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Must Do:Last Digit Concepts with Example

Concept: The last digit of any power Last digit of any power follow a cycle pattern and repeat after a certain power at a time. From the above explanation it is clear that after the power of four number of digit will be same. So find out the last digit we divide the power of any number  by 4. Digit (d) d^2 d^3 d^4 d^5 1 1 1 1 1 2 4 8 6 2 3 9 7 1 3 4 6 4 6 4 5 5 5 5 5 6 6 6 6 6 7 9 3 1 7 8 4 2 6 8 9 1 9 1 9 0 0 0 0 0          v  The last digit of power  of 1  is always 1 v    The last digit of power of 2 repeat in a cycle of 4, 8, 6, 2 v    The digits of powers of 3 repeat in a cycle of 9, 7, 1, 3 v    The last digit of power of 4 repeat in a cycle of 6, 4 v    The last digit of power of 5 & 6 is always same. v    The la...
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Must Do: Divisiblity Concepts with Example Questions

Concept – Divisibility of a number Divisibility by 2  — A number is divisible by 2 if the unit digit is zero or divisible by 2. Ex.  – 2, 4, 8, 16, 18 etc. are all divisible by 2. Divisibility by 3  — A number is divisible by 3 if the sum of digits of the number is divisible by 3.  Ex.  – if 43n25 is divisible by 3 then find the minimum value n Sol.  4+3+n+2+5 is divisible by 3  So n=1,4,7 Minimum value of n=1  Divisibility by 4  — A number is divisible by 4 if the number formed by the last two digits is divisible by 4 . Ex.  – 56248 is divisible by 4 since 48 is divisible by 4.  Divisibility by 5  — A number is divisible by 5 if unit’s digit is 0 or 5.  Ex.  – 1225, 13750, 245 etc. are all divisible by 5.  Divisibility by 7  — The unit digit of given number is doubled and then it is subtracted from the number obtained after omitting the unit digit.  If the remainde...
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Important Mensuration formulas and short notes for 3D figures

We have already discussed  Mensuration 2D Short notes , here we will discuss all about Mensuration 3D figures. You can also know some important facts of 3D figures. In this article, abbreviations used are TSA = Total Surface Area, CSA = Curved Surface Area. SSC CGL Tier II 2017 Mock Tests on Latest Pattern - Attempt Now Available in Hindi & English. Get Detailed Analysis & All India Rank # Cuboid : Given is the cuboid of lenth  l,  breadth  b  and height  h.  T.S.A. = 2(lb + bh + lh) Volume = lbh Diagonal =    Important:  If area of faces of cuboid are x,y and z Then, volume of cuboid  # Cube Let the side of given cube is 'a'. T.S.A. = 6a 2 Volume = a 3 Diagonal of cube =   # Sphere let the radius of given sphere is ' r'  and in case of sphere  total surface area is equal to curved surface area . C.S.A. = T.S.A. =  Volume =    # Hemi-Sphere Assume ...
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