A typist charges ₹ 145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are ₹ 180. Using matrices, find the charges of typing one English and one Hindi page separately. However, typist charged only ₹ 2 per page from a poor student Shyam for 5 Hindi pages. How much less charged from this poor boy? Which values are reflected in this problem?(CBSE 2016)

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award rs x each, ₹ y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with total award money of ₹ 1,600. School B wants to spend ₹ 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹ 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for the award.(CBSE 2014)

If a, b and c are all non-zero and , then prove that .(CBSE 2016)

A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2,800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interest. Using matrix method, find the amount invested by the trust. Interest received on this amount will be given to Help age India as donation. Which value is reflected in this question?(CBSE 2016)

Ishan wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by Using matrices, find the dimensions of the plot. Also, give a reason why he wants to donate the plot for a school.(CBSE 2016)