$CATEGORY: Maths - TicTacLearn/1. Real Numbers/1. Real Numbers--Revisiting Irrational Numbers

//Multiple Choice

The Euclid's Division Lemma states that {
= a\=bq+r where 0 ≤  r < b
~ a\=bq+r where 0 < r  ≤b
~ a\=bq-r where 0 ≤  r < b
~ a\=bq+r where 0 ≤ r  ≤b
}

Which of the following is incorrect When a\=23 and b\=5, what is the value of r using Euclid's Division Lemma {
~ 23\=5*4+3
= 23\=5×5-2
~ 23\=5×4+3 where  0 ≤  r < 5
~ r\=3
}

Euclid's Division Lemma is used to find the ____ of two positive integers. {
~ Sum
~ Product
= HCF
~ LCM
}

If a\=50 and b\=8; what is the value of q and r are {
= q\=6 ; r\=2
~ q\=6 ; r\=3
~ q\=7 ; r\=3
~ q\=6 ; r\=4
}

The range in Euclid's Division Lemma is {
~ r>b
= 0 ≤ r <b
~ r <0
~ 0 < r ≤b
}

//True or False

The a\=20 and b\=6, then q\=3 and r\=3 satisfies Euclid's Division Lemma {F}

The remainder ( r) in Euclid's Division Lemma can be equal to b as per the theorem. {F}

The quotient (q) in Euclid's Division Lemma is always less than a {T}

Euclid’s Division Lemma is used to calculate the Highest Common Factor (HCF) of two numbers. {T}

In Euclid’s Division Lemma, the value of q is the quotient obtained when a is divided by b . {T}

The Euclid’s Division Lemma is applicable only to integers {T}

Euclid’s Division Algorithm is based on repeated application of Euclid’s Division Lemma. {T}

The Euclid’s Division Lemma can be used to express a as a multiple of b  only when  r\=0 {T}

//Numericals

If a\=17 and b\=5, find the remainder r when a is divided by b. {
= 2
~ 3
~ 4
~ 5
}

Using Euclid’s Division Lemma, find the HCF of 56 and 42 {
~ 7
= 14
~ 21
~ 28
}

Find q and r when 100 is divided by 9 {
~ q\=11 , r\=1
~ q\=10, r\=0
~ q\=12, r\=4
= q\=11; r\=2
}

If a\=48 and b\=7, express a in terms of b using Euclid’s Division Lemma. {
~ 48\=7×6+7
~ 48\=7×6+6
= 48\=7×6+1
~ None of the above
}

What is the HCF of 72 and 120 using Euclid’s Division Lemma. {
~ 12
~ 18
= 24
~ 36
}

//Fill in the blanks

Euclid’s Division Lemma states that for any two positive integers  a and b , there exist unique integers q  and  r such that a\=bq+r , where r is ____ {
= 0 ≤ r  <b
~ b ≤ r  <0
~ a≤ r  <b
~ None of the above
}

If a \=35 and b\=6 and q\=5 then r is \=____ as per Euclid’s Division Lemma Theorem. {
= 5
~ 4
~ 3
~ 2
}

The remainder r in Euclid's Division Lemma is always _____ than b. {
= Less
~ More
~ equal
~ None of the above
}

If b>a, then the remainder r is equal to _____ as per Euclid’s Division Lemma Theorem. {
~ b
= a
~ c
~ None of the above
}

Euclid's Division Lemma states that q is the _____ obtained when a is divided by b {
~ remainder
~ divisor
= quotient
~ None of the above
}

In Euclid’s Division Lemma, if r\=0 means that a is _____ divisible by b {
~ Partially
= Completely
~ Not
~ None of the above
}

The algorithm based on repeated application of Euclid’s  Division Lemma is called Euclid’s _____ {
~ Factorization
~ Pythagoras Theorem
= Division Algorithm
~ None of the above
}

If a\=50 and b\=7 then q\=_____ and r\=1 {
~ 50
= 7
~ 57
~ None of the above
}

Euclid’s  Division Lemma is applicable only to _____ numbers. {
~ Whole
~ Prime
= Integers
~ None of the above
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=a\=bq+r is used -> the basic equation of Euclid Division Lemma
=The remainder r in Euclid's Division Lemma is -> always less than b
=b>a -> r\=a
=Euclid’s Division Algorithm -> Process of repeated divisions
}



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