Real NumbersImportant Questions The sum of the squares of three consecutive even numbers is 596. Find the numbers. Read More » In a workshop, the number of teachers of English, Hindi and Science are 36, 60 and 84 respectively. Read More » A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number. Read More » State true or false for each of the following statements and justify in each case:(i) 2 x 3 x 5 x 7 + 7 is a Read More » Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai Read More » Write the smallest number which is divisible by both 306 and 657. Read More » A part of monthly hostel charges is fixed and the remaining depends on the number of days Read More » A Mathematics Exhibition is being conducted in your School and one of your friends is making a model Read More » A seminar is being conducted by an Educational Organisation, where the participants will be educators Read More » To enhance the reading skills of grade X students, the school nominates you and two of your friends to Read More » Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Read More » Prove that (2-√3)/5 is an irrational number. It is given that √3 is an irrational number. Read More » Prove that (2 + √3) / 5 is an irrational number. It is given that √3 is an irrational number. Read More » In a school, there are two sections of class X. There are 40 students in the first section Read More » A 2-digit number is such that the product of its digits is 18. When 63 is subtracted Read More » Three bells ring at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together? Read More » The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m. Read More » Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method. Read More » The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers. Read More » Sum of two numbers is 105 and their difference is 45. Find the numbers. Read More » The denominator of a fraction is one more than twice the numerator. If the sum of the Read More » Teaching Mathematics through activities is a powerful approach that enhances students’ Read More » Can the number (8n), n being a natural number, end with the digit 0? Give reasons. Read More » 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 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, 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 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. 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 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 »
In a workshop, the number of teachers of English, Hindi and Science are 36, 60 and 84 respectively. Read More »
A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number. Read More »
State true or false for each of the following statements and justify in each case:(i) 2 x 3 x 5 x 7 + 7 is a Read More »
Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai Read More »
A part of monthly hostel charges is fixed and the remaining depends on the number of days Read More »
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model Read More »
A seminar is being conducted by an Educational Organisation, where the participants will be educators Read More »
To enhance the reading skills of grade X students, the school nominates you and two of your friends to Read More »
Prove that (√2 + √3)2 is an irrational number, given that √6 is an irrational number. Read More »
Prove that (2-√3)/5 is an irrational number. It is given that √3 is an irrational number. Read More »
Prove that (2 + √3) / 5 is an irrational number. It is given that √3 is an irrational number. Read More »
In a school, there are two sections of class X. There are 40 students in the first section Read More »
Three bells ring at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together? Read More »
The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers. Read More »
Teaching Mathematics through activities is a powerful approach that enhances students’ Read More »
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. 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 Read More »
Prove that 5-2√3 is an irrational number. It is given that √3 is an irrational 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 2-digit number is seven times the sum of its digits. The number formed by reversing the digits Read More »
The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 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 »
