ICSE Class X: Important Questions of Maths - SOLVED (2010)

Quadratic Equations

Q. 1. Find the length of a diagonal of a square whose sides are 10 m long. Give an exact answer and an approximation to two decimal places.

Ans: 14.14 meter 

Q. 2. The hypotenuse of a right triangle has a length of 13 cm. The sum of the lengths of the two legs is 17 cm. Find the lengths of the legs.

Ans: 5 and 12 cm

Q. 3.The area of a rectangle is 180 square meters. If the rectangle's length is increased by 3 meters and the width is decreased by 2 meter, its area does not change. Find the perimeter of the original rectangle.

Ans: Length = 15  and  Width = 12

Q. 4.If from the square of a number, five times the number is subtracted we get 50, what is the number?

Ans: -5  

Q. 5.The sum of 2 digits of a number is 9. The sum of the squares of the digits is 5/7 of the number itself. Find the number

Ans: 63

Q. 6.Find two Consecutive odd integers whose product is 1599

Ans: 39 and 41

 Q. 7.A rectangular playing ground is twice as long as it is wide, If both dimensions are increased by 4 m, the area is increased by 88 sq m. Find the dimension of the original ground 

Ans: 6 m  by 12 m

Q. 8.Find two consecutive odd positive integers, sum of whose squares is 290.

Ans: 11 and 13.

Q. 9. A rectangular garden is to be designed whose breadth is 3 m less than its length. Its area is to be 4 sqm more than the area of a garden that has already been made in the shape of an isosceles triangle with its base as the breadth of the   rectangular garden and of altitude 12 m. find its length and breadth.

Ans: 4.

Q. 10. The sum of a number and its square is 90. Find the number.

Ans: –10   or 9.

 Q. 11. A two-digit number is such that the product of digits is 8. When 18 is added   to it, they interchange their places. Determine the number.

Ans: 24

Q. 12. The age of the father is square of the age of his daughter. 15 years later, the father is double as old as daughter. Find their present ages.

Ans: D=  5 yrs  and F=25  yrs

Q. 13. The sum of a number and its square is 90. Find the number.

Ans: –10   or 9.

Q. 14. Sum of the squares of 3 consecutive numbers is 194. Find them.

Q. 15. The product of two consecutive odd numbers is 323. Find them.

Q. 16. The perimeter of a rectangle is 36 cm and its area is 80 sq.cm. Find its dimensions.

Q. 17. The area of a rectangular land is 240 m2. If 8 m is decreased from its length it will become a square. Determine the length and breadth of the land.

Q. 18. The sides of a right angle triangle are (x – 1.8) cm, (x + 1.8) cm and (x + 1) cm. Find the area of the triangle.

Q. 19. The sum of ages of a father and the son is 45 years. Five years hence the product of their ages will be 600. Find their present ages.

Q. 20. The product of age of a man, 6 years before, and 10 years later is 960. Find his present age.

Q. 21. Five times a certain number is equal to three less than twice the square of the number. Find the number.

Q. 22. Find two consecutive positive even integers whose product is 224.

Q. 23. The length of a verandah is 3 m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Find the length and breadth of the verandah.

Q. 24. In a class of 60 students, each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys. If the total contribution then collected is Rs.1600. How many boys are there in the class?

Q. 25. In a flowerbed, there are 23 rose plants in the first row, 19 in the second, 15 in the third, and so on. There are 7 rose plants in the last row. How many rows are in the flowerbed?

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