illustrative examples

The following are the Illustrative Examples: If P(n) is the statement n 2 -n+41 is prime, prove that P(1), P(2) are true but P(41) is not true. Prove by P.M.I , n < 2 n for all n ..

Example 1: - Find the compounded ratio of a) 5:14 and 7:15 b) a+b:a-b; (a 2 -b 2 ):(a 2 +b 2 ) and a 2 +b 2 :(a+b)..

1) If a:b::c:d, show that 2a+3b:2a-3b::2c+3d:2c-3..

1. Find the compounded ratio of a) 5:14 and 7:15 b) a+b:a-b; (a 2 -b 2 ):(a 2 +b 2 ) and a 2 +b 2 :(a+b) 2 . 2. In the ratio 7:8, if the consequent is 40, what is the antecedent? 3. Find a) reciprocal ratio of 3:5 b) duplicate ratio of 2:3 c) triplicate ratio of 3:4 d) sub duplica..

Variations, the raw materials for evolutionary change, are controlled by genes. When there is an error in DNA copying during sexual reproduction it leads to variation. Variations occur due to microevolution, that is, evolution on a small scale-within a species or a single population. It is defined..

In the above figure, the metal to be deposited is silver and is used as anode. The object to be plated is used as cathode. When the current flows through the electrolyte, the silver rod continuously dissolves into the solution and gets deposited on the object (ke..

Let us consider the case of a projectile, which explodes in flight. The force of gravity continues to act on the total mass of the projectile, now scattered into fragments. The centre of mass of the fragments continues along the parabolic trajectory. It is the same, as was followed by the intact pr..

are dual of each other w.r.t. connectives ' ' and ' ..

01. When a body moves along a frictionless horizontal surface, its weight and the normal reaction of the surface are both perpendicular to the direction of motion. Hence, these forces, namely the weight of the body and the normal reaction do no work. 02. If a stone tied at the end of a string is w..