Real Numbers Important Questions Solve the following pair of linear equations: x/a – y/b =0, a x + b y = a2 + b2 Read More » Solve the following pair of linear equations: (a – b)x + (a + b)y = a2 – 2ab -b2, (a +b) (x + y) = a2 + b2 Read More » Solve the following pair of linear equations: 152x – 378y = -74, -378 x + 152y = -604 Read More » Solve the following pair of linear equations: ax + by = c, bx + ay = 1 + c Read More » Solve the following pair of linear equations: px + qy = p – q, qx – py = p + q Read More » Find two consecutive odd positive integers, the sum of whose squares is by using the quadratic formula. Read More » Find the HCF of 506 and 1155. Read More » Find the LCM and HCF of 404 and 96 and verify that LCM x HCF = product of the two numbers.120. Read More » ABCD is a rectangle if the value of AB=12 is given. Find the values of x and y. Read More » Mrs. Gupta arranged some snacks for her child’s birthday party. After the guest left she had some food left over. She did not want to waste food and so she contacted a local NGO. She gave 60 pieces of pastries,168 pieces of cookies, and 330 chocolate bars to the team. Now the NGO workers want to make the maximum number of packets with those foods so that no food is left for distributing to the beggars at the roadside. Find the greatest number of packets that they can make. Read More » A number consists of two digits. Where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number. Read More » Solve for x and y : x / 2 + 2y / 3 = − 1; x − y / 3 = 3 Read More » Prove that 3 root 2 is an irrational number. Read More » Find the greatest 3-digit number which is divisible by 18, 24 and 36. Read More » A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number. Read More » 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 »

Solve the following pair of linear equations: (a – b)x + (a + b)y = a2 – 2ab -b2, (a +b) (x + y) = a2 + b2 Read More »

Find two consecutive odd positive integers, the sum of whose squares is by using the quadratic formula. Read More »

Find the LCM and HCF of 404 and 96 and verify that LCM x HCF = product of the two numbers.120. Read More »

Mrs. Gupta arranged some snacks for her child’s birthday party. After the guest left she had some food left over. She did not want to waste food and so she contacted a local NGO. She gave 60 pieces of pastries,168 pieces of cookies, and 330 chocolate bars to the team. Now the NGO workers want to make the maximum number of packets with those foods so that no food is left for distributing to the beggars at the roadside. Find the greatest number of packets that they can make. Read More »

A number consists of two digits. Where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number. Read More »

A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number. 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 »