The total number of three-digit numbers, with one digit repeated exactly two times, is ______.
Correct Answer: 243
Solution and Explanation
The correct answer is: 243
C-1 : All digits are non-zero
\(C_2^9.2.\frac{3!}{2}=216\)
C-2 : One digit is 0
0,0,x⇒9C1.1.=9
0,x,x⇒9C1.2.=18
Total = 216 + 27 = 243
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Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations