Real NumbersImportant Questions Solve 2 by root x + 3 by root y = 2 ; 4 by root x – 9 by root y = -1, x, y > o Read More » The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? Read More » National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same art form and the number of students in each group is the same. Read More » Prove that root 2 is an irrational number. Read More » The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next? Read More » Using prime factorisation, find HCF and LCM of 96 and 120. Read More » Prove that root 3 is an irrational number. Read More » Prove that root 5 is an irrational number. Read More » The two numbers are in the ratio of 2 : 3 and their LCM is 180. What is the HCF of the these numbers? Read More » Prove that 6 – root 7 is an irrational number, given that root 7 is an irrational number. Read More » Prove that 4^n can never end with digit 0, where n is a natural number. Read More » Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m., when will they ring together again? Read More » Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers. Read More » Prove that 2 + √3 is an irrational number, given that √3 is an irrational number. Read More » Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case. Read More » Prove that root 5 is an irrational number. Read More » Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively. Read More »

The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? Read More »

National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same art form and the number of students in each group is the same. Read More »

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next? Read More »

The two numbers are in the ratio of 2 : 3 and their LCM is 180. What is the HCF of the these numbers? Read More »

Prove that 6 – root 7 is an irrational number, given that root 7 is an irrational number. Read More »

Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a.m., when will they ring together again? Read More »

Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers. Read More »

Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case. Read More »

Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively. Read More »