Number System Test - 4

Face Value of any number remains the same irrespective of the place, for 7 it is 7

Place Value = Place Multiplier x  Face Value 

= 10000 x 7
= 70000

• Option A: Place value of 9 = 9 x 1000 = 9000
• Option B: Place value of 9 = 9 x 100 = 900
• Option C: Place value of 9 = 9 x 1 = 9
• Option D: Place value of 9 = 9 x 10 = 90

(a) 8 is the Base of Octal Number System
(b) 16 is the Base of Hexadecimal Number System
(c) 2 is the Base of Binary Number System
(d) 10 is the Base of Decimal Number System

(a) −√4 = −2 is a Real Number as well as a Rational Number
(b) −√3 is a Real number and an irrational number
(c) √−4 is an imaginary number

► All the digits written once = 2116
► All the digits without Bar written once = 21
► Number of digits with bar after decimal = 2
► Number of digits without bar after decimal = 0
► Rational form = 

► √16 = 4, which is a natural number, rational number as well as a real number.

(16a + 6) will always be even, whether the a is odd or even.

• For a = 1 (odd)
  (16 * 1) + 6 = 16 + 6 = 22 (even)
• For a = 2 (even)
  (16* 2) + 6 = 32 + 6 = 38 (even)

As it is given, 7a - 3 is odd

⇒ 7a = odd +3 i.e. even (say, x)
∵ a is an integer
⇒ For 7a = x, x should be completely divisble by 7
⇒ a = x/7 i.e. even/odd = even

• Option A: 0 is an integer but not positive(it is neutral).
• Option B: 1 is an integer also positive and the smallest.
• Option C:  0.5 is not even an integer.
• Option D:  2 is an integer as well as positive but not the smallest.  

• Option A: 93 is divisible by 3
• Option B: 97 is not perfectly divisible by any number.
• Option C: 95 is divisible by 5
• Option D: 91 is divisible by 7

We do not need to do the multiplication in this question.
► 1837 is Odd
► 1712 is Even
► 1839 is Odd

Odd x Even x Odd = Even

Only option 1 is Even rest all are Odd. 

► 999 is the Largest composite number, it is divisible by 1, 3, 9, 111, 333, 999. 

► 517^th Whole number = 516
► 516^th Natural Number = 516

• 516 - 516 = 0

► Prime and Composite are properties of Natural numbers.
► 0 is not a natural number.
► 1 is neither prime nor composite.
► 2 is a prime number divisible by 1 and 2 only.
► 4 is a composite number divisible by 1,2 and 4. Smallest among all. 

► Only pair of consecutive prime numbers is (2, 3)

Consecutive (difference is 1) ==> only pair possible is (2,3), no other pair possible since 2 is the only even prime, any other 2 consecutive numbers will have an even number, which is not prime.