Number Systems - Test Papers

 CBSE Test Paper 01

CH-1 Number Systems


  1. 12×15 =

    1. 5

    2. 56

    3. 65

    4. 6

  2. Which of the following is equal to ‘x’?

    1. (x4)1312

    2. x127×x712

    3. (x3)23

    4. x127x57

  3. An irrational number between 5 and 6 is

    1. none of these

    2. 5+6

    3. 56

    4. 5×6

  4. 23+3 is equal to

    1. 26

    2. 36

    3. 3

    4. 33

  5. If x=3+8 , then the value of (x2+1x2) is

    1. 32

    2. 34

    3. 6

    4. 12

  6. Fill in the blanks:

    The two rational number which are their own multiplicative inverses are ________.

  7. Fill in the blanks:

    The value of 253 is ________.

  8. Find:12513

  9. Identify whether 45 is rational number or irrational number.

  10. Write the decimal form and state its kind of decimal expansion.36100

  11. Simplify the expression: (52)(5+2)

  12. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π=cd This seems to contradict the fact that is irrational. How will you resolve this contradiction?

  13. Find three different irrational numbers between the rational numbers  59 and 911.

  14. Rationalize a denominator of the following: 313+1

  15. Prove that: 33×62×9852×1/253×(15)4/3×31/3 = 282

CBSE Test Paper 01
CH-1 Number Systems


Solution

  1. (c) 65
    Explanation:
    12=3×22=23 
    and 15=5×3
    so, 12×15=23×3×5
    =2×35=65
  2. (c) (x3)23
    Explanation:
    (x3)23
    =(x32)23

    =x
  3. (d) 5×6
    Explanation:
    We know that,
    If a and b are two distinct positive rational numbers such that ab is not a perfect square of a rational number,then

     ab is an irrational number lying between a and b,

    Here also we have 5 and 6 two distinct rational numbers and 5×6=30 is not a perfect square,
    So irrational number between 5 and 6 =5×6

  4. (d) 33
    Explanation:
    23+3
    =3(2+1)
    =33
  5. (b) 34
    Explanation:
    given x=(3+8)
    1x=1(3+8)=1(3+8)×(38)(38)
    =(38)(32(8)2)=(3+8)(98)=(38)
    (x+1x)=(3+8)+(38)=6
    (x+1x)2=62=36
    (x2+1x2)+2×x×1x=36
    (x2+1x2)+2=36
    (x2+1x2)=362=34
  6. 1, -1

  7. 5+3

  8. 12513
    We know that an=1an
    We conclude that 12513 can also be written as 112513,or (1125)13
    We know that a1n=an, where a>0.
    We know that (1125)13 can also be written as
    (1125)3=(15×15×15)3=15.
    Therefore, the value of 12513 will be 15.

  9. We have,
    45 = 9×5 = 35
    Since 3 is a rational number and 5 is an irrational number. Therefore, the product 35 = 45 is an irrational number.

  10. 36100 = 0.36
    The decimal expansion is terminating.

  11. (52)(5+2)