Class 9th | Chapter 1 Number System | Practices paper - 2

  Section A consists of 5 questions of 1 mark each

 1.which of the following is a rational number ?
A. `1+\sqrt{3}`
B.`π`
C.`2\sqrt {3}`
D.0

2. the decimal expansion of `\sqrt {2}` is : 
A. finite decimal 
B.1.4121
C.non terminating recurring 
D.Terminating recurring

3. which of the following is a rational number ?
A. 1+`\sqrt {3}`
B. `π`
C. `2\sqrt{3}`
D.0

4. the rational number not lying between `-1/5` and `-2/5` is 
A. 0
B. `1/-4`
C.`-3/10`
D.`-7/25`

5.Every rational number is  :
A.a natural number
B. an integer
C.a real number 
D.a whole number

 Section B consists of 2 questions of 2 mark each

6. let `x` be a rational number and `y` be an irrational number. Is x+y necessarily an irrational ? justify your answer with an example .

7. find the value of `[1^3 + 2^3 + 3^3 + 8^2]^(-5/2)`. 

Section C consists of 2 question of 3 mark each

8. Rationalise the denominator of `\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}`.

9. simplify  `\frac{2}{\sqrt{5}+\sqrt{3}}` + `\frac{1}{\sqrt{3}+\sqrt{2}}` - `\frac{3}{\sqrt{5}+\sqrt{2}}`

Section D consists of  2 question of 5 mark each

10. if `a=\frac {\sqrt {5}+\sqrt{10}}{\sqrt{10}-\sqrt{5}}` and `b=\frac {\sqrt {10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}}`, then Show that `\sqrt{a}-\sqrt{b}-2\sqrt{ab}=0`.

11. Find the value of `\frac{2}{(216)^(-2/3)}`-`\frac{4}{(243)^(-1/5)}`+`\frac{1}{(256)^(-3/4)}`

Section E consists of  1 case study  of 4 mark each