Class 9th | Chapter 1 Number System | Practices paper - 1

 Section A consists of 5 questions of 1 mark each

 1.Simplify : ` \frac{13^\frac{1}{5}}{13^\frac{1}{3}}`
A. `13^\frac{2}{15}`
B.`13^\frac{8}{15}`
C.`13^\frac{1}{3}`
D.`13^\frac{-2}{15}`

2. The value of `(125)^-\frac{1}{3}`
A. 25
B.`\frac{1}{5}`
C.5
D.`\frac{1}{25}`

3. the value of `\root[3]{216}-\root[3]{125}`
A. 1
B.0
C.2
D.-1

4. `(5+\sqrt{8})+(3-\sqrt{2})-(\sqrt{2}-6)`, when simplified is :
A. Positive and irrational 
B. Negative and irrational 
C.Positive and rational 
D.Negative and rational 

5.`(-2-\sqrt{3})(-2+\sqrt{3})` when simplified is :
A. Positive and irrational 
B. Negative and irrational 
C.Positive and rational 
D.Negative and rational 

 Section B consists of 2 questions of 2 mark each

6. Find the three irrational numbers between `5/7` and `9/11`.

7. How many irrational numbers lie between `\sqrt {2}` and `\sqrt{3}` ? find any three irrational numbers lying between `\sqrt {2}` and `\sqrt{3}`. 

Section C consists of 2 question of 3 mark each

8. Express 0.2353535... in form of `p/q` , where p and q are integres and q `\ne` 0 .

9. Represent `\sqrt {4.2}` on the number line 

Section D consists of  2 question of 5 mark each

10. if `a=\frac {\sqrt {3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}` and `b=\frac {\sqrt {3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}`, then find the value of `a^2 + b^2`.

11. if `\frac {9^n × 3^2 × (3^-\frac{n}{2})^-2-27^n}{3^(3m)×2^3} = 1/27` , prove that `m-n=1`.

Section E consists of  1 case study  of 4 mark each