Q. How many numbers will divisible by 6 between 1 to 100 ?
A. First: find the number that is near to 100 and less than 100 and will divisible by 6..
How will you find it ?
Answer is you should know the divisibility rule of number 6 .. That is any number which divisible by 3 amd 2 will also be divisible by 6
So this number will be 96 near to 100
2nd : find the number nearest to 1 and greater than 1 which is divisible by 6 .. this will be 6
So numbers are
6 , 12 ,18 , ……………96 -> all are divisible by 6
This series is an A.P
Formula of nth term of AP
Tn = a +(n-1)d
a = first term = 6
n = number of term =?
Tn = Last term or nth tearm = 96
d = difference between two consecutive term = 6
96 = 6 +(n-1)6
n-1 = 90/6 = 15
n = 16 Ans

Maximum and Minimum value of Trigonometric function

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Trigonometry Formula and Important concept for JEE
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There are Three terms
(1) Undefined
(2) Infinity
(3) Indeterminate

(1) Undefined
Let varify division rule, let we are deviding M by n and it will give x ( M is multiple of n)
M/n = x
that means if we will multiply n with x ..it will give M
as n×x = M
Let suppose we are dividing H by 0 and it will give T
H/0 = T
so
T×0 = H ( so here T is not defined that can give H when multiplied by Zero(0)
So any number / 0 = Undefined ( remember not infinity)

(2) Infinity
it can be defined as ny large Quantity with respect to very small quantity
if we compare 1kg sugar with respect to
.00000000000000000000000000000000000000000000000000000000000000001 gram sugar
so 1kg sugar is treated as infinity ..
Lim x->0(1/x) = infinity

(3) Indeterminate
let x/y = m
so x = y×m
if x = 0 and y =0
0 = 0×m
m may be 1, 2, 3 , 4 , 5 2000, 40000, and so on ...
so 0/0 called indeterminate form
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Solve this Problem

The Difference between Expression, Equation, Inequality and Identity is given below
(1) Definition of Equations:
Equation, statement of equality between two expressions consisting of variables and/or numbers.
or
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
or
In other word if we use equality between two expression, it become equation
Example:
Quadratic Equation
ax² + bx + c = 0

Linear Equation
4x − 8 = −5 + 3x

Cubic Equation
ax³ + 4x² +4 =0

Quartic equation
ax⁴ +f = 0
Differential Equation
(d2y/dx2)+ 2 (dy/dx)+y = 0
(2) Definition of Expression:
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The structure of an expression is:
3x + 4
x+y
4a+7b+4c
(3) Definition of Inequality:
This is also called inequations
If we use these inequality symbols, less than (<), greater than (>), less than or equal (≤), greater than or equal (≥) and the not equal symbol (≠) between two expression or between expression and number so it become inequality
Example of Linear Inequality
4x - 1 > 9
10 ≥ 77x - 2
-448 > 56x + 12

Example of modulus Inequality
|x+5| > 4

Example of Quadratic Inequality
X² +4x -1>0

(4) Definition of Identity
An identity is an Equation that is true for all value of variable,
One variable identity
(x +2)² = x² + 4x + 4
Two variable identity
(x + 2y)² = x² + 4y² + 4xy
Function :
F(x) = x² + 4x +1
F(x) = Sin(x)
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Q1. Solve for x ?
{x²} + {x} = 1
Where { } denotes fractional part of x function.

Q2. Solve for x ?
[x²] + [x] = 1
Where [ ] denotes  greatest Integer less than or equal to x

Q3. Solve for x
If x[x] = 15
[ ] Denotes greatest integer less than or equal to x.

Q If 4 {x} = x + [x], where {x} and [x] denotes fractional part of x function and greatest integer function less than or equal to x respectively , then x=? [IIT-JEE 1994]