Real Numbers Important Questions Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Read More » Can the number (15n), n being a natural number, end with the digit 0? Give reasons. Read More » If √2 is given as an irrational number, then prove that (5 – 2√2) is an irrational number. Read More » Check whether 6n can end with the digit 0 for any natural number n . Read More » In a 2-digit number, the digit at the unit’s place is 5 less than the digit Read More » The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number. Read More » Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational number. Read More » Show that the number 5×11×17+3×11 is a composite number Read More » In a teachers’ workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 Read More » Find the smallest number that is divisible by each of 8, 9 and 10. Read More » February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Read More » 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. 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 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 »

If √2 is given as an irrational number, then prove that (5 – 2√2) is an irrational number. Read More »

The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number. Read More »

In a teachers’ workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 Read More »

February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. 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 »

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 »

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 »