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Exam Questions What is the unit digit in the number of (2137) 753 ? a) 1 b) 2 c) 7 d) 9 Answer: To find the unit dight in the number(2137) 753 , we need to focus on the circle of unit digits in the number are raised to powers. Here, we have to focus on the when the power rised and which number is in the unit place. The unit digit of 2137 is 7. When the number 7 will rise the power as following patterns are repeats. 7 1 has a unit digit of 7 7 2 has a unit digit of 9 7 3 has a unit digit of 3 7 4 has a unit digit of 1 7 5 has a unit digit of 7 SInce, the pattern repeats every four powers, now we can find the reminder when 753 is divided by 4: 753/4 = 188 and with give a reminder of 1. This means that the unit digit of (2137) 753 will be same as unit dight of (2137) 1 ∴ the unit digit of (2137) 753 . That is option c is correct.

In Partial Differential Equation questions are solving to some important forms Lagrange's Linear Equation, Charpit's Method and etc. Here the concept of solutions are very vital to understand for solving the P.D Equation. Types of Solutions There are four types of solutions are listed below - Complete Solution Particular Solution Singular Solution General Solution Complete Solution When a partial differential equation f(x,y,z,p,q) = 0      ...(i) where, z is the function of independent variables x and  y and f   be the function of dependent variables. Here we obtain a relation g(x,t,z,a,b) = 0 there are many arbitary constants as a number of independent variables, then g(x,y,z,p,q) = 0 is called the complete solution or integral of eq( i ) for example, z = ax + by +f(a,b) is the complete solution of z = px +qy +f(p,q) Particular Solution First of all we have a differential equatio...