Multiple Choice Questions

1. A Rational number can be in the form of
A) Terminating decimal           B) Non - terminating recurring decimal
C) Either A or B                         D) Neither A nor B
 

2. Which of the following notation is not correct?
A) N ⊂ W       B) W ⊂ Z       C) Z ⊂ Q       D) Q ⊂ Q'
 

3. The rational number among the following real numbers is -
A) 43.12312341235...       B) 43.123123123...      
C) 43.121231234...            D) 43.123112311123...
 

4. The equivalent rational number of  in the form of  where q is of the form 2ⁿ 5^m
(n and m are non - negative integers) is -

 

5. The sum of a Rational and an Irrational number is
      A) Irrational        B) Rational          C) Integer          D) Natural 
 

6. The correct statement among the following is
      A) The sum of two irrational numbers is always irrational.
      B) The sum of two irrational numbers need not be irrational.
      C) The product of two irrational numbers is always irrational.
      D) The quotient of two irrational numbers is always irrational.
 

7. The logarithmic form of 64 = 8² is
A) log₂ 8 = 64        B) log₈ 2 = 64        C) log₂ 64 = 8        D) log₈ 64 = 2
 

8. Exponential form of log₅ 125 = 3 is
A) 5³ = 125        B) 3⁵ = 125        C) 125³ = 5        D) 125⁵ = 3
 

9. log_a 1 = 
A) 1        B) 0        C) a        D) 
 

10. log_a xy =
A) log_a x × log_a y        B) log_a x - log_a y         C) log_a x + log_a y      D) 
 

11. log₅ 5 =
A) 5         B) 5²         C) 1         D) 5⁵
 

12. 

A) log_a x × log_a y         B) log_a x - log_a y          C) log_a x + log_a y         D) 
 

13. log_a x^m =
A) m log_a x        B) x log_a m        C) m log_x a        D) x log_a - m
 

14. log_x  = 1
A)          B) 2         C) 1         D) 
 

15. The rational number among the following is
A) log_a 1       B) log_a 2       C) log_a 3       D) log_a 4
 

16. If the pH of a tomato is 4.2 then the hydrogen ion concentration is 
  [Formula for calculating pH is pH = -log₁₀[H⁺]]
A) 6.3 × 10^-5        B) 6.3 × 10^-6        C) 6.3 × 10^-7        D) 6.3 × 10^-8
 

17. 2 log 3 + 3 log 5 - 5 log 2 = 
A) log

       B) log 1125 - log 32      C) log 9 + log 125 - log 32       D) All the above
 

18. For any natural number 'n', 4ⁿ never ends with
A) 4         B) 0         C) 6         D) None
 

19. For any natural number 'n', 6ⁿ ends with
A) 1         B) 4         C) 5         D) 6
 

20. a(b + c) = ab + ac where a, b, c ∊ R
A) Commutative Property   B) Associative Property    C) Identity    D) Distributive Property
 

KEY 

1-A;   2-D;   3-B;   4-A;   5-A;   6-B (Hint:  + (- ) = 0, a rational number)   7-D;  
8-A;   9-B;   10-C;   11-C;   12-B;   13-A;   14-A;   15-A [... loga 1 = 0, a rational number]
16-A;   17-D;   18-B [Hint: 4ⁿ = (2)²ⁿ ⇒ 2 is the only prime factor of 4ⁿ for any natural number n.

∵ 5 is not present in the prime factorisation, 4ⁿ never ends with zero ⩝ n ∈ N ]; 
19-D;   20-D.
 

Writer: V. Padma Priya