Real NumbersImportant Questions 23. Prove that 4 – 2 √5 is an irrational number given that √5 is irrational. Read More » 27. The dimensions of a window are 156 cm x 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed. Read More » 21 a. Prove that 2 + 3√5 is an irrational number given that √5 is an irrational number. Read More » 21 b. If the HCF of 210 and 55 is expressed as 210 × 5 + 55m, then find the value of m. Read More » 26. A trader has three different types of oils of volume 870 L, 812 L and 638 L. Find the least number of containers of equal size required to store all the oil without getting mixed. Read More » 24. Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time. Read More » 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 »
27. The dimensions of a window are 156 cm x 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed. Read More »
21 a. Prove that 2 + 3√5 is an irrational number given that √5 is an irrational number. Read More »
21 b. If the HCF of 210 and 55 is expressed as 210 × 5 + 55m, then find the value of m. Read More »
26. A trader has three different types of oils of volume 870 L, 812 L and 638 L. Find the least number of containers of equal size required to store all the oil without getting mixed. Read More »
24. Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time. 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 »
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