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Chapter 4 : Mathematical Induction

Mathematical induction is a method of mathematical proof typically used to establish a given statement for all natural numbers. It is a form of direct proof, and it is done in two steps. The first step, known as the base case, is to prove the given statement for the first natural number. The second step, known as the inductive step, is to prove that the given statement for any one natural number implies the given statement for the next natural number. From these two steps, mathematical induction is the rule from which we infer that the given statement is established for all natural numbers.

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IT Quiz

The Operating System developed by Canonical Ltd is.............

• Windows
• Redhat
• Ubuntu
• Mac OS

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Mental Ability: Test 1

1. Raju is shorter than Gopi but taller than Rahim who is taller than Meena. Who is the shortest of the four ?

• Gopi
• Raju
• Rahim
• Meena

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Chapter 3. Trigonometric Functions

In mathematics, the trigonometric functions (circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component).

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Chapter 2. Relations and Functions

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first components from A and second components from B, and, in particular, a subset of A×A is called a "relation on A." For a binary relation R, one often writes aRb to mean that (a,b) is in R×R.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

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Practicing Entrance Exams: Online/Offline

Chapter 1. SETS

A set is a collection of distinct objects, considered as an object in its own right. For example, the numbers1, 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {1,2,4,6}. Sets are one of the most fundamental concepts in mathematics.

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