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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

D. State whether the following statements are true (t) or False (F).
1. If a is any rational number, then a = 1.
0
–m
2. a = –a m
3. 2 > (–1) 135
0
mn
m n
4. If a and b are two rational numbers and m, n are integers, then a b = (ab) .
5. (2 × 2 ) = 2 –12
3
2 –2
E. answer the following questions.
1. Simplify.
    3 7  3    2 
9

3
(a) 5 × 5 × 5 9 (b) (–7) ÷ 7 6 (c)     ÷    ×   
0
6
6



    2 2   2  
−1
−2

1
  3 − 1  − 1     −   2    1 − 3  1 − 3   1 − 3

(d) 6 +    (e)    5    (f)    −    ÷  
−
1


   2              3  2    4
2. Solve each of the following:
1
−
5
(
2
1
1
5
−
–1 –1
–1 –1
–1
(a) 2 ÷ ) ×    − 8   (b) (6 – 8 ) + (2 – 3 )
–1
−
3. Using laws of exponents, simplify and express each of the following in the exponential form with
positive exponent.
3
3
–4
–4
(a) 3 × 2 –4 (b)    5 ×    2 (c) (3 ÷ 3 –10 ) × 3 –5 (d) − ( ) ×   5 4
4
3
 
4

4

  3
4. Find the value of x in the following:
x
2
5
2
2



(a)   − 7 ×   − 11 =   9x (b)   3    − 6 =   2 − 1
5
5
 
  ×  
 
 
 
 
 
8
9
9
9
8
8
  3 2   3 −4
–2
5. If x =   ×   , find the value of x .
  2
  2
6. Write the following numbers in standard form.
(a) 0.000007 (b) 0.000000564
7. Express the following numbers in the usual form.
(a) 3 × 10 –8 (b) 1.0001 × 10 9 (c) 5.8 × 10 2 (d) 3.61492 × 10 6
9
7
8. The diameters of the Sun and the Earth are 1.4 × 10 m and 1.275 × 10 m, respectively. Compare the
two diameters.
9. Venus is the second planet from the sun. Our nearest neighbour ‘Venus’
is known as the Morning Star or Evening Star. Its distance from the Sun
is about 108,200,000 km, and its radius is 6051.8 km. Venus is also called
Earth’s sister or twin. Case study
Based on the above information answer the following questions:
(a) Express the distance of Venus from the Sun in standard form.
(b) Express the radius of Venus in ‘metre’ in standard form.
(c) If a satellite launch vehicle on Venus has a speed of 20,000 km/h, then find the time it will
take to reach the Sun from the Venus.
(d) If the speed of light is 3 × 10 km/s, then how long will it take to reach on the surface of
5
Venus from the Sun?
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