-1$.

Consequently, the residues of cotangent are equal to 1 and the residues of tangent equal to $-1$.

Title residues of tangent and cotangent ResiduesOfTangentAndCotangent 2013-03-22 18:57:35 2013-03-22 18:57:35 pahio (2872) pahio (2872) 6 pahio (2872) Example msc 33B10 msc 30D10 msc 30A99 Residue TechniqueForComputingResidues ResiduesOfGammaFunction


text:
# Exporting Static Sites From Tiddlywiki

## Summary

In the first section of this tutorial, we set-up a Tiddlywiki server, created some content, and exported it as a static site.

In this section, we're going to be more selective about what gets included in the site. Then we're going to change which templates get used for the static build, so as to separate the format and styling of our site from that of Tiddlywiki itself.

## Changing the Output Filter

The command that we used previously to generate our static pages is applying a simple filter to select which pages to output. At the moment, it just says [!is[system]], meaning all the "non system" tiddlers, ie; any content at all, gets output - each tiddler gets a page.

We can change this rule to whatever we like. For now, we're going to keep it simple and just require tiddlers to have a tag, Live in order to get output, but the rule could be as complicated as you like.

The filter we need to use is [!is[system]tag[Live]] and now our build.sh file looks like this

tiddlywiki --rendertiddlers [!is[system]tag[Live]] $:/core/templates/static.tiddler.html static text/plain --rendertiddler$:/core/templates/static.template.css static/static.css text/plain

## Finding and Cloning the Templates

We can also see that the commands we are currently running in build.sh use the tiddlers $:/core/templates/static.tiddler.html and $:/core/templates/static.template.css as templates for everything they output.

We could make changes by over-writing these templates, but that's likely to get messy later and it's better to keep what we're doing separate from anything that comes in the core.

Instead we'll find them, clone them, give them names that indicate they're part of our project, and change the references to them in build.sh so that it now looks like this

tiddlywiki --rendertiddlers [!is[system]tag[Live]] $:/didaxy/templates/static.tiddler.html static text/plain --rendertiddler$:/didaxy/templates/static.template.css static/static.css text/plain

And the relevant tiddlers are called $:/didaxy/templates/static.tiddler.html and $:/didaxy/templates/static.template.css.

Running build.sh produces the same output we had previously, only now using our new templates.

## Examining the HTML

Now lets take a look at those templates to see what's going on, starting with the HTML.

\define tv-wikilink-template() $uri_doubleencoded$.html
\define tv-config-toolbar-icons() no
\define tv-config-toolbar-text() no
\define tv-config-toolbar-class() tc-btn-invisible
<!doctype html>

<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="generator" content="TiddlyWiki" />
<meta name="tiddlywiki-version" content="{{$:/core/templates/version}}" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <meta name="apple-mobile-web-app-capable" content="yes" /> <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" /> <meta name="mobile-web-app-capable" content="yes"/> <meta name="format-detection" content="telephone=no"> <link id="faviconLink" rel="shortcut icon" href="favicon.ico"> <link rel="stylesheet" href="static.css"> <title><$view field="caption"><$view field="title"/></$view>: {{$:/core/wiki/title}}</title>   {{$:/StaticBanner||$:/core/templates/html-tiddler}}
 <$importvariables filter="[[$:/core/ui/PageMacros]] [all[shadows+tiddlers]tag[$:/tags/Macro]!has[draft.of]]">
<$view tiddler="$:/core/ui/ViewTemplate" format="htmlwikified"/>
</$importvariables>
   Note the use of backticks to distinguish regular html from wikitext syntax. That's important. Everything in this code between <body... and  is the content of the page and we can see that really, the core business of this template is to wrap another tiddler called $:/core/ui/ViewTemplate.

There's probably a lot of stuff in here that we don't need, but as a rule of thumb we're going to only delete what we have to, so that we don't inadvertently break things we don't understand.

All we're going to do for now, then, is repeat the procedure of cloning $:/core/ui/ViewTemplate, renaming it $:/didaxy/template/static-view-template and changing the reference in the HTML template accordingly.

In addition to the main content, represented now by $:/didaxy/template/static-view-template, which we'll get to in a moment, we also find reference (near the top) to a tiddler called $:/StaticBanner.

$:/StaticBanner doesn't exist right now, but it does give us a pretty good clue as to how we might be able to include a header into our pages. What we'll do is change the reference to point to a tiddler of our own, called $:/didaxy/static-header, into which we'll put a bit of content to test it ("this is some header content" will do for now).

By analogy, we're also going to add our own footer, unsurprisingly called $:/didaxy/static-footer with some equally witty content. Now our template looks like this ...  {{$:/didaxy/static-header||$:/core/templates/html-tiddler}}
 <$importvariables filter="[[$:/core/ui/PageMacros]] [all[shadows+tiddlers]tag[$:/tags/Macro]!has[draft.of]]">
<$view tiddler="$:/didaxy/template/static-view-template" format="htmlwikified"/>
</$importvariables>
 {{$:/didaxy/static-footer||$:/core/templates/html-tiddler}}     If we rebuild our site now we should see that in deed our header and footer content, drab though it may be, is being inserted into the right places at the head and the foot of each page. ## Modifying the view template filters Next, we want to get rid of the extraneous information from the page - we don't want the tiddler title to be there, or the tags or the date, though your preference may vary. The tiddler title will still be the title of page, but we want to be able to decide whether or not to include it a part of the content of the page. Above, we cloned the view-template into $:/didaxy/template/static-view-template which initially looks like this

\define frame-classes()
tc-tiddler-frame tc-tiddler-view-frame $(missingTiddlerClass)$ $(shadowTiddlerClass)$ $(systemTiddlerClass)$ $(tiddlerTagClasses)$
\end
\define folded-state()
$:/state/folded/$(currentTiddler)$\end <$set name="storyTiddler" value=<<currentTiddler>>><$set name="tiddlerInfoState" value=<<qualify "$:/state/popup/tiddler-info">>><$tiddler tiddler=<<currentTiddler>>><div class=<<frame-classes>>><$list filter="[all[shadows+tiddlers]tag[$:/tags/ViewTemplate]!has[draft.of]]" variable="listItem"><$transclude tiddler=<<listItem>>/></$list>
 </$tiddler></$set></$set>

Again, we're not going to change anything we don't need to, lest we break something.

Upon inspection, we can see that all this is doing is including all the tiddlers that have the tag $:/tags/ViewTemplate, just as it does when rendering a regular Tiddlywiki. The tiddlers that carry this tag to begin with are; $:/core/ui/ViewTemplate/title
$:/core/ui/ViewTemplate/unfold$:/core/ui/ViewTemplate/subtitle
$:/core/ui/ViewTemplate/tags$:/core/ui/ViewTemplate/classic
$:/core/ui/ViewTemplate/body$:/core/ui/ViewTemplate/import
$:/core/ui/ViewTemplate/plugin In theory, all we need to do to exclude those tiddlers from our static site is remove the tag but if we do that, they'll also disappear from the wiki itself, which is going to make it pretty hard to use. Instead we need to change the tag that's being used in the filter and add that tag to the ones that we do want to include. We'll use the tag $:/tags/StaticViewTemplate in a bid to be somewhat consistent and because we're not 100% sure what all of those tiddlers do, we'll give our new tag to all of them to start with.

Rebuild the site and everything should still be working. Now we can go back and remove our new tag from the templates that we want to remove from the output, which ends up being these ones.

$:/core/ui/ViewTemplate/title$:/core/ui/ViewTemplate/subtitle
$:/core/ui/ViewTemplate/tags Which gives us, rebuilding again, a nice clean output, consisting of only the content of our tiddlers and none of their 'metadata'. NB: we could probably have been much more aggressive in removing stuff from the lists and templates here and may be able to come back and do a better job when we have everything else working. ## Examining the CSS Now let's look at the css in $:/didaxy/templates/static.template.css

{{$:/boot/boot.css||$:/core/templates/plain-text-tiddler}}

{{$:/core/ui/PageStylesheet||$:/core/templates/wikified-tiddler}}

All it's doing is transcluding content from two other places. One of them is the boot.css file which is written as a regular text file and so transcluded through the plain-text template and the other is the PageStyleSheet which is itself written in wikitext and so transcluded through the wikified-tiddler template.

Given that our goal is to separate the styling of our site from that of Tiddlywiki, the simplest thing to do here is to start from scratch so let's just delete everything in $:/didaxy/templates/static.template.css, rebuild again, and see what we get. A naked website! This is good. Now let's go back to $:/didaxy/templates/static.template.css and add a reference to a new stylesheet of our own, like so

{{$:/didaxy/styles/static-styles.css||$:/core/templates/plain-text-tiddler}}

and into \$:/didaxy/styles/static-styles.css, put some css. (We'll choose something that makes it obvious our code is working)

body {
background-color: red;
}

Now rebuild again and you should see that all our awfully formatted pages have a terrible red background. Success!

## A Note On Viewing The Output and Refreshing CSS

It's particularly useful, when debugging this and similar processes, to know how to easily view the source code of a web page in your browser. On Firefox for Mac, for example, you can press command-U. Find "view source" or similar in the menus of your browser and take note of the keyboard shortcut for next time.

The Source should open in a new tab for you to examine. Also, links in the source code to other resources - such as a link to the static.css file that our site is using - should be clickable. If you click the link now you should see the css that we entered above, in a new tab again.

Sometimes, when updating css styles you might not see your changes reflected when you refresh the page. This is because browsers sometimes keep a cache of the css file and don't update it automatically. By keeping the 'view-source' of your css open in a different tab and refreshing that page too, you can force the browser to refresh your css.


text:
# Random singlet state in Ba5CuIr3O12 single crystals

@article{Volkov2020RandomSS,
title={Random singlet state in
Ba5CuIr3O12
single crystals},
author={Pavel A. Volkov and C. J. Won and Denis Ivanovich Gorbunov and Jaewook Kim and Mai Ye and Heung-Sik Kim and Jedediah H. Pixley and Sang‐Wook Cheong and Girsh Blumberg},
journal={Physical Review B},
year={2020},
volume={101},
pages={020406}
}
• Published 15 January 2020
• Materials Science, Physics
• Physical Review B
We study the thermodynamic and high-magnetic-field properties of the magnetic insulator ${\mathrm{Ba}}_{5}{\mathrm{CuIr}}_{3}{\mathrm{O}}_{12}$, which shows no magnetic order down to 2 K, consistent with a spin-liquid ground state. While the temperature dependence of the magnetic susceptibility and the specific heat shows only weak antiferromagnetic correlations, we find that the magnetization does not saturate up to a field of 59 T, leading to an apparent contradiction. We demonstrate that the…
3 Citations

## Figures and Tables from this paper

Phase diagram of the anisotropic triangular lattice Hubbard model
• Physics
• 2021
picture: The first type of ordering we consider is shown in Figure S2(a). Evidently, along one lattice vector the spins are ferromagnetically aligned, while along the two other bonds of the
Characterizing random-singlet state in two-dimensional frustrated quantum magnets and implications for the double perovskite Sr$_2$CuTe$_{1-x}$W$_{x}$O$_6$
• Physics
• 2020
Motivated by experimental observation of the non-magnetic phase in the compounds with frustration and disorder, we study the ground state of the spin-$1/2$ square-lattice Heisenberg model with
Hexagonal Perovskites as Quantum Materials.
• Materials Science
Chemical reviews
• 2020
Hexagonal oxide perovskites are of contemporary interest due to their potential for geometrical frustration of the ordering of magnetic moments or orbital occupancies at low temperatures, which is especially relevant to their significance as quantum materials.

## References

SHOWING 1-10 OF 54 REFERENCES
Exotic Low-Energy Excitations Emergent in the Random Kitaev Magnet Cu_{2}IrO_{3}.
• Physics
Physical review letters
• 2019
A many-faceted impact of quenched disorder in a Kitaev spin system due to its peculiar bond character is marked, pointing towards the presence of additional low-lying excitations on the background of bond-disordered spin liquid.
Rearrangement of Uncorrelated Valence Bonds Evidenced by Low-Energy Spin Excitations in YbMgGaO_{4}.
• Physics
Physical review letters
• 2019
It is argued that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids and extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice.
Orbital order and fluctuations in Mott insulators
Basic mechanisms controlling orbital order and orbital fluctuations in transition metal oxides are discussed. The lattice driven classical orbital picture, e.g. like in manganites LaMnO$_3$, is
Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO_{4}.
• Physics
Physical review letters
• 2017
We suggest that a randomization of the pseudodipolar interaction in the spin-orbit-generated low-energy Hamiltonian of YbMgGaO_{4} due to an inhomogeneous charge environment from a natural mixing of
Trimer-based spin liquid candidate Ba4NbIr3O12
• Physics
Physical Review Materials
• 2019
Ba4NbIr3O12, a previously unreported material with a triangular planar geometry of Ir3O12 trimers, is described. Magnetic susceptibility measurements show no magnetic ordering down to 1.8 K despite
Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Physics
Physical Review X
• 2018
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids
Scaling and data collapse from local moments in frustrated disordered quantum spin systems
• Physics
Nature Communications
• 2018
It is shown that recently observed scaling behavior common to several disordered quantum magnets can be understood as the emergence of a universal random-singlet regime.
Static and dynamical spin correlations of the S = 1 2 random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices
• Physics
• 2015
Inspired by the recent theoretical suggestion that the random-bond $S=1/2$ antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin
Randomness-induced quantum spin liquid behavior in the s=12 random J1−J2 Heisenberg antiferromagnet on the square lattice
• Physics
Physical Review B
• 2018
We investigate the ground-state and finite-temperature properties of the bond-random $s=1/2$ Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor
Random antiferromagnetic quantum spin chains.
• Fisher
• Physics
Physical review. B, Condensed matter
• 1994
The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a


text:
# Convert to Exponential Form y = natural log of x-5

For logarithmic equations, is equivalent to such that , , and . In this case, , , and .
Substitute the values of , , and into the equation .
Convert to Exponential Form y = natural log of x-5


text:
# Murphy diagrams in R

July 16, 2015
By

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

At the recent International Symposium on Forecasting, held in Riverside, California, Tillman Gneiting gave a great talk on “Evaluating forecasts: why proper scoring rules and consistent scoring functions matter”. It will be the subject of an IJF invited paper in due course.

One of the things he talked about was the “Murphy diagram” for comparing forecasts, as proposed in Ehm et al (2015). Here’s how it works for comparing mean forecasts.

It is well-known that the mean of the forecast distribution is obtained by minimizing the squared error loss function, $$S(x,y)=(x-y)^2$$ where $$x$$ is the point forecast and $$y$$ is the actual observation. That is
$\text{E}(Y) = \text{min arg}_x S(x,y).$

An old result that is not so well known is that there are other loss functions which would also lead to the forecast mean. In fact, Savage (1971) showed that any scoring function is consistent for the mean if and only if it is of the form
$\label{savage} S(x,y) = \phi(y) – \phi(x) – \phi'(x)(y-x)$

where the function $$\phi$$ is convex with subgradient $$\phi'$$. Setting $$\phi(u)=u^2$$ gives the usual squared error result. So when comparing point forecasts that are intended to be estimates of the mean, it may not be appropriate to only compare the MSE values. A different scoring function that satisfies condition (1) may give a different ranking of competing forecasts.

Ehm et al (2015) showed that any scoring function satisfying condition (1) can be written as
$S(x,y) = \int_{-\infty}^\infty S_{\theta}(x,y) dH(\theta)$

where $$H$$ is a non-negative measure and
$S_{\theta}(x,y) = \begin{cases} |y-\theta| & \text{if} \min(x,y)\le\theta < \max(x,y) \\ 0 & \text{otherwise}. \end{cases}$

Different $$H$$ measures give different scoring functions, but $$S_{\theta}(x,y)$$ is the same for all such scoring functions.

So if we have point forecasts for $$n$$ events, we can calculate the average value of $$S_{\theta}(x,y)$$ for each $$\theta$$:
$s(\theta) = \frac{1}{n}\sum_{i=1}^n S_{\theta}(x_i,y_i)$

and plot this as a function of $$\theta$$. This is what Ehm et al call a “Murphy diagram”. A similar approach can be taken for quantile and expectile forecasts (with a different function $$S_\theta(x,y)$$ of course).

I have written some R code for producing these plots. Here it is applied to rolling one-step forecasts computed using ETS and ARIMA models. The data was simulated from an ARIMA model, so we would expect the ARIMA forecasts to be better:

    source("https://robjhyndman.com/Rfiles/murphy.R")
library(forecast)
set.seed(2015)
y <- arima.sim(n = 300, list(ar = c(0.8897, -0.4858), ma = c(-0.2279, 0.2488)),
sd = sqrt(0.1796))

# Rolling one-step forecasts
f1 <- f2 <- ts(numeric(300)*NA)
for(i in 30:299)
{
fit1 <- ets(window(y,end=i))
fit2 <- auto.arima(window(y,end=i))
f1[i+1] <- forecast(fit1, PI=FALSE, h=1)$mean f2[i+1] <- forecast(fit2, h=1)$mean
}

murphydiagram(y, f1, f2)
legend("topleft", lty=1, col=c("blue","red"), legend=c("ETS","ARIMA"))

    murphydiagram(y, f1, f2, type='diff', main="ETS - ARIMA")

The shaded region shows 95% pointwise confidence intervals for the difference between the two functions.

Currently my R code only works for the mean function, but it would be easy enough to modify the function to handle quantiles and expectiles as well.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.


text:
# Thread: Powers that are fractions?

1. ## Powers that are fractions?

I have a question I'm not sure how to answer because I've never seen a power that is a fraction before. I need to simplify;

x^(1/3) times x^(2/3)

After some googling I think the fraction represents a cubed root, so the answer should be;

cubed root of (x times x^2)

Is that right?

2. ## Re: Powers that are fractions?

Yes.

$\sqrt[3]{x} \sqrt[3]{x^2} = \sqrt[3]{x*x^2} = x$ (for real x).

3. ## Re: Powers that are fractions?

Originally Posted by Badgers
I have a question I'm not sure how to answer because I've never seen a power that is a fraction before. I need to simplify;

x^(1/3) times x^(2/3)

After some googling I think the fraction represents a cubed root, so the answer should be;

cubed root of (x times x^2)

Is that right?
The index laws hold for powers that are ANY numbers, so you can use \displaystyle \begin{align*} a^m \cdot a^n = a^{m + n} \end{align*} to simplify.

\displaystyle \begin{align*} x^{\frac{1}{3}} \cdot x^{\frac{2}{3}} &= x^{\frac{1}{3} + \frac{2}{3}} \\ &= x^1 \\ &= x \end{align*}

4. ## Re: Powers that are fractions?

Oh, rad! You guys are awesome! Thanks


text:
# Thread: Unable to simplify equation

1. ## Unable to simplify equation

I have the function f(n) = n2 + (n2 - (n-1)) + (n2 - 2(n-1)) + (n2 - 3(n-1))

I tried pulling an "n-1" out like so:
f(n) = n2 + (n-1) [ (n2-1) + (n2-2) + (n2-3) ]

But when I run test cases on it against the original, it doesn't come out right.
I'm pretty positive I can't take an "n^2" out to simplify it.

Is that the simplest I can express that equation?

2. ## Re: Unable to simplify equation

Hello, jonarmani!

I have the function $f(n) \:=\:n^2+ \big[n^2 - (n-1)\big] + \big[n^2 - 2(n-1)\big] + \big[n^2 - 3(n-1)\big]$

I tried pulling an "n-1" out like so:
$f(n) \:=\: n^2 + (n-1) \big[(n^2-1) + (n^2-2) + (n^2-3)\big]$ . Illegal!

But when I run test cases on it against the original, it doesn't come out right.
I'm pretty positive I can't take an "n^2" out to simplify it.

Is that the simplest I can express that equation?

Why not add the four polynomials?

$n^2 + (n^2 - n + 1) + (n^2 - 2n + 2) + (n^2 - 3n +3)$

. . . . . . . . $=\;\;4n^2 - 6n + 6 \;\;=\;\;2(2n^2 - 3n + 3)$

Thank you!!!


text:
# Moment of inertia factor

Distribution of mass in a celestial body

The moment of inertia factor is a dimensionless quantity where the mass distributes inside a planet or satellite. The moment of inertia factor is defined as ${\displaystyle {\frac {C}{MR^{2}}}}$,


text:
## Winter 2013 Midterm #8B

$E_{cell} = E_{cell}^{\circ}-\frac{RT}{nF}\ln Q$

Helena Vervaet 1N
Posts: 26
Joined: Wed Sep 21, 2016 2:59 pm

### Winter 2013 Midterm #8B

When I was solving for the concentration of Fe2+ ions, I used the Nernst Equation that included ln instead of log. For most of the other problems in that midterm, answers using either ln or log were both stated as acceptable, but for #8B (pg.135) it looks like only the log equation should have been used. Can someone explain to me when you should use equations with ln vs. log?

Chem_Mod
Posts: 18400
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 435 times

### Re: Winter 2013 Midterm #8B

It does not matter whether you use the equation using ln or log. However, the answers using the different equations will not be exactly the same because the log equation is less accurate due to the constant. The log version of the nernst equation presents (RT/F) as a constant, rather than having to plug in the corresponding values when calculating. However, note that the temperature used to calculate this constant is assumed to be 298 K (25 degrees Celsius).

Melanie_Wong_1K
Posts: 22
Joined: Fri Jul 22, 2016 3:00 am

### Re: Winter 2013 Midterm #8B

This question actually concerns both #8b and 7 of the 2013 Midterm.

When you're using the Nerst Equation, how do you find n? The moles aren't given in either of the problems but the answer to #7 says n=10 and for #8b n=2. They don't seem to relate to the amount of moles in the chemical equations either.

Return to “Appications of the Nernst Equation (e.g., Concentration Cells, Non-Standard Cell Potentials, Calculating Equilibrium Constants and pH)”

### Who is online

Users browsing this forum: No registered users and 1 guest


text:
# Basic Matrix Row Operations Tips

There are four basic operations in mathematics: adding, subtracting, dividing and multiplying. It looks easy for a mathematician or a student who has maths as his or her major. In fact, these operations are quite simple: 2+2=4, 5-4=1 and so on. However, mathematics would have never become so much popular if it was so easy. An math homework may take ages for an ordinary high school, college or university student to find correct solutions. That is why many students require homework help in mathematics. There is nothing wrong in having problems or questions in maths. After all, we are not all geniuses. At the same time, it is still possible to get correct answers taking advantage of tips and special custom writing service companies which can be found online.

As already said above, there are 4 basic operations in maths. In case of matrices there are only three raw operations that this article will focus on.

Row switching. Every matrix consists of rows and columns of numbers. As the name of the operation suggests we switch rows of numbers and indicate substitutions with arrows. A word of advice – make sure you correctly copy the rows when switching them.

Row multiplication. In such a case you can either multiply rows of the two matrices or multiply a matrix by a certain number (in fact, anything you like). Thus, in case of two matrices you should multiply relevant numbers of the rows (for example, first right top numbers of matrix A and matrix B and so on). In case you multiply the whole matrix by one number, you perform multiplication operation with all matrix numbers.

Row addition. This operation is quite easy. One has to add relevant number of matrices (number 1 row 1 matrix A plus number 1 row 1 matrix B, and so on).

Students who need maths help can look for an online maths solver which a service that solves maths equations. In such a way you will not only get solutions to maths tasks but also learn solving “mechanics.”

0 Shares
Filed under Math.


text:
# Optimal bandwidth cost for Oblivious RAM

Goldreich and Ostrovsky show that any ORAM algorithm must have bandwidth cost $\Omega(logN)$, where $N$ is the total number of blocks outsourced. This is in Theorem C of this paper. But they didn't give any proof for this Theorem. Is there other papers that have proved this theorem?

• This "theorem" is in the introduction, and is labeled "informal statement". Have you read the rest of the paper? (I haven't.) – fkraiem May 4 '15 at 10:21
• I went over the paper, but didn't find this theorem appears again. But there is a Theorem in sections 6, which is about the number of steps. – Jan Leo May 4 '15 at 12:40
• I would guess that the proof would be in Ostrovsky's PhD thesis. – mikeazo May 4 '15 at 20:14

See Theorem 6, page 38-39..

Also, this lower bound ignores any ability of the "RAM" to perform computation. Typically, there are two application scenarios for ORAM:

1) A literal processor communicating along a literal CPU bus to a literal stick of RAM

2) A client communicating over the internet to a cloud server

In the latter case, it makes sense for the cloud server to provide computational resources to 'speed up' the oblivious simulation. Two works have shown how to achieve $O(1)$ bandwidth overhead (pushing the $\Omega(log(N))$ requisite overhead onto the server's computation instead):

Also, very recent work based on program obfuscation allows you to implement a "one-shot ORAM," i.e. ORAM with a single round of communication and asymptotically succinct space/time for the server:

• Thanks, in Theorem 6, they assume m=t, where m is the number of outsourced blocks and t is the number of steps. But what if t is not equal to m, e.g. t is 1? This is another paper that consider server's work: cs.umd.edu/~elaine/docs/burstoram.pdf – Jan Leo May 5 '15 at 7:54
• Ah-- then the lower bound is $|x|$ where $x$ is the input to the RAM. Consider a program that just looks up the value stored in the RAM at index $x\in [N]$. The insecure program makes 1 access, while the ORAM must make $\log(N)$ to be oblivious. And if you have less than $\log(N)$ bits of input, then you can't index all $N$ locations in the memory array anyway. (My $N$ = your $m$) – Daniel Apon May 8 '15 at 1:09
• OK, that make some sense. But I still would like to ask why need to index all $N$ locations? Suppose there is a ORAM scheme uses only $n<log(N)$ bandwidth. Of course, it can only index at most $2^n$ locations. But If the server cannot figure out where is the $(N-2^n)$ locations, the scheme is still secure, isn't it? – Jan Leo May 9 '15 at 19:10
• This would be kind of like installing 5 gigabytes of RAM in a 32-bit machine. =) But if you can find a good use, go for it! – Daniel Apon May 12 '15 at 2:52