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# Author: Class of Achievers

## The mean of 10 numbers is 12.5. The mean of first six numbers is 15 and the mean of last five numbers is 10. Find the sixth number.

## Triangle ABC is right angled at C. If p is the length of the perpendicular from C to AB and a, b, c are the lengths of the opposite angles A, B and C respectively then prove that 1/p^2 = 1/a^2 + 1/b^2.

## While teaching about the Indian national flag, the teacher asked the students how many are there in a blue colour wheel? One student replied that it is 8 times the number of colours in the flag. While the other says the sum of the number of colour in the flag and number of lines in the wheel of the flag is 27. Convert the statements given by the students into linear equations of two variables and find the number of lines in the wheel.

## On a highway two places A and B are 120 km apart. A car from A and a second car from B start at the same time. If the cars travel in the same direction at different speeds, they meet in 6 hours, however if they travel towards each other, then they meet in 1 hour. What are their speeds?

## If the mth term of A.P. be 1/n and its nth term be 1/m, then show that its (mn)th term is 1.

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