#### Term 2 Real Numbers Book Back Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. Which of the following statement is false?

(a)

The square root of 25 is 5 or −5

(b)

$\sqrt{25}$=5

(c)

-$\sqrt{25}$=-5

(d)

$\sqrt{25}$=±5

2. $\left( 0.000729 \right) ^{ \frac { -3 }{ 4 } }\times \left( 0.09 \right) ^{ \frac { -3 }{ 4 } }$ = ______

(a)

$\frac { { 10 }^{ 3 } }{ { 3 }^{ 3 } }$

(b)

$\frac { { 10 }^{ 5 } }{ { 3 }^{ 5 } }$

(c)

$\frac { { 10 }^{ 2 } }{ { 3 }^{ 2 } }$

(d)

$\frac { { 10 }^{ 6 } }{ { 3 }^{ 6 } }$

3. Which is the best example of a number written in scientific notation?

(a)

0.5 x 105

(b)

0.1254

(c)

5.367 x 10-6

(d)

12.5 x 102

4. What is 5.92 x 10-3 written in decimal form?

(a)

0.000592

(b)

0.00592

(c)

0.0592

(d)

0.592

5. The length and breadth of a rectangular plot are 5 x 105 and 4 x 104 metres respectively. Its area is ______

(a)

9 x 101 m2

(b)

9 x 109 m2

(c)

2 x 1010 m2

(d)

20 x 1020 m2

6. 3 x 2 = 6
7. The mass of the Earth is 5.97 x 1024 kg and that of the Moon is 0.073 x 1024 kg. What is their total mass?

8. Write the following in scientific notation: (300000)3 x (2000)4

9. Write the following in scientific notation: (4000000)3 ÷ (0.00002)4

10. 3 x 3 = 9
11. Find the value of a and b if $\frac { \sqrt { 7 } -2 }{ \sqrt { 7 } +2 }$=a$\sqrt{7}$+b

12. Represent the following information in scientific notation:
(i) The world population is nearly 7000,000,000.
(ii) One light year means the distance 9460528400000000 km.
(iii) Mass of an electron is
0.000 000 000 000 000 000 000 000 000 00091093822 kg.

13. (i) Add 3$\sqrt{7}$ and 5$\sqrt{7}$ . Check whether the sum is rational or irrational. (ii) Subtract 4$\sqrt{5}$ from  7$\sqrt{5}$ . Is the answer rational or irrational?

14. 2 x 5 = 10
15. Simplify the following using multiplication and division properties of surds:
(i) $\sqrt { 3 } \times \sqrt { 5 } \times \sqrt { 2 }$
(ii) $\sqrt { 35 } \div \sqrt { 7 }$
(iii) $\sqrt [ 3 ]{ 27 } \times \sqrt [ 3 ]{ 8 } \times \sqrt [ 3 ]{ 125 }$
(iv) $(7\sqrt { a } -5\sqrt { b } )(7\sqrt { a } +5\sqrt { b } )$
(v) $\left[ \sqrt { \frac { 225 }{ 729 } } -\sqrt { \frac { 25 }{ 144 } } \right] \div \sqrt { \frac { 16 }{ 81 } }$

16. Arrange surds in descending order:
(i) $\sqrt [ 3 ]{ 5 } ,\sqrt [ 9 ]{ 4 } ,\sqrt [ 6 ]{ 3 }$
(ii) $\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 3 ]{ \sqrt [ 4 ]{ 7 } } ,\sqrt { \sqrt { 3 } }$