ICSE Board Practice

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ICSE Grade X - Problems on Quadratic Equations
Question 1
1.
    • One pipe can fill a cistern in
    • 2
    • hours less than the other.
    • The two pipes together can fill it in
    • 7
      7
      15
    • hrs.
    • Find the time that each pipe will take to fill the cistern.
  • 16 hr , 18 hr
  • 13 hr , 15 hr
  • 14 hr , 16 hr
  • 15 hr , 17 hr
  • 11 hr , 13 hr
Question 2
2.
    • 60 is divided into two parts such that the sum of their reciprocals is
    • 15
      224
    • .
    • Find the two parts
  • (
    26
    ,
    34
    )
  • (
    28
    ,
    32
    )
  • (
    30
    ,
    30
    )
  • (
    27
    ,
    33
    )
  • (
    29
    ,
    31
    )
Question 3
3.
    • The sum of the numerator and denominator of a fraction is
    • 12
    • .
    • If
    • 6
    • is added to both the numerator and denominator,
    • the fraction is increased by
    • 4
      15
    • . Find the fraction
  • 5
    9
  • 3
    9
  • 3
    7
  • 1
    9
  • 9
    3
Question 4
4.
A two digit number is such that the product of the digits is 12. When 36 is subtracted from the number, the digits are reversed. Find the number
  • 65
  • 61
  • 59
  • 63
  • 62
Question 5
5.
Find two natural numbers which differ by 7 and the sum of whose squares is 4537
  • (
    41
    ,
    49
    )
  • (
    44
    ,
    51
    )
  • (
    43
    ,
    50
    )
  • (
    45
    ,
    52
    )
  • (
    46
    ,
    53
    )
Question 6
6.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 32 . Find the three numbers.
  • 10, 11, 12
  • 8, 9, 10
  • 5, 6, 7
  • 6, 7, 8
  • 7, 8, 9
Question 7
7.
    • Find the number which exceeds its reciprocal by
    • 16
      16
      17
  • 16
  • 17
  • 18
  • 15
  • 20
Question 8
8.
The perimeter of a rectangular room is 70.00 m and the length of its diagonal is 26.40 m . Find the dimensions of the room
  • 22.00 m , 13.00 m
  • 23.00 m , 12.00 m
  • 26.00 m , 9.00 m
  • 24.00 m , 11.00 m
  • 25.00 m , 10.00 m
Question 9
9.
    • The denominator of a fraction exceeds the numerator by
    • 2
    • .
    • The square of the fraction is equal to
    • 25
      49
    • . Find the fraction
  • 5
    7
  • 1
  • 5
    9
  • 3
    7
Question 10
10.
Twice the square of a number exceeds 2 times the number by 312. Find the number
  • (-11)
  • (-14)
  • (-9)
  • (-12)
  • (-13)