As you asking for the IIT JEE Examination Shortcuts here I am giving you the Some shortcut tricks to Solve the Mathematics questions of the IIT JEE Examination that is as follow


If you had 343, you would double the last digit to get six, and subtract that from 34 to get 28.If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again

Example -:
623: 62 - (3 × 2) = 56 = 7 × 8
483: 48 − (3 × 2) = 42 = 7 × 6

Multiplication of any two numbers, lies between 11 and 19
Let me explain this rule by taking examples
13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247
Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it.
Example.
18*14 = (18+4)*10 + (8*4) = 220 + 32 = 252
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3196)


Multiplication of 11 with any number of 3 digits.
Let me explain this rule by taking examples
1. 352*11 = 3---(3+5)---(5+2)---2 = 3872
Means insert the sum of first and second digits, then sum of second and third digits between the two terminal digits of the number
2. 213*11 = 2---(2+1)---(1+3)---3 = 2343
Example.
Here an extra case arises
Consider the following examples for that
1) 329*11 = 3--- (3+2) +1--- (2+9-10) ---9 = 3619
Means, if sum of two digits of the number is greater than 10, then add 1 to previous digit and subtract 10 to the associated digit.
2) 758*11 = 7+1---(7+5-10)+1---(5+8-10)---8 = 8338


Magical Division Rule For 2
If a number is divisible by two it will end in an even number or a 0.
Example.
For example
28964
given number end with 2 then it will be divisible by 2.
and
89450
given number end with 0 it will also be divisible by 2.


Golden Division Rule For 3
If a number is divisible by three the sum of its digits will be divisible by 3.
Example.
372 = 3 + 7 + 2 = 12

A corollary of this is that any number made by rearranging the digits of a number divisible by 3 will also be divisible by 3.


Exceptional Division Rule For 4
If a number is divisible by four the last two digit are divisible by 4 (or are zeros).
Example.
45624
last two digit is 24
24 is divisible by 4 then 45624 is divisible by 4.
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Incredible Division Rule For 5
If a number is divisible by five the last digit will be 5 or 0.
Example.
48905
last digit is 5 then 48905 is divisible by 5
and
56890
last digit is 0 then 56890 is also divisible by 5

Phenomenal Division Rule for 6
If a number is divisible by six the last digit will be even and the sum of the digit divisible by 3.
Example.
46536
last digit is 6 (even) and
sum of digit
4+6+5+3+6 = 24
24 is divisible by 3
then 46536 is divisible by 6.