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.