Number System questions SSC Lesson#2

Number System questions Lesson Number 2

Q1. 0.1333……. × 0.6666……….. = ?

= 0.1\bar{3} × 0.\bar{6}

= (13-1)/90 × 6/9

= 8/90

= 0.0888…..

Q2. 2.\bar{4} × 0.\bar{6} × 3 × 0.1\bar{6} × 0.\bar{2}\bar{7} × (0.8\bar{3} ÷ 3 × 0.1\bar{6} = ?

a) 0.\bar{8}\bar{1}\bar{4}

b) 0.\bar{1}\bar{1}

c) 1.\bar{1}

d) 1.\bar{3}\bar{6}

Solution :-

= [(2+4/9) × 6/9 × 3 × (16-1)/90] × [(27/99) × (83-8)/90 ÷ (16-1)/90]

= [(22/9) × 6/9 × 3 × 1/6] × [3/11 × 75/90 ÷ 1/6]

= 44/54 × 15/11

= 10/9

= (11-1)/9

= 1.\bar{1}

Q3. 22.\bar{4} + 11.5\bar{6}\bar{7} - 33.5\bar{9} = ?

a) 0.\bar{3}\bar{2}

b) 0.4\bar{1}\bar{2}

c)  0.3\bar{1}

d) 0.\bar{4}\bar{1}\bar{2}

Solution :-

= 22.4\bar{4}\bar{4} + 11.5\bar{6}\bar{7} - 33.5\bar{9}\bar{9}

= 0.412

Q4. 0.\bar{5}\bar{7} - 0.4\bar{3}\bar{2} + 0.3\bar{5} = ?

a) 0.\bar{4}\bar{9}\bar{4}

b) 0.498

c) 0.4\bar{9}\bar{8}

d) 0.4\bar{9}\bar{4}

Solution :-

0.\bar{5}\bar{7} = 0.5\bar{7}\bar{5}

0.3\bar{5} = 0.3\bar{5}\bar{5}

Now, 0.5\bar{7}\bar{5} - 0.4\bar{3}\bar{2} + 0.3\bar{5}\bar{5}

= 0.4\bar{9}\bar{8}

Q5. A = 0.3\bar{1}\bar{2}, B = 0.4\bar{1}\bar{5} & C = 0.30\bar{9}

We can write this 0.31\bar{2}\bar{1} + 0.41\bar{5}\bar{1} + 0.30\bar{9}\bar{9}

= 1.03\bar{7}\bar{1}

= 1 + 0.03\bar{7}\bar{1}

= 1 + (371-3)/9900

= 1 + 368/9900

Q6. 0.5\bar{6} - 0.7\bar{2}\bar{3} + 0.3\bar{9} × 0.\bar{7}

a) 0.\bar{1}\bar{5}\bar{8}

b) 0.1\bar{5}\bar{8}

c) 0.\bar{1}\bar{5}\bar{4}

d) 0.1\bar{5}\bar{4}

Solution :-

Firstly 0.3\bar{9} × 0.\bar{7} = (39-3)/90 × 7/9 = 28/90 = 0.311….

0.5\bar{6}\bar{6} - 0.7\bar{2}\bar{3} + 0.3\bar{1}\bar{1}

= 0.1\bar{5}\bar{4}

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Odd & Even Number

Odd # ⇒ 1, 3, 5, 7, 9, ………… (2n-1)

Even # ⇒ 2, 4, 6, 8, 10, 12, ………….. (2n)

0 न तो odd है और ना ही even है

Odd & Even Number (Addition & Substraction) :-

1. Odd ± Odd = Even
2. Odd ± Eevn = Odd
3. Even ± Even = Even
4. Odd + Odd + Odd = Odd
5. Even + (Even + Even) = Even
6. Even + (Odd + Odd) = Even

Odd & Even Number (Multiplication) :-

1. Odd ×  Odd = Odd
2. Odd × Even = Even
3. Even × Odd × Odd = Even
4. Odd × Odd × Odd = Odd

Prime and Composite Number

Prime Number (अभाज्य संख्या) : Factor (1 & itself) = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ………

• 1-25 ⇒ 9
• 25-50 ⇒ 6
• 1-50 ⇒ 15
• 51-100 ⇒ 10
• 101-150 ⇒ 10

1 न तो भाज्य संख्या है और न ही अभाज्य संख्या है

Composite Number (भाज्य संख्या) :- वे संख्याए जिनके 2 से ज्यादा factor हो जैसे :- 4, 6, 8, 9, 10, 12, 14, 15, ……….

1-100 ⇒ 99-25 = 74

Twin-Prime : जिन भाज्य संख्या का अंतर 2 हो जैसे : (17, 19), (29, 31), ………….

Co-Prime (सह-अभाज्य संख्या) : जिन संख्या का कोमॉन फैक्टर सिर्फ 1 हो उसे ही Co-Prime कहते है