Find the LCM and HCF of 408 and 170 by applying the fundamental theorem of arithmetic.

Find the greatest number consisting of 6 digits which is exactly divisible by 24,15,36?

What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?

Find the least number that is divisible by the first ten natural numbers.

Find the remainders when 70004 and 778 is divided by 7

Prove that 2ⁿ + 6 x 9ⁿ is always divisible by 7 for any positive integer n,

Find the remainder when 2⁸¹ is divided by 17.

The duration of flight travel from Chennai to London through British Airlines is approximately 11 hours. The airplane begins its journey on Sunday at 23:30 hours. If the time at Chennai is four and half hours ahead to that of London’s time, then find the time at London, when will the flight lands at London Airport

In an A.P., sum of four consecutive terms is 28 and their sum of their squares is 276. Find the four numbers.

A mother divides Rs. 207 into three parts such that the amount are in A.P. and gives it to her three children. The product of the two least amounts that the children had Rs. 4623. Find the amount received by each child.

The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.

The ratio of 6^th and 8^th term of an A.P is 7:9 Find the ratio of 9^th term to 13^th term

In a winter season let us take the temperature of Ooty from Monday to Friday to be in A.P. The sum of temperatures from Monday to Wednesday is 0⁰ C and the sum of the temperatures from Wednesday to Friday is 18⁰ C. Find the temperature on each of the five days

Priya earned Rs.15,000 in the first month. Thereafter her salary increased by Rs. 1500 per year. Her expenses are Rs. 13,000 during the first year and the expenses increases by Rs. 900 per year. How long will it take for her to save Rs. 20,000 per month

Find the sum of 0.40 + 0.43 + 0.46 + ....+ 1

How many terms of the series 1 + 5 + 9 + ....must be taken so that their sum is 190?

The 13^th term of an A.P is 3 and the sum of the first 13 terms is 234.Find the common difference and the sum of first 21 terms.

Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

A mosaic is designed in the shape of an equilateral triangle, 12 ft on each side. Each tile in the mosaic is in the shape of an equilateral triangle of 12 inch side. The tiles are alternate in colour as shown in the figure. Find the number of tiles of each colour and total number of tiles in the mosaic.

The sum of first n, 2n and 3n terms of an A.P are S₁, S₂ and S₃ respectively prove that S₃ = 3 (S₂ - S₁)