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Class 10
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Maths
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Real Numbers
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Hard Questions
Real Numbers
Maths
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Hard Qs
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Use Euclids division lemma to show that the cube of any positive integer is of the form
$9m,9m+1$
or
$9m+8.$
Hard
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>
Use Euclid's division lemma to show that the square of any positive integer is either of the form
$3m$
or
$3m+1$
for some integer m, but not of the form
$3m+2$
.
Hard
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>
The length and breadth of a rectangular field is 110 m and 30 m respectively. Calculate the length of the longest rod which can measure the length and breath of the field exactly.
Hard
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>
Show that any positive even integer is of the form
$4q$
or
$4q+2$
, where
$q$
is a whole number.
Hard
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>
There are 75 rose and 45 lily flowers. These are to be made into bouquets containing both the flowers. All the bouquets should contain the same number of flowers. Find the number of bouquets with maximum number of flowers that can be formed and the number of flowers in them.
Hard
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What is the greatest number which divides
$392,486$
and
$627$
so as to leave the same remainder in each case?
A
$47$
B
$43$
C
$37$
D
$34$
Hard
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>
Express
$3825$
as a product of prime factors
Hard
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>
Use Euclids division algorithm to find the HCF of:
(i)
$135$
and
$225$
(ii)
$196$
and
$38220$
(iii)
$867$
and
$225$
Hard
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>
Prove that the product of three consecutive positive integers is divisible by 6.
Hard
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>
Show that any positive odd integer is of the form
$6q+1$
, or
$6q+3$
, or
$6q+5$
, where
$q$
is some integer.
Hard
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>