Free Printable Real Numbers

1.

Which of the following is non-terminating decimal

a)

1/2

b)

12/5

c)

17/14

d)

9/10

2.

The product of a non-zero rational and an irrational numbers is

a)

Always irrational

b)

Always rational

c)

Rational r irrational

d)

1

3.

Which of the following is not a terminating decimal

a)

23/32

b)

41/75

c)

41/50

d)

23/2³5²

4.

What will be the least possible number of the planks, if three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length?

a)

20

b)

21

c)

22

d)

23

5.

Three sets of physics, chemistry and mathematics books have to be stacked in such a way that all the books are stored topic wise and the number of books in each stack is the same. The number of physics books is 192, the number of chemistry books is 240 and the number of mathematics books is 168. Determine the number of stacks of physics, chemistry and mathematics books

a)

8,10,7

b)

8,8,8

c)

7,10,8

d)

10,8,7

6.

Two tanks contain 504 and 735 litres of milk respectively. Find the maximum capacity of a container which can measure the milk of either tank an exact number of times.

(a)

7.

$\sqrt{3\ -\ 2\sqrt{2}}$ is

a)

$\sqrt{2}+1$

b)

$\sqrt{2}-1$

c)

2

d)

1

8.

The simplest rationalizing factor of $\sqrt{3}+\sqrt{5}$ is

a)

$\sqrt{3}+\sqrt{5}$

b)

$\sqrt{3}-\sqrt{5}$

c)

1

d)

none of these

9.

If x is a positive integer, then any one of x, x+2, x+4 is divisible by (a) .

10.

If n is an odd positive integer, then n² - 1 is divisible by (a)

11.

A circular field has a circumference of 360 km. Two cyclists Peter and John start together and can cycle at speeds of 12 km/h and 15 km/h, respectively, round the circular field. The time taken by them to meet again at the starting point is

a)

(a) 180 hrs

b)

(b) 120 hrs

c)

(c) 150 hrs

d)

(d) 130 hrs

12.

The traffic lights at three different road-crossing change after every 36 seconds, 60 seconds and 72 seconds. If they change simultaneously at 8 am, after what time will they change again simultaneously ?

a)

LCM ( 36,60,72)

b)

HCF ( 36,60, 72)

c)

NONE OF THE ABOVE

13.

If a= 2³x 3, b= 2 x 3 x 5, c = 3ⁿx 5 and LCM(a,b,c) =2³x 3²x 5, then n =

a)

1

b)

2

c)

3

d)

4

14.

There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. The total number of sections thus formed is:

a)

22

b)

16

c)

36

d)

42

15.

$Can\ \ a\ number\ \ of\ a\ form\ \ 4^nend\ in\ ‘0’?$

a)

Yes

b)

No

c)

Sometimes yes sometimes no

d)

None of these

16.

Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for the first time?

a)

12:20

b)

12:11

c)

12:12

d)

none of these

17.

Rahul has 40 cm long red and 84 cm long blue ribbon. He cuts each ribbon into pieces such that all

pieces are of equal length. What is the length of each piece?

a)

4 cm as it is the LCM of 40 and 84

b)

4 cm as it is the HCF of 40 and 84

c)

8 cm as it is the LCM of 40 and 84

d)

8 cm as it is the HCF of 40 and 84

18.

Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All

three flash together at 8:00 am. At what time will the three bulbs flash altogether again?

a)

9:00 am

b)

9:12 am

c)

10:00 am

d)

10:12 am

19.

What will be the least possible number of the planks, if three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length?

a)

5

b)

6

c)

7

d)

None

20.

Eason is making activity baskets to donate to charity. She has 12 coloring books and 36 crayons. The greatest number of baskets she can make if each type of toy is equally distributed among the baskets is

a)

2

b)

12

c)

36

d)

6

21.

How many number of positive integers n are there for which $\sqrt[]{n-1}+\sqrt[]{n+1}$ is a rational?

a)

0

b)

1

c)

2

d)

Infinite

22.

Two runners P and Q stop after 3 hrs and 5 hrs respectively while running. After ab hours (where ab is a two digit number) both of them will pause together for the first time, if they started running at the same time. Find the value of a + b

a)

8

b)

3

c)

5

d)

6

23.

Find the HCF of the first 1000 even natural numbers.

a)

2

b)

1000

c)

2000

d)

4000

24.

For any positive integer a, $a^3-a$ is divisible by

a)

2

b)

6

c)

4

d)

none

25.

There is a number $6^n$ , where n is a natural number. Check if there is any value of n ∈ N exists, for which $6^n$ is divisible by 7.

a)

7

b)

14

c)

1

d)

No value of n

26.

Find a number which is greater than 3 and when it gets divided by 4, 5 and 6 always leaves 3 as remainder

a)

7

b)

8

c)

9

d)

63

27.

If the L.C.M and H.C.F of two numbers are 168 and 28 respectively, then find the number of possible such pairs.

a)

0

b)

1

c)

2

d)

3

28.

Find the value of n, if the HCF of 65 and 117 is expressed as 65n – 117.

a)

0

b)

1

c)

2

d)

3

29.

If $a$ is a rational number, then $5^{2a}-2^{2a}$ is divisible by

a)

both 3 & 7

b)

9

c)

3 only

d)

none

30.

The number $3^{13}-3^{10}$ is not divisible by:

a)

2

b)

3

c)

13

d)

5

31.

The number $10^A-1$ is divisible by 11 for,

a)

All value of A

b)

Even value of A

c)

Odd values of A

d)

A must be a multiple of 11

32.

Find the largest number which will divide 398, 436 and 542 and leave 7, 11 and 15 as remainders, respectively

a)

17

b)

16

c)

20

d)

19

33.

The sum of three consecutive even numbers is always divisible by

a)

4

b)

3

c)

2

d)

12

34.

Find the unit's digit of ( $9^0+9^1+9^2+9^3+......+9^{2009}.$ )

a)

9

b)

5

c)

0

d)

7

35.

Find the greatest number which when divides 969 and 2059, leaves remainder as 9 and 11 respectively

a)

118

b)

64

c)

32

d)

124

Real Numbers - II

Total questions: 35

Worksheet time: 18mins

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