Using Euclid’s division algorithm, check whether 231, 396 are co-prime or not. Justify your answer.
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State whether the following are true or false. Justify your answer.
False , the value if tan 60° = √3= 1.73 True, The value of sec A increase from 1 to ∞. False, Cos A is the abbreviation used for the cosine of angle...
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State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B.
Solution: (i) It is not true, in general. This relation is true for some particular values of A and B. For example, if A = 0 and B = 90, Then, Sin (A+B)...
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State whether each of the following statement is true or false. Justify your answer.
(i) False As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6} ⇒ {2, 3, 4, 5} ∩ {3, 6} = {3} (ii) False As a ∈ {a, e, i,...
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Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
Solution: No, every positive integer cannot be only of the form 4q + 2. Justification: Let a be any positive integer. Then by Euclid’s division lemma, we have a = bq + r, where...
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Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.
Solution: No. Justification: Let a be any positive integer. Then by Euclid’s division lemma, we have a = bq + r, where 0 ≤ r < b For b = 3, we have a = 3q...
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Use Euclid’s division algorithm to find HCF of 441, 567, 693.
Solution: By Euclid’s division algorithm, 693 = 567 x 1 + 126 567 = 126 x 4 + 63 126 = 63 x 2 + 0 So, HCF(441, 63) = 63 So, HCF (693, 567) =...
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Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.
Solution: Since, 1, 2 and 3 are the remainders of 1251, 9377 and 15628 respectively. So, 1251 – 1 = 1250 is exactly divisible by the required number, 9377 – 2 = 9375...
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Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
Correct answer is option (C) 0 ≤ r < b
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State whether each of the following statement is true or false. Justify your answer
(i) False As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6} ⇒ {2, 3, 4, 5} ∩ {3, 6} = {3} (ii) False As a ∈ {a, e, i, o, u}, a...
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Use Euclid’s algorithm to find the HCF of 4052 and 12576.
Since 12576 > 4052, we apply the division lemma to 12576 and 4052, to get 12576 = 4052 × 3 + 420 Since the remainder 420 ≠ 0, we apply the division...
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