Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics

Mathematics

Solutions of Statistics from Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics

The detailed solutions to all the exercises of Statistics from Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics for NDA & NA EE are provided here. The topics covered are such as Mode, Correlation and, Median. Students can practice frequently asked questions from this chapter.

Attempt the free practice questions on Chapter 31: Statistics, Exercise 1: Practice Exercise with hints and solutions to strengthen your understanding. Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics solutions are prepared by Experienced Embibe Experts.

Subject Experts Solutions for Chapter: Statistics, Exercise 1: Practice Exercise

Harmonic Progression and Harmonic Mean

Variance and Standard Deviation for Ungrouped Distribution

Discrete Frequency Stats: Mean, Variance, SD

Arithmetic Mean of Grouped and Ungrouped Data

Variance - Properties, Merits and Demerits

Standard Deviation - Properties, Merits and Demerits

Variance and SD for Grouped Frequency Distribution

Variance and SD of Continuous Distribution

Two Regression Lines

This chapter introduces the basic concepts of vectors and explains the properties of different types of vectors. The addition and multiplication of vectors are also discussed here.

Vector Algebra

This chapter teaches us how determinants are used for solving linear equations. The determinant is a function of the entries of a square matrix. It helps in characterizing some properties of the matrix and the linear map represented by a matrix.

Determinants

This chapter states that set theory is a branch of mathematical logic that studies set, informally known as the collection of objects. It is used as a foundational system for the whole of mathematics. Students solve questions based on this concept.

Set Theory

Areas Bounded by Regions

This chapter outlines the basics of differential equations and their formation. We further learn about linear and exact differential equations, variable separable form, and applications of differential equations.

Differential Equations

This chapter gives an overview of logarithm. It has objective type questions and answers for practice. Here, the aspirants will learn to apply the basic properties of the logarithm.

Logarithm

Coordinate System and Straight Lines

This chapter teaches us about permutations and combinations. A review of facts and formulae are given here. We will also discuss objective questions on fundamental principles of accounting, multiplication, and addition principles.

Permutations and Combinations

This chapter teaches us about the equation of a circle. It discusses the interaction between a circle and a line. It also provides information on parametric equations of a circle, pole and polar, and coaxial system of circles.

Circle

Limits, Continuity and Differentiability

This chapter focuses on the basics of three-dimensional geometry. It discusses lines and planes in 3D along with direction cosines and direction ratios. Further, it describes skew lines, coplanar lines, and the family of planes.

Three Dimensional Geometry

This chapter talks about complex numbers. It helps us to represent complex numbers geometrically using Argand diagrams. We learn about carrying out operations of complex numbers and the ways to find the two square roots of a complex number.

Complex Numbers

Measurement of Angles and Trigonometric Ratios

This chapter discusses the properties of triangles. We will learn the relation between the sides and angles of a triangle. Projection rules such as sine, cosine, and tangent rules are given. We will also study the half-angle formula of a triangle.

Properties of Triangles

This chapter sheds light on derivatives and gradient functions. It covers concepts such as differentiation of power functions, scalar multiple rules, addition or subtraction rule, tangents and second derivatives. It also explains the chain rule.

Differentiation

This chapter focuses on the application of derivatives. It explains Maclaurin's theorem, Taylor's theorem, and Euler's theorem on homogeneous functions. It describes the monotonicity of functions and maxima and minima of functions.

Application of Derivatives

This chapter talks about inverse trigonometric functions. We will learn to reduce a trigonometric function into a bijective function. Graphs of these are explained here. We will also understand the properties of inverse trigonometric functions.

Inverse Trigonometric Functions

This chapter gives explanation to questions based on height and distance. It discusses the concept of angle of elevation and finding the distance between two objects.

Height and Distance

Binary Numbers

Solved Paper 2017 (II)

This chapter covers the topics that are more likely to be asked in the upcoming examinations. It discusses topics such as blood relation, distance and direction, clock and calendar, and counting of figures.

Miscellaneous

Solved Paper 2018 (II)

This chapter talks about sequence and series. We will?learn about arithmetic progression and word problems of arithmetic progressions here. Arithmetic mean, geometrical progression, and some special series are also highlighted.

Sequence and Series

This chapter provides knowledge of matrices. Types of matrices are described here. We will learn scalar multiple of matrix and multiplication of matrices, transpose of a matrix. It explains determinants, adjoint, and inverse and rank of a matrix.

Matrices

This chapter throws light on the concept of probability. It is the measure of the likelihood of an event to occur. MCQs with explanatory answers are provided for practice.

Probability

Quadratic Equations and Inequalities

This chapter highlights definite integrals. It explains definite integral as a limit of sum and interpretation of definite integral as an area. The fundamental theorem of integral calculus is identified here. The reduction formula is also discussed.

Definite Integrals

This chapter discusses relations and functions. It explains relations on a set. It covers different types of functions, the composition of functions and invertible functions. Furthermore, it explains the concepts of binary operations.

Relations and Functions

This chapter explains integration by substitution and parts methods using some formulas. It discusses the evaluation of some special integrals. We also learn the differences between integration and differentiation through examples and exercises.

Indefinite Integrals

Conic Section

This chapter provides knowledge on binomial expansion and its applications. It discusses series involving binomial coefficients and teaches us how to find the sum of coefficients in binomial expansion. It explains the binomial theorem for any index.

Binomial Theorem

Solved Paper 2018 (I)

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Subject Experts solutions for Mathematics Chapter Solutions of Statistics from Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics

Solutions of Statistics from Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics

Subject Experts Mathematics Solutions from Chapter 31 - Statistics

Exercise Questions from Statistics

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