Real Numbers - Ncert Solutions for Class 10 Maths CBSE

Chapter 1 - Real Numbers Excercise Ex. 1.1Solution 1(i) 135 and 225 Step 1: Since 225 > 135, apply Euclid's division lemma, to a =225 and b=135 to find q and r such that 225 = 135q+r, 0 r<135 On dividing 225 by 135 we get quotient as 1 and remainder as 90 i.e 225 = 135 x 1 + 90 Step 2: Remainder r which is 90 0, we apply Euclid's division lemma to b =135 and r = 90 to find whole numbers q and r such that 135 = 90 x q + r, 0 r<90On dividing 135 by 90 we get quotient as 1 and remainder as 45i.e 135 = 90 x 1 + 45Step 3: Again remainder r = 45 0 so we apply Euclid's division lemma to b =90 and r = 45 to find q and r such that 90 = 90 x q + r, 0 r<45On dividing 90 by 45 we get quotient as 2 and remainder as 0 i.e 90 = 2 x 45 + 0Step 4: Since the remainder is zero, the divisor at this stage will be HCF of (135, 225). Since the divisor at this stage is 45, therefore, the HCF of 135 and 225 is 45. (ii) 196 and 38220Step 1: Since 38220 > 196, apply Euclid's division lemmato a =38220 and b=196 to find whole numbers q and r such that 38220 = 196 q + r, 0 r < 196On dividing 38220 we get quotient as 195 and remainder r as 0 i.e 38220 = 196 x 195 + 0Since the remainder is zero, divisor at this stage will be HCF Since divisor at this stage is 196 , therefore, HCF of 196 and 38220 is 196.NOTE: HCF( a,b) = a if a is a factor of b. Here, 196 is a factor of 38220 so HCF is 196. (iii) 867 and 255 Step 1: Since 867 > 255, apply Euclid's division lemma, to a =867 and b=255 to find q and r such that 867 = 255q + r, 0 r<255On dividing 867 by 255 we get quotient as 3 and remainder as 102i.e 867 = 255 x 3 + 102 Step 2: Since remainder 102 0, we apply the division lemma to a=255 and b= 102 to find whole numbers q and r such that 255 = 102q + r where 0 r<102On dividing 255 by 102 we get quotient as 2 and remainder as 51 i.e 255 = 102 x 2 + 51Step 3: Again remainder 51 is non zero, so we apply the division lemma to a=102 and b= 51 to find whole numbers q and r such that 102 = 51 q + r where 0 r < 51 On dividing 102 by 51 quotient is 2 and remainder is 0i.e 102 = 51 x 2 + 0Since the remainder is zero, the divisor at this stage is the HCFSince the divisor at this stage is 51,therefore, HCF of 867 and 255 is 51. Concept Insight: To crack such problem remember to apply the Euclid's division Lemma which states that "Given positive integers a and b, there exists unique integers q and r satisfying a = bq + r, where 0 r < b" in the correct order. Here, a > b. Euclid's algorithm works since Dividing 'a' by 'b', replacing 'b' by 'r' and 'a' by 'b' and repeating the process of division till remainder 0 is reached, gives a number which divides a and b exactly. i.e HCF(a,b) =HCF(b,r)Note that do not find the HCF using prime factorisation in this question when the method is specified and do not skip steps.

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MASTER IN CURRENT AFFAIRS "DECEMBER 2018" (HINDI) INPORTANT FOR SSC,BANK, RAILWAY NTPC ,GROUP D, ETC

We feel immense pleasure in bringing the 'December 2018' edition of our very own 'Masters in Current Affairs', a platform where you get all the exam related information at a single place. It is designed especially for the forthcoming examinations. Its regular sections such as News Maker, News Diary, One-liners etc. cover each and every news in details which is important for examinations. Rest of the news are covered in 'Chalte - Chalte' i.e. one-liner news, which you can find at the bottom of each page. Some important issues of this month were discussed in featured articles. One among them is ‘#Me too MOVEMENT’, with many local and international alternatives, is a movement against sexual harassment and sexual assault.#MeToo spread virally in October 2017 as a hashtag used on social media in an attempt to demonstrate the widespread prevalence of sexual assault and harassment, especially in the workplace. The #MeToo campaign helped women from all around the world in throwing light on sexual abuse. Not only that, it also gave women the opportunity to support each other, to empower themselves and to have a chance to talk about a serious issue that usually remains in the dark. And all the minute details are mentioned inside. Then an article about ‘END OF SECTION 497 ‘, The Supreme Court's decision to scrap Section 497 of the Indian Penal Code, thereby decriminalising adultery, cannot be seen as a cheer for promiscuity. The fact is that adultery won't get any less harmful for marriage just because it no longer comes under the purview of being a criminal act. On the contrary, the psychological damage to a marriage is mutually exclusive from legal fiat. The law cannot re-ignite the dying embers of a marriage scorched by suspicion and much more is given the whole article. Later we’ll see ‘RUPEE CRISIS’, as INDIA could be braced to see its financial troubles deepen, with the rupee languishing even further before stabilizing against the US dollar, according to an economic analyst. The rupee has been crippled by soaring oil prices and higher interest rates, with the crisis-hit currency losing around 15 percent of its value versus the American tender. The Indian currency breached the 74-mark for the first time ever against the US dollar this month, but the worst could still be yet to come for the rupee. And all the other important details are mentioned inside. And an article about ‘NOBLE PRIZE 2018’, The Nobel Prize in Physics 2018 was awarded “for groundbreaking inventions in the field of laser physics” with one half to Arthur Ashkin “for the optical tweezers and their application to biological systems” and the other half jointly to Gérard Mourou and Donna Strickland “for their method of generating high-intensity, ultra-short optical pulses” and much more in the article given inside. In this edition, we are providing the complete solution of IBPS CLERK (PRE) 2018 and CDS MODEL PAPER for your self-assessment. There is a separate section named Que.-TM for your self-evaluation, which includes all the possible MCQ's from this month's current affairs. This will be highly beneficial for all the upcoming examinations. Your advice or suggestions will be much appreciated and welcomed.

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