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#### Real Number System Important Questions

8th Standard

Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 50
10 x 1 = 10
1. The additive inverse of $\frac { -3 }{ 5 }$ is __________ .

(a)

$\frac { -3 }{ 5 }$

(b)

$\frac { 5 }{ 3 }$

(c)

$\frac { 3 }{ 5 }$

(d)

$\frac { -5 }{ 3 }$

2. ________ has no reciprocal.

(a)

0

(b)

1

(c)

-1

(d)

$\frac {1}{4}$

3. The multiplicative inverse of 2-4 is

(a)

2

(b)

4

(c)

24

(d)

-4

4. (-2)-2 is equal to

(a)

$\frac{1}{2}$

(b)

$\frac{1}{4}$

(c)

$\frac{-1}{2}$

(d)

$\frac{-1}{4}$

5.  $\frac { 2 }{ 5 } \times \frac { 4 }{ 7 } =$ ____________

(a)

$\frac { 14 }{ 20 }$

(b)

$\frac { 8 }{ 35 }$

(c)

$\frac { 20 }{ 14 }$

(d)

$​​\frac { 35 }{ 8 }$

6. $\left( 1-\frac { 1 }{ 2 } \right) +\left( \frac { 3 }{ 4 } -\frac { 1 }{ 4 } \right)$

(a)

0

(b)

1

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 3 }{ 4 }$

7. Which of the following numbers is a perfect cube?

(a)

125

(b)

36

(c)

75

(d)

100

8. The number of zeros at the end of the cube of 100 is

(a)

1

(b)

2

(c)

4

(d)

6

9. Which of the following is false?

(a)

Cube of any odd number is odd.

(b)

A perfect cube does not end with two zeros.

(c)

The cube of a single digit number may be a single digit number.

(d)

There is no perfect cube which ends with 8.

10. Find the smallest number by which the number 108 must be multiplied to obtain a perfect cube

(a)

2

(b)

3

(c)

4

(d)

5

11. 10 x 2 = 20
12. Simplify: $\left( 1\frac { 1 }{ 3 } +\frac { 2 }{ 3 } \right) \times \frac { 8 }{ 15 }$

13. By observing the unit’s digits, which of the numbers 3136, 867 and 4413 can not be perfect squares?

14. Simplify: ${ \left( \frac { 3 }{ 2 } \right) }^{ 5 }$

15. Find the value of the following:
34 x 3-3

16. Find the value of the following:
${ \left( \frac { 3 }{ 8 } \right) }^{ 5 }\times { \left( \frac { 3 }{ 8 } \right) }^{ 4 }\div { \left( \frac { 3 }{ 8 } \right) }^{ 9 }$

17. Find the square root of 529 using long division method.

18. Simplify:
$\frac { { \left( { 2 }^{ 2 } \right) }^{ 3 } }{ { \left( { 3 }^{ 2 } \right) }^{ 2 } }$

19. Find the value of the following :
(-4)3

20. Find the cube root of 512.

21. Is 250 a perfect cube? If not, then by which smallest natural number should 250 be divided so that the quotient is a perfect cube?

22. 10 x 3 = 30
23. Name the property under addition used in each of the following :
$\frac { 4 }{ 9 } +\left( \frac { 7 }{ 8 } +\frac { 1 }{ 2 } \right) =\left( \frac { 4 }{ 9 } +\frac { 7 }{ 8 } \right) +\frac { 1 }{ 2 }$.

24. Name the property under multiplication used in each of the following:
$\frac { 2 }{ 7 } \times \left( \frac { 9 }{ 10 } +\frac { 2 }{ 5 } \right) =\frac { 2 }{ 7 } \times \frac { 9 }{ 10 } +\frac { 2 }{ 7 } \times \frac { 2 }{ 5 }$.

25. Use distributive property of multiplication of rational numbers and simplify:
$\frac { -5 }{ 4 } \times \left( \frac { 8 }{ 9 } +\frac { 5 }{ 7 } \right)$

26. Find the value of m for which
8m-3 = 1

27. Simplify: $\frac { 11 }{ 12 } \div \left( \frac { 5 }{ 9 } \times \frac { 18 }{ 25 } \right)$

28. Write down the unit digits of the following:
(i) 782
(ii) 272
(iii) 412
(iv) 352
(v) 422

29. Using the given pattern, find the missing numbers:
12 + 22 + 2 2 = 32
23 + 32 + 62 = 72
32 + 42 + 122 = 132
42 + 52 + ___ = 212
52 + ___ + 302 = 312
62 + 72 + ___ = ___

30. Find the square root of the following :$\frac{9}{64}$

31. Find the square root of the following numbers by the factorization method :
5929

32. Write the approximate value of the following numbers to the accuracy stated:
3576274 to the nearest Lakhs.