$CATEGORY: Maths - TicTacLearn/1. Real Numbers/1. Real Numbers--Euclid's Division Lemma

//Multiple Choice

The Euclid’s division lemma states that for any positive integers a and b there exist unique integers q and r such that a \= bq + r, where r must satisfy\: {
~ 1 < r < b
~ 0 < r ≤ b
= 0 ≤ r < b
~ 0 < r < b
}

The  HCF of 78 and 980 is {
= 2
~ 1
~ 4
~ None of the above
}

The HCF of 250 and 75 is {
~ 1
~ 5
= 25
~ None of the above
}

Find the HCF of 81 and 675 using the Euclidean division algorithm. {
~ 9
~ 5
= 27
~ None of the above
}

HCF of 225 and 867 is {
~ 3
~ 5
~ 1
~ None of the above
}

HCF of 196 and 38220 is {
~ 4
= 196
~ 200
~ None of the above
}

//True or False

The Euclid’s Division Lemma gives the relation between the various components of Division. {T}

The HCF of 4052 and 12576 is 4 {T}

The HCF   of 136, 170 and 255 using Euclid’s Division Algorithm is 25 {F}

The HCF of 240, 260, 370 using Euclid's Algorithm is 20 {T}

HCF of 65 and 117 based on Euclid’s algorithm is 13 {T}

//Numericals

Find the HCF of 56 and 24 by using Euclid’s Division Lemma {
= 8
~ 10
~ 12
~ None of the above
}

Verify  Euclid’s Division Lemma for a\=17 and b\=5 {
= Euclid's Division Lemma holds true
~ Euclid's Division Lemma is false
~ Not applicable
~ None of the above
}

Ramu empties the water from two water tanks of  420 litres and 130 litres by using the mug. What is the maximum capacity of the mug he should use so that no water remains in the tanks? {
= Maximum capacity of mug is 10 litres
~ Maximum capacity of mug is 20 litres
~ Maximum capacity of mug is 5 litres
~ Maximum capacity of mug is 15 litres
}

//Fill in the blanks

In the Euclid’s Division Lemma if we have___ a and b, then there exist unique integers q and r which satisfy the condition  a \= bq + r where 0 ≤ r < b. {
~ Two whole numbers
= Two positive integers
~ Two prime numbers
~ None of the above
}

The basis of the Euclidean division algorithm is_____.  {
= Euclid’s division lemma
~ Pythagoras Theorem
~ Prime factorization
~ All of the above
}

The Euclid’s division algorithm is used to calculate the _____ of two positive integers a and b. {
~ LCM
= HCF
~ LCM and HCF
~ LCM or HCF
}

HCF is the largest number which exactly divides two or more positive integers. That means, on dividing both the integers a and b the remainder is _____. {
~ One
~ Infinity
= Zero
~ None of the above
}

HCF of 196 and 38,220  is _____ {
~ 197
~ 200
= 196
~ None of the above
}

HCF of 4052 and 12576 is _____ {
~ 4
~ 3
~ 2
= 1
}

HCF of 867 and 225 is _____ {
= 3
~ 2
~ 1
~ None of the above
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Euclid’s Division Lemma -> a \= bq + r, 0 ≤ r < b
=HCF of 867 and 225 -> 3
=HCF of 196 and 38,220 -> 196
=HCF of 4052 and 12576 -> 4
}



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