Mathematics For Class IX
Number Systems
(Q.1) If
(A) 216
(B) 198
(C) 192
(D) 261.
( 1 mark )
, then
( 1 mark )
is
(Q.2) The value of
(A)
(B)
(C)
(D)
(Q.3)
(A)
(B)
(C)
( 1 mark )
equals to
(D)
(Q.4) What is the sum of least and greatest number if
arranged in ascending order?
(A)
(B)
(C)
and
are
( 1 mark )
(D)
( 1 mark )
(Q.5)
is a
(A) negative rational number.
(B) positive rational number .
(C) either positive or negative rational number .
(D) neither positive nor negative rational number.
( 1 mark )
(Q.6)
is
(A) an rational number.
(B) irrational number.
(C) an integer.
(D) natural number.
( 1 mark )
(Q.7) The value of
is
(A) an irrational number.
(B) a terminating decimal.
(C) an integer.
(D) a natural whole number.
(Q.8) The rationalising factor of
is
( 1 mark )
(A)
(B)
(C)
(D)
(Q.9) Value of
is
( 1 mark )
(A)
.
(B)
.
(C)
.
(D)
.
(Q.10) Which of the following is not irrational?
(A)
(B)
(C)
(D)
( 1 mark )
(Q.11) In the given figure O is the centre of given semicircle and AB = x, BC =
y.
( 1 mark )
Then DB is
(A)
(B)
(C)
(D)
(Q.12) The greatest among
(A)
.
(B)
.
is
( 1 mark )
(C)
.
(D) none of these.
(Q.13) If both 'a' and 'b' are rational numbers, then 'a' and 'b' from the
( 1 mark )
following
are
(A)
(B)
(C)
(D)
( 1 mark )
(Q.14) The fraction
has a value equal to
(A)
(B) 1
(C)
(D)
(Q.15) The product of
(A)
(B)
and
is
( 1 mark )
.
.
(C)
.
(D) none.
(Q.16) What is the percentage of least number in the greatest number if
( 1 mark )
are arranged in ascending order?
(A)
(B) 10%
(C) 20%
(D) 25%
(Q.17) The average of the middle two rational numbers if
are
( 1 mark )
arranged in ascending order is
(A)
.
(B)
.
(C)
.
(D)
.
(Q.18) A rational number between
and
is
( 1 mark )
(A)
(B) 0.29
(C)
(D) all the above
(Q.19) Which of the following statement is true?
( 1 mark )
(A)
(B)
(C)
(D)
(Q.20) pie is
(A) rational
( 1 mark )
(B) irrational
(C) imaginary
(D) an integer
(Q.21) Arrange the following numbers in descending order:
( 1 mark )
(A)
(B)
(C)
(D)
, then x is
(Q.22) If
(A) a rational number .
( 1 mark )
(B) not a rational number.
(C) an integer
(D) a natural number
(Q.23) If
, then x is
(A) a rational number
(B) not a rational number
(C) an integer
(D) a natural number
( 1 mark )
( 1 mark )
(Q.24) If
, then x is
(A) a rational number
(B) not a rational number
(C) an integer
(D) a natural number
(Q.25) The value of
( 1 mark )
is
(A) 0
(B) 1
(C) 2
(D) 4
(Q.26) The value of
( 1 mark )
(A) 0
(B) 1
(C) 2
(D) 4
(Q.27) The irrational number between 2 and 3 is
(A)
(B)
(C)
(D)
(Q.28) The number
(A) rational number
(B) irrational number
(C) can't say
is
( 1 mark )
( 1 mark )
(D) none
(Q.29) Every Whole number is a Natural number. (True/False)
(Q.30) If
( 1 mark )
, then x is rational or irrational number
( 1 mark )
(Q.31) Insert three rational numbers between
( 1 mark )
(Q.32) Find two rational numbers between 1 and 2
(Q.33)
(Q.34) Is
( 1 mark )
( 1 mark )
is a terminating or non termination decimal number.
( 1 mark )
a rational number?
(Q.35) Every integer is a Rational Number.
( 1 mark )
(Q.36) Every rational number is an Integer.
( 1 mark )
(Q.37) Is
( 1 mark )
a rational number?
(Q.38) The product of
and
( 1 mark )
is
(Q.39) Is 2 a rational number? Can you write it in the form
, where p and q
( 1 mark )
are integers.
(Q.40) The greatest among
is
( 1 mark )
(Q.41)
Simplify
( 2 Marks )
(i)
(ii)
( 2 Marks )
(Q.42) Rationalize the denominator in
.
(Q.43) Rationalize the denominations of the following
( 2 Marks )
(i)
(ii)
( 2 Marks )
(Q.44) Simplify:
(Q.45) Find two irrational nos. between 2 ad 2.5 is
( 2 Marks )
(Q.46) Insert a rational & an irrational no. between 2 and 3.
( 2 Marks )
(Q.47) Identify
( 2 Marks )
as rational number or irrational number.
(Q.48) Give examples of two irrational numbers the product of which is:
i)
ii)
A rational number
An irrational number
(Q.49) Identify
as rational nos. between 2 ½ and 3.
( 2 Marks )
( 2 Marks )
(Q.50) Define an irrational no. Is 1.01001000100001 …… irrational? If so, why? ( 2 Marks )
(Q.51) How to insert irrational numbers between two given rational numbers.
( 2 Marks )
(Q.52) What can the maximum number of digits be in the repeating block of
( 2 Marks )
digits in division of
?
(Q.53) Express 0.99999 ………..in the form are you surprised by your answer?
( 2 Marks )
(Q.54) Find the decimal representation of:
(Q.55) Express
( 2 Marks )
in the decimal form of long division method.
( 2 Marks )
(Q.56) Find the three rational numbers between - 2 and 5.
( 2 Marks )
(Q.57) Insert 100 rational numbers between
( 2 Marks )
(Q.58) Insert 10 rational number between
(Q.59) Find five rational numbers between
( 2 Marks )
and
( 2 Marks )
(Q.60) Find six rational numbers between 3 and 4.
(Q.61) Is zero a rational number? Can you write it in the form
q are integers.
( 2 Marks )
, where p and
( 2 Marks )
(Q.62) Find five rational numbers between 1 and 2.
( 2 Marks )
(Q.63)
Are the following statements true on false? Give reasons for your answers
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
( 3 Marks )
(Q.64)
Rationalize the denominator of
(i)
( 3 Marks )
(ii)
(iii)
( 3 Marks )
(Q.65) Simplify:
(Q.66) Rationalize the denominators of the following:
(i)
( 3 Marks )
(ii)
(iii)
(Q.67) Represent
on the number line.
(Q.68) Visualize 3.765 on the number line using successive magnification.
( 3 Marks )
( 3 Marks )
(Q.69) Are the square roots of all the +ve integers are irrational? If not, give an ( 3 Marks )
example of the square root of a number that is a rational number.
(Q.70)
True or False Justify.
i)
Every irrational no. is a real number.
ii)
Every point on the no. Line is of the form
natural
number.
iii) Every real no. is an irrational number.
, where m is a
( 3 Marks )
(Q.71) Find three different irrational numbers between the rational numbers
( 3 Marks )
and
(Q.72) You know that
=
Can you predict what the decimal
( 3 Marks )
expansions of
are without actually doing the long
division? If so how?
(Q.73) Look at several examples of rational number in the
form
(
)
( 3 Marks )
where
and integers with no common factors other than 1 and having
terminating decimal representations. Can you guess what property must
satisfy?
(Q.74)
State whether the following statements are true or false. Give reasons for your
answers.
(i)
Every natural number is a whole number.
(ii)
Every integer is a whole number
(iii)
Every rational number is a whole number.
( 3 Marks )
(Q.75)
Simplify
(i)
( 4 Marks )
(ii)
(iii)
(iv)
(Q.76) Simplify
(i)
( 4 Marks )
(ii)
(Q.77) Simplify
(i)
( 4 Marks )
(ii)
(Q.78)
Rationalize the denominator of
(i)
( 4 Marks )
(ii)
(Q.79) Simplify
(i)
( 4 Marks )
(ii)
(Q.80)
Simplify
( 4 Marks )
(i)
(ii)
(Q.81)
Simplify
( 4 Marks )
(i)
(ii)
(Q.82) Construct the square root spinal.
( 5 Marks )
(Q.83) Represent
on the number line
( 5 Marks )
(Q.84) To represent
on a number line.
( 5 Marks )
(Q.85) To represent
on a number line.
( 5 Marks )
(Q.86)
Find:
(i)
( 6 Marks )
(ii)
(iii)
(Q.87)
Find
(i)
(ii)
(iii)
( 6 Marks )
(iv)
(Q.88) Simplify
(i)
( 6 Marks )
(ii)
(Q.89) Express the following in the form
, where p and q integers and q? 0.
(i)
(ii)
.
= 0.4777. (1)
( 6 Marks )
(iii)
(Q.90) Identify the following as rational or irrational number.
(i)
(ii)
0.020020002…
( 7 Marks )
(iii)
(iv)
(v)
(vi)
(vii)
0.10110111011110
0.375
22.3782378….
(Q.91)
Simplify
(i)
(ii)
(iii)
( 8 Marks )
(iv)
(Q.92) Examine, whether the following nos. are rational or irrational.
(i)
(ii)
( 8 Marks )
(iii)
(iv)
(Q.93)
Identify the following as rational or irrational number.
(i)
(ii)
0.020020002…
( 8 Marks )
(iii)
(iv)
(v) 0.10110111011110 ……
(vi) 0.375
(vii) 22.3782378….
(Q.94)
Classify the following numbers as rational or irrational.
(i)
(ii)
(iii)
(iv)
(v)
( 10 Marks )
0.3796, which is terminating
7.478478 …..., which is non- terminating and recurring.
1.1010010001 ……
(Q.95)
Write the following in decimal form and say what kind of decimal expansion each
has:
( 12 Marks )
(i)
(ii)
(iii)
(iv)
(v)
(vi)