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Class 6
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Maths
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Whole Numbers
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Hard Questions
Whole Numbers
Maths
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Study the following statements.
Statement-1: Addition and multiplication are commutative for whole numbers.
Statement-2: Division of whole numbers is distributive over addition.
Which of the following options hold?
A
Both Statement-1 and Statement-2 are true.
B
Statement-1 is true but Statement-2 is false.
C
Statement-1 is false but Statement-2 is true.
D
Both Statement-1 and Statement-2 are false.
Hard
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In whole numbers, closure property is not satisfied with respect to operations _____.
A
(+,
$÷$
)
B
(+, x)
C
(-, x)
D
(-,
$÷$
)
Hard
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Prove that any integer
$a≥7$
is the sum of two relatively prime integers. (We say two integers
$m$
and
$n$
are relatively prime if their HCF (i.e., GCD) is
$1$
)
Hard
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Which of the following statements is correct?
A
Subtraction is commutative for integers.
B
Division is associative for rational numbers.
C
Multiplication is not associative for whole numbers.
D
Addition is closed for natural numbers.
Medium
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Simplify the following using the rules for identities :
(i)
$28×32$
(ii)
$102×98$
Hard
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Which of the following operations satisfies the associative law for whole numbers?
A
Subtraction and division
B
Subtraction and multiplication
C
Division and multiplication
D
Addition and multiplication
Hard
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>
(25 x 22) x 25 = 25 x (22 x 25) is an example of property.
A
Commutative
B
Associative
C
Closure
D
Distributive
Hard
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>
Find the number of natural numbers less than
$1000$
and divisible by
$5$
can be formed with ten digit, each digit not occurring more than once in each number is.
Medium
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Prove that the fraction
$m(n+1)−nm(n+1)+1 $
is irreducible for every positive integers
$m$
and
$n$
.
Hard
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In a bangle shop, if the shopkeeper displays the bangles in the form of a square, he is left with
$38$
bangles. If he wants to increase the size of square by one unit each side of the square he found that
$25$
bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was .............. .
A
$1690$
B
$999$
C
$538$
D
Can't be determined
Hard
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