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16 questions · timed · auto-graded

Question 12 Marks
i. In the following pattern, draw the next two figures.


ii. Construct a table to describe the figures in the above pattern.
iii. If $n$ denotes the number of figures and $L$ denotes the number of matches, find $L$ in terms of $n$.
iv. Find how many matches are required to make the :
(1) 12 th figure
(2) 20th figure
Answer
i.

ii.
n 1 2 3 4 5
L 2 4 6 8 10
iii. $
L =2 n
$
(1) 12th figure 12th figure has $=2 \times 12=24$
(2) 20 th figure $=2 \times 20=40$
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Question 22 Marks
Solve:
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
Answer
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + = 98765
123456 x 8 + 6 = 987654
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Question 32 Marks
Solve:
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
Answer
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
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Question 42 Marks
Solve:
1 x 9 + 1 = 10
12 x 9 + 2 = 110
123 x 9 + 3 = 1110
Answer
1 x 9 + 1 = 10
12 x 9 + 2 = 110
123 x 9 + 3 = 1110
1234 x 9 + 4 = 11110
12345 x 9 + 5 = 111110
123456 x 9 + 6 = 1111110
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Question 52 Marks
The product of the two numbers is 528. If the product of their unit’s digits is 8 and the product of their ten’s digits is 4; find the numbers.
Answer
Product of unit’s digit = 8 = 2 x 4
Unit’s digits are 2 and 4
Thus, the numbers are either 24 and 22
24 x 22 = 528
The required numbers are 528
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Question 62 Marks
Find the difference between the smallest number of eight digits and the largest number of five digits.
Answer
Smallest number of eight digits = 10000000
and, largest number of five digits = 99999
Difference = 10000000 – 99999 = 9900001
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Question 72 Marks
Evaluate :
9999 x 8
Answer
9999 x 8
= (9000 + 900 + 90 + 9) x 8
=9000 x 8+900 x 8 + 90 x 8 + 9 x 8
= 72000 + 7200 + 720 + 72
= 79992
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Question 82 Marks
Evaluate :
15 x 49372
Answer
15 x 49372
= 15 x (40000 + 9000 + 300 + 70 + 2)
= 15 x 40000 + 15 x 9000 + 15 x 300+ 15 x 70 + 15 x 2
= 600000 + 135000 + 4500 + 1050 + 30
= 740580
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Question 92 Marks
Evaluate :
6214 x 12
Answer
6214 x 12
=(6000 + 200 + 10 + 4) x 12
=6000 x 12+ 200 x 12 + 10 x 12 +4 x 12
= 72000 + 2400 + 120 + 48
= 74568
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Question 112 Marks
Find the product of the :
Greatest number of four digits and the greatest number of three digits
Answer
Greatest number of four digits = 9999
and Greatest number of three digits = 999
Required product = 9999 x 999
= 9999 x (1000 – 1)
= 9999 x 1000 – 9999 x 1 (using distributivity)
=(10000-1) x1000 – (10000-1) x 1
= 10000 x 1000 –1 x 1000 – 10000 + 1
= 10000000 – 1000 – 10000 + 1
= 10000001 – 11000
= 9989001
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Question 122 Marks
(16 – 8) x 24 = _________ = _______
16 x 24 – 8 x 24 =_______ – ______ = _______
Is (16 – 8) x 24 = 16 x 24 – 8 x 24 ? ________
Is the type of result always true ? ________
Name the property used here _________
Answer
16 – 8) x 24 =8 x 24=192
16 x 24 – 8 x 24 =384192=192
Is (16 – 8) x 24 = 16 x 24 – 8 x 24 ?Yes.
Is the type of result always true ?Yes
Name the property used hereDistributivity.
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Question 132 Marks
12 x (9 – 6) = _______ = ________
12 x 9 – 12 x 6 = ________ = _________
Is 12 x (9 – 6) = 12 x 9 – 12 x 6 ? _______
Is this type of result always true ? ______
Name the property used here _______
Answer
12 x (9-6)=12 x 3=36
12 x 9- 12 x 6 =108 – 72=36
Is 12 x (9 – 6) = 12 x 9 – 12 x 6 ?=Yes
Is this type of result always true ?Yes
Name the property used hereDistributive property.
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Question 142 Marks
Consider two whole numbers a and b such that a is greater than b.
(i) Is a – b a whole number ? Is this result always true ?
(ii) b-a a whole number ? Is this result always true ?
Answer
Let us take a as 2 and has 1
(i) a – b = 2 – 1 = 1,
Yes, a – b is a whole number and the result will always remain the same.
(ii) b – a = 1 – 2 = -1
No, a – b can never be a whole number. Yes, the result always be true.
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Question 152 Marks
Which property of addition is satisfied by :
8 x (8 + 0) = 8 x 8 + 8 x 0
Answer
8 x (8 + 0) = 8 x 8 + 8 x 0
8 x (8 + 0) = 8 x 8 = 64
and 8 x 8 + 8 x 0 = 64 + 0 = 64
The property used as Distributive property over addition satisfied by 64.
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Question 162 Marks
Represent the following whole numbers on a number line :
0, 3, 5, 8, 10
Answer
$
\text { Number line used to represent whole numbers } 0,3,5,8,10 \text { is as given below: }
$
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[2 Mark Question Answer] - MATHS STD 6 Questions - Vidyadip