# Arithmetic Maths

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### Important Maths Formula

• प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
• सम संख्या (Even) –  (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
• विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
• (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
• घातांक के नियम (Low Of Formula Exponents)
• 1. (am)(an) = am+n
• 2. (ab)m = ambm
• 3. (am)n = amn
• a2 – b2 = (a – b)(a + b)
• (a+b)2 = a2 + 2ab + b2
• a2 + b2 = (a – b)2 + 2ab
• (a – b)2 = a2 – 2ab + b2
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
• (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
• (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 = (a + b)(a2 – ab + b2)
• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
• (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
• a4 – b4 = (a – b)(a + b)(a2 + b2)
• a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

1. The average of first 50 natural numbers is …………..

A. 25.30
B. 25.5
C. 25.00
D. 12.25
B. 25.5
2. A fraction which bears the same ratio to 1/27 as 3/11 bear to 5/9 is equal to ……….. .
A. 1/55
B. 55
C. 3/11
D. 1/11
A. 1/55

3. The number of 3-digit numbers divisible by 6, is ………….. .

A. 149
B. 166
C. 150
D. 151
C. 150
4. What is 1004 divided by 2?
A. 52
B. 502
C. 520
D. 5002
B. 502

5. A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?

A. 78
B. 136
C. 156
D. 196
C. 156

#### 6. 106 × 106 – 94 × 94 = ?

A. 2004
B. 2400
C. 1904
D. 1906

B. 2400

7. Which of the following numbers gives 240 when added to its own square?

A. 15
B. 16
C. 18
D. 20

A. 15

8. The simplest form of 1.5 : 2.5 is …………… .

A. 6 : 10
B. 15 : 25
C. 0.75 : 1.25
D. 3 : 5
D. 3 : 5
9. 125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content be raised to 25%?
A. 15/2 gallons.
B. 17/2 gallons.
C. 19/2 gallons.
D. 81/3 gallons.

D. 81/3 gallons.

10. Evaluation of 83 × 82 × 8-5 is …………. .

A. 1
B. 0
C. 8
D. None of these.
A. 1.

Topic name:-Arithmetic Math

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