CHSE Odisha Class 12 Logic Book Solutions (+2 2nd Year)

CHSE Odisha 12th Class Logic Book Solutions (+ 2 2nd Year)

Unit 1 ଅନୁମାନ – ଅନୁମାନର ପ୍ରକାରଭେଦ – ଅବ୍ୟବହିତ ଓ ବ୍ୟବହିତ

Unit 2 ବ୍ୟବହିତ ଅନୁମାନ ଓ ମିଶ୍ର ତ୍ରିପଦୀଯୁକ୍ତି

Unit 3 ତର୍କଦୋଷ ଓ ପ୍ରତୀକାତ୍ମକ ତର୍କଶାସ୍ତ୍ର

Unit 4 ମିଲ୍‌ଙ୍କ ପରୀକ୍ଷଣ ପଦ୍ଧତି, ବୈଜ୍ଞାନିକ ବ୍ୟାଖ୍ୟାନ

Unit 5 ନ୍ୟାୟଙ୍କ ଜ୍ଞାନ ସିଦ୍ଧାନ୍ତ ଓ କର୍ମବାଦ

CHSE Odisha Class 12 Logic Book Syllabus (+2 2nd Year)

Unit 1 ଅନୁମାନ – ଅନୁମାନର ପ୍ରକାରଭେଦ – ଅବ୍ୟବହିତ ଓ ବ୍ୟବହିତ
ଅନୁମାନ – ଅନୁମାନର ପ୍ରକାରଭେଦ – ଅବ୍ୟବହିତ ଓ ବ୍ୟବହିତ ଅନୁମାନ – ଅବ୍ୟବହିତ ଅନୁମାନ – ସମବର୍ତ୍ତନ, ବ୍ୟାବର୍ତ୍ତନ; ବ୍ୟବହିତ ଅନୁମାନ– ତ୍ରିପଦୀଯୁକ୍ତି, ଏହାର ଅବୟବାବଳୀ, ନ୍ୟାୟ-ସଂସ୍ଥାନ, ନ୍ୟାୟରୂପ, ତ୍ରିପଦୀଯୁକ୍ତିର ସାଧାରଣ ନିୟମାବଳୀ, ନ୍ୟାୟରୂପ-ମାନଙ୍କର ନିର୍ଦ୍ଧାରଣ ପ୍ରକ୍ରିୟା ।

Unit 2 ବ୍ୟବହିତ ଅନୁମାନ ଓ ମିଶ୍ର ତ୍ରିପଦୀଯୁକ୍ତି
ପ୍ରତ୍ୟେକ ସଂସ୍ଥାନର ସ୍ବତନ୍ତ୍ର ନିୟମାବଳୀ, ଆରିଷ୍ଟୋଟଲଙ୍କ ମୌଳିକ ସୂତ୍ର, ସାକ୍ଷାତ୍ ଓ ଅସାକ୍ଷାତ୍ ରୂପାନ୍ତରୀକରଣ ।
ମିଶ୍ର ତ୍ରିପଦୀଯୁକ୍ତି – ବିଭିନ୍ନ ପ୍ରକାର : ପ୍ରାକଳ୍ପିକ ନିରପେକ୍ଷ, ବିଯୋଜକ – ନିରପେକ୍ଷ, ବୈକଳ୍ପିକ — ନିରପେକ୍ଷ, ଦ୍ବିଶୃଙ୍ଗକ ନ୍ୟାୟ, ଦ୍ବିଶୃଙ୍ଗକ ଯୁକ୍ତିର ପ୍ରକାରଭେଦ, ଦ୍ବି ଶୃଙ୍ଗକ ଯୁକ୍ତିର ଆକାରଗତ ବୈଧତା, ବସ୍ତୁଗତ ସତ୍ୟାସତ୍ୟ ବିଚାର, ଦ୍ବିଶୃଙ୍ଗକ ଯୁକ୍ତିର ପ୍ରତିରୋଧ ।

Unit 3 ତର୍କଦୋଷ ଓ ପ୍ରତୀକାତ୍ମକ ତର୍କଶାସ୍ତ୍ର
ତର୍କଦୋଷ – ଅବରୋହୀ ତର୍କଦୋଷ, ଅବରୋହୀ – ଅନୁମାନ ସମ୍ପର୍କୀୟ ତର୍କଦୋଷ, ଆପାତଃ ତର୍କଦୋଷ । ଆରୋହୀ ତର୍କଦୋଷ – ଅବୈଧ ସାମାନ୍ୟକରଣ ତର୍କଦୋଷ, ଦୁଷ୍ଟ ଉପମା କିମ୍ବା ଦୁର୍ବଳ ଉପମା ତର୍କଦୋଷ, ବଳକା ତର୍କଦୋଷ, ଅବାନ୍ତର ପ୍ରସଙ୍ଗ ଦୋଷ ।
ପ୍ରତୀକାମୂକ ତର୍କଶାସ୍ତ୍ର ଏବଂ ଏହାର ବୈଶିଷ୍ଟ୍ୟ- ତର୍କବାକ୍ୟମୂଳକ ଚଳ- ତର୍କଶାସ୍ତ୍ରୀୟ ସ୍ଥିରାଙ୍କ- ସତ୍ୟଫଳନ – ସତ୍ୟସାରଣୀ- ସତ୍ୟ ସାରଣୀ ପଦ୍ଧତି । ସାକ୍ଷାତ୍ ସତ୍ୟସାରଣୀ ପଦ୍ଧତି ସାହାଯ୍ୟରେ ବୈଧତା ପରୀକ୍ଷା ।
ପୁନରୁକ୍ତିକ ତର୍କବାକ୍ୟମୂଳକ ସୂତ୍ର- ବିରୁଦ୍ଧ ତର୍କବାକ୍ୟମୂଳକ ସୂତ୍ର- ଆପାତିତ ତର୍କବାକ୍ୟମୂଳକ ସୂତ୍ର । ବିଭିନ୍ନ ଉଦାହରଣମାନଙ୍କର ସାକ୍ଷାତ୍ ସତ୍ୟ ସାରଣୀ ପଦ୍ଧତି ସାହାଯ୍ୟରେ ବୈଧତା ପରୀକ୍ଷା ।

Unit 4 ମିଲ୍ଲଙ୍କ ପରୀକ୍ଷଣ ପଦ୍ଧତି, ବୈଜ୍ଞାନିକ ବ୍ୟାଖ୍ୟାନ
ମିଲ୍‌ଙ୍କ ପରୀକ୍ଷଣ ପଦ୍ଧତି—ମିଲ୍‌ଙ୍କ ପାଞ୍ଚଟି ପରୀକ୍ଷଣ ପଦ୍ଧତି— (୧) ଅନ୍ବୟ ପଦ୍ଧତି, (୨) ବ୍ୟତିରେକ ପଦ୍ଧତି, (୩) ସଂଯୁକ୍ତ ପଦ୍ଧତି, (୪) ସହଚାରୀ ପରିବର୍ତ୍ତନ ପଦ୍ଧତି, (୫) ପରିଶେଷ ପଦ୍ଧତି ।
ବୈଜ୍ଞାନିକ ବ୍ୟାଖ୍ୟାନ– ବୈଜ୍ଞାନିକ ବ୍ୟାଖ୍ୟାନର ଲକ୍ଷଣ ।

Unit 5 ନ୍ୟାୟଙ୍କ ଜ୍ଞାନ ସିଦ୍ଧାନ୍ତ ଓ କର୍ମବାଦ
ନ୍ୟାୟଙ୍କ ଜ୍ଞାନ ସିଦ୍ଧାନ୍ତ – ପ୍ରତ୍ୟକ୍ଷ ଓ ଅନୁମାନ, ବ୍ୟାପ୍ତି ଓ ଏହାର ନିର୍ଦ୍ଧାରଣ ପ୍ରକ୍ରିୟା
କର୍ମବାଦ – ଭଗବତ୍ ଗୀତାର ନିଷ୍କାମ କର୍ମ, ଗାନ୍ଧିଜୀଙ୍କ ଅହିଂସାବାଦ

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha Class 12 Alternative English Approaches to English Book 1, 2 Solutions

CHSE Odisha Class 12 Approaches to English Book 1, 2 Solutions (+2 2nd Year)

CHSE Odisha Class 12 Approaches to English Book 1 Solutions

Prose

Unit 1 THE WONDER WORLD OF SCIENCE

Unit 2 OUR ENVIRONMENT

Unit 3 THE WORLD OF BUSINESS

Unit 4 THE CHANGING WORLD

CHSE Odisha Class 12 Approaches to English Book 2 Solutions

Poems

Short Stories

One-Act Plays

Grammar & Usage

CHSE Odisha Class 12 Alternative English Syllabus

CHSE Odisha Class 12 Alternative English Syllabus
CHSE Odisha Class 12 Alternative English Syllabus 1

CHSE Odisha Class 12 Alternative English Question Pattern and Distribution of Marks

Alternative English +2 2nd Year
Full Marks – 100, Time – 3 Hours

1. Reading Comprehension.
(a) A prescribed prose piece or extract (10 Marks)
(5 questions including inferential questions are to be answered)
(b) A prescribed poem/extract (10 Marks)
(5 questions including inferential questions and those on poetic devices, figures of speech, mode, tone, and style, etc.)
(c) A prescribed story/one-act play or its extract (10 Marks)
(5 questions including Inferential questions and those on literary devices, tone, etc.)
(d) An unseen passage of at least 200 words. (10 Marks)
(5 questions including inferential ones)

2. Reading-related skills.
(a) Un Guided note-making based on the passage 1(d) (10 Marks)

3. Writing skills.
(a) Designing and writing a brochure (10 Marks)
(b) Writing dialogues of a face-to-face/telephonic conversation. (10 Marks)
(c) Rewriting a poem/short story as a different form of discourse i.e. a page of a diary, a newspaper report/article, or a script for a play, etc. (10 Marks)
(d) Adding a suitable beginning/ending/title to a given poem/story. (5 Marks)

4. Grammar and usage (in context) (15 Marks)
(3 questions on the prescribed grammar units including modified close tests.

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha Class 12 Math Notes – Elements of Mathematics Class 12 Notes

CHSE Odisha 12th Class Math Notes | Elements of Mathematics Class 12 Notes CHSE Odisha

CHSE Odisha Class 12 Economics Book Solutions (+2 2nd Year)

CHSE Odisha 12th Class Economics Book Solutions (+ 2 2nd Year)

CHSE Odisha Class 12 Economics Book Solutions in Odia Medium

Chapter 1 ଅର୍ଥଶାସ୍ତ୍ରର ସଂଜ୍ଞା, ପରିସର ଓ ବିଷୟବସ୍ତୁ

Chapter 2 ଅର୍ଥବ୍ୟବସ୍ଥାର ପରିଚୟ ଏବଂ ଅର୍ଥଶାସ୍ତ୍ରର କେନ୍ଦ୍ରୀୟ ସମସ୍ୟାବଳୀ

Chapter 3 ମୌଳିକ ଧାରଣା (ମାନବୀୟ ଅଭାବ, ଉପଯୋଗିତା, ଦ୍ରବ୍ୟ, ମୂଲ୍ୟ, ଦର ଓ ସମ୍ପଦ)

Chapter 4 ଉପଭୋଗର ନିୟମ

Chapter 5 ଚାହିଦା

Chapter 6 ଉତ୍ପାଦନ

Chapter 7 ପରିବ୍ୟୟ

Chapter 8 ଆୟ

Chapter 9 ଯୋଗାଣ

Chapter 10 ବଜାର

Chapter 11 ସମଷ୍ଟି ଅର୍ଥନୀତି

Chapter 12 ଜାତୀୟ ଆୟ

Chapter 13 କେନ୍‌ସଙ୍କ ଆୟ ନିର୍ଦ୍ଧାରଣ ତତ୍ତ୍ବ

Chapter 14 ମୁଦ୍ରା

Chapter 15 ବ୍ୟାଙ୍କ

Chapter 16 ରାଷ୍ଟ୍ରବିତ୍ତ

Chapter 17 ବଜେଟ୍

CHSE Odisha Class 12 Economics Book Solutions in English Medium

  • Chapter 1 Definition of Economics, Scope and Subject, Matter of Economics
  • Chapter 2 Meaning of Economy and Central Problems of An Economy – Scarcity and Choice, What, How and for Whom to Produce?
  • Chapter 3 Basic Concepts (Wants, Utility, Goods, Value, Price and Wealth)
  • Chapter 4 Laws of Consumption
  • Chapter 5 Demand
  • Chapter 6 Production
  • Chapter 7 Cost
  • Chapter 8 Revenue
  • Chapter 9 Supply
  • Chapter 10 Market
  • Chapter 11 Macroeconomics
  • Chapter 12 National Income
  • Chapter 13 Keynesian Theory of Income Determination
  • Chapter 14 Money
  • Chapter 15 Banking
  • Chapter 16 Public Finance
  • Chapter 17 Budget

CHSE Odisha Class 12 Economics Syllabus (+2 2nd Year)

Second Year CHSE (2022-2023)
Economics Paper-II
(Elementary Micro and Macro Economics)

Part A: Introductory Micro Economics

Unit I Introduction
Definition, scope, and subject matter of economics, Meaning of economy and central problems of an economy – scarcity and choice, what, how and for whom to produce?, Basic concepts – wants, utility, goods, value, price and wealth.

Unit II Consumption and Demand
Laws of consumption – marginal and total utility, law of diminishing marginal utility, the law of equi marginal utility and conditions of consumer’s equilibrium, Demand – meaning and determinants, individual and market demand, demand schedule and demand curve, movement along and shifts in the demand curve, Price elasticity of demand – concept, determinants, measurement of price elasticity of demand; percentage and geometric methods (linear demand curve), the relation of price elasticity of demand with total expenditure.

Unit III Production
Meaning of production and production function – short run and long run, Total, Average, and Marginal Product, Law of variable proportions, and returns to a factor.

Unit IV Cost, Revenue and Supply
Cost – money and real cost, implicit and explicit cost, fixed and variable cost, Total, average and marginal costs in the short run and their relationship (simple analysis), Revenue – Total, average and marginal revenue and their relationship, Supply – meaning and law of supply

Unit V Market
Meaning and forms of market, pure and perfect competition, price determination under perfect competition and effects of shifts in demand and supply, Meaning and features of monopoly, monopolistic competition and oligopoly.

Part B: Introductory Macro Economics

Unit VI Introduction
Meaning of macroeconomics, Distinction between macro-and microeconomics, the subject matter of macroeconomics

Unit VII National Income
Meaning and aggregates related to national income – GNP, NNP, GDP, and NDP at market price and factor cost, National disposable income (Gross and Net), Private Income, Personal income, Personal disposable income, Nominal and real national income, Income determination – Aggregate Demand and Supply and their components, simple Keynesian Theory of Income Determination.

Unit VIII Money, Banking and Public Finance
Meaning and Functions of Money, Meaning and Functions of Commercial Banks, Functions of Central Bank, Meaning of Public Finance and Difference between public and private finance, Budget – Meaning and objectives, a balanced and unbalanced budget, surplus and deficit budget.

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha Class 12 Math Book Solutions | Elements of Mathematics Class 12 CHSE Odisha Solutions Pdf Download

CHSE Odisha 12th Class Math Book Solutions | Elements of Mathematics Class 12 Solutions CHSE Odisha Pdf Download

Elements of Mathematics CHSE Solutions Class 12 Chapter 1 Relation and Function

CHSE Math Solution Class 12 Pdf Chapter 2 Inverse Trigonometric Functions

Elements of Mathematics Class 12 Volume 2 Chapter 3 Linear Programming

Elements of Mathematics Class 12 Book Solutions Chapter 4 Matrices

CHSE Odisha Class 12 Math Book Pdf Download Chapter 5 Determinants

Elements of Mathematics Class 12 CHSE Odisha Pdf Download Chapter 6 Probability

Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability

Plus 2 2nd Year Science Math Book Pdf Chapter 8 Application of Derivatives

Elements of Mathematics Class 12 Solutions CHSE Odisha Pdf Download Chapter 9 Integration

Class 12 Elements of Mathematics Book Pdf Chapter 10 Area Under Plane Curves

CHSE Odisha Class 12 Math Book Pdf Chapter 11 Differential Equations

Elements of Mathematics Class 12 Odisha Pdf Download Chapter 12 Vectors

Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 13 Three Dimensional Geometry

CHSE Odisha Class 12 Maths Syllabus (+2 2nd year)

Mathematics (+2 2nd year)
Course Structure

Unit Topic Marks No. of Periods
I Relations and Functions & Linear Programming 20 45
II Algebra and Probability 20 45
III Differential Calculus 20 45
IV Integral Calculus 20 45
V Vector 3-D Geometry 20 45
Total 100 220

General Instructions:

  1. All questions are compulsory in Group A, which are very short answer-type questions. All questions in the group are to be answered in one word, one sentence, or as per the exact requirement of the question. (1 × 10 = 10 Marks)
  2. Group B contains 5(five) questions and each question has 5 bits, out of which only 3 bits are to be answered (Each bit carries 4 Marks) (4 × 15 = 60 Marks)
  3. Group-C contains 5(five) questions and each question contains 2/3 bits, out of which only 1(one) bit is to be answered. Each bit caries 6(six) Mark (6 × 5 = 30 Marks)

Unit I Relations and Functions

Chapter 1 Relations and Functions
Types of relations, reflexive, symmetric, transitive, and equivalence relations. One-to-one and onto functions, composite functions, the inverse of a function. Binary operations.

Chapter 2 Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Chapter 3 Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P) problems, mathematical formulation of L.P problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit II Algebra

Chapter 4 Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices; Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restrict to square matrices of order 2). concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Chapter 5 Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle, and Adjoint and inverse of a square matrix. Consistency, inconsistency, and a number of solutions of a system of linear equations by examples, solving a system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

Chapter 6 Probability
Conditional probability, multiplication theorem on probability. Independent events, total probability, Baye’s theorem, Random variable, and its probability distribution, mean and variance of a random variable. Independent (Bernoulli) trials and Binomial distribution.

Unit III Differential Calculus

Chapter 7 Continuity and Differentiability
Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

Chapter 8 Applications of Derivatives
Applications of derivatives: rate of change of bodies, increasing and decreasing functions, tangents, and normals, use of derivatives in approximation, maxima, and minima (first derivative test motivates geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

Unit IV Integral Calculus

Chapter 9 Integration
Integration as the inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions, and by parts, Evaluation of simple integrals of the following types and problems based on them.
\(\int \frac{d x}{x^2 \pm a^2}, \int \frac{d x}{x^2 \pm a^2}, \int \frac{d x}{a^2-x^2}, \int \frac{d x}{a x^2+b x+c}\)
\(\int \frac{d x}{a x^2+b x+c}, \int \frac{p x+q}{a x^2+b x+c} d x\)
\(\int \frac{p x+q}{a x^2+b x+c} d x, \int \sqrt{a^2 \pm x^2} d x\)
\(\int \sqrt{x^2-a^2} d x\)
\(\int \sqrt{a x^2+b x+c} d x, \int(p x+q) \sqrt{a x^2+b x+c} d x\)
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Chapter 10 Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ ellipses (in standard form only). The area between any of the two above-said curves (the region should be clearly identifiable).

Chapter 11 Differential Equations
Definition, order, and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by the method of separation of variables, solutions of homogeneous differential equations of the first order and first degree. Solutions of linear differential equation of the type:
\(\frac{dy}{dx}\) + py = q, wherep and q are functions of x or constants.
\(\frac{dx}{dy}\) + px = q, where p and q are functions of y or constants.

Unit V Vectors and Three-Dimensional Geometry

Chapter 12 Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties, and application of scalar (dot) product of vectors, vector (cross) product of vectors, a scalar triple product of vectors, and Coplanarity of three vectors.

Chapter 13 Three-dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Books Recommended:
Bureau’s Higher Secondary (+2) Elements of Mathematics, Part-II, Published by Odisha State Bureau of Text Book Preparation and Production, Bhubaneswar.

CHSE Odisha Class 12 Text Book Solutions

Plus Two Second Year Optional Odia Question Answer – Sahitya Dipti Question Answer (+2 2nd Year)

Class 12 Odia Optional Book Solutions – Sahitya Dipti Part 2 Question Answer ସାହିତ୍ୟ ଦୀପ୍ତି

Plus Two Second Year Optional Odia Question Answer | ସାହିତ୍ୟ ଦୀପ୍ତି Sahitya Dipti Part 2 Question Answer

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 10 Area Under Plane Curves Ex 10 Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Exercise 10

Question 1.
Find the area bounded by
(i) y = ex, y = 0, x = 4, x = 2
Solution:
Area = \(\int_2^4\)ex dx
= \(\left[e^x\right]_2^4\)
= e4 – e2

(ii) y = x2, y = 0, x = 1
Solution:
Area = \(\int_0^1\)x2 dx
= \(\left[\frac{x^3}{3}\right]_0^1\)
= \(\frac{1}{3}\)

CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10

(iii) xy = a2, y = 0, x = α, x = β (β > α > 0)
Solution:
Area = \(\int_\alpha^\beta y\)y dx
= \(\int_\alpha^\beta \frac{a^2}{x}\) dx
= a2\([\ln x]_\alpha^\beta\)
= a2 ln (β/α)

(iv) y = sin x, y = 0, x = \(\frac{\pi}{2}\)
Solution:
Area = \(\int_0^{\frac{\pi}{2}}\)sin x dx
= \([-\cos x]_0^{\frac{\pi}{2}}\)
= -cos\(\frac{\pi}{2}\) + cos θ = 1

Question 2.
Find the area enclosed by
(i) y = ex, x = 0, y = 2, y = 3
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.2

(ii) y2 = x, x = 0, y = 1
Solution:
Area = \(\int_0^1\)x dy
= \(\int_0^1\)y2 dy
= \(\left[\frac{y^3}{3}\right]_0^1\)
= \(\frac{1}{3}\)

(iii) xy = a2, x = 0, y = α, y = β (β > α > 0)
Solution:
Area = \(\int_\alpha^\beta\)x dy
= \(\int_\alpha^\beta \frac{a^2}{y}\)dy
= a2\([\ln y]_\alpha^\beta\)
= a2 ln (β/α)

(iv) y2 = x3, x = 0, y = 1
Solution:
Given curve is y2 = x3
⇒ x = y2/3
It passes through the origin. So the required area
= \(\int_0^1\)x dy
= \(\int_0^1 y^{\frac{2}{3}}\) dy
= \(\left[\frac{y^{\frac{5}{3}}}{5 / 3}\right]_0^1\)
= \(\frac{3}{5}\)

CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10

Question 3.
(i) Determineellipse the area with in the ellipse
\(\frac{x^2}{a^2}\) + \(\frac{y^2}{b^2}\) = 1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.3(1)
The ellipse is symmetrical about x-axis and y-axis.It is divided into 4 equal parts by the coordinate axes. So required area
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.3(1.1)

(ii) Find the area of the circle x2 + y2 = 2ax.
Solution:
Given circle is x2 + y2 = 2ax
⇒ x2 – 2ax + a2 + y2 = a2
⇒ (x – a)2 + y2 = a2 … (1)
The centre of the circle is (a, 0) and radius is a.
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.3(2)

(iii) Find the area of the portion of the parabola y2 = 4x bounded by the double ordinate through (3, 0).
Solution:
Given parabola is y2 = 4x
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.3(3)

(iv) Determine the area of the region bounded by y2 = x3 and the double ordinate through (2, 0)
Solution:
Given curve is y2 = x3
⇒ y = ±x3/2 … (1)
The curve passes through the origin and symmetrical about x-axis because the power of y is even.
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.3(4)

CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10

Question 4.
(i) Find the area of the regions into which the circle x2 + y2 = 4 is divided by the line x + √3y = 2.
Solution:
Given circle and the straight line are x2+ y2 = 4 and x+ √3y = 2
The circle has the centre at (0, 0) and radius ‘2’.
The eqn. (2) can be written as
y = –\(\frac{1}{\sqrt{3}}\)x + \(\frac{2}{\sqrt{3}}\)
Slope of the strainght line = –\(\frac{1}{\sqrt{3}}\)
The line makes and angle of 150° with x-axis making intercept \(\frac{2}{\sqrt{3}}\) from y-axis.
It intersects x-axis at (2, 0).
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(1)
Solveing (1) and (2),
ge wet (2 – 3√y)2 + y2 = 4
4 + 3√y2 – 4√3y + y2 = 4
4y2 – 4√3y = 0
y(y – √3) = 0
y = 0 or y = √3
When y = 0, x = 2
When y = √3, x = -1
Thus the straight line intersects the circle at (2, 0) and (-1, √3).
Area of the portion ACBA.
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(1.1)

(ii) Determine the area of the region between the curves y = cos x and y = sin x, bounded by x = 0.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(2)
The curves y = cos x and y = sin x are shown in the above figure. The region included between these two curves in [0, \(\frac{\pi}{4}\)] is OABO.
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(2.1)

(iii) Find the area enclosed by the two parabolas y2 = 4 ax and x2 = 4ay.
Solution:
The given parabolas are y2 = 4ax and x2 = 4ay.
The graphs of the two parabolas are shown in the figure.
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(3)
⇒ x4 = 64 a4
⇒ x4 – 64 a3x = 0
⇒ x (x3 – (4a)3) = 0
⇒ x (x – 4a) (x2 + 4ax + 16a2) = 0
⇒ x = 0, 4a
When x = 0, y = 0 and
when x = 4a, y = 4a
Thus the two parabolas intersect at (0, 0) and (4a, 4a).
Area between two parabolas
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(3.1)

(iv) Determine the area common to the parabola y2 = x and the circle x2+ y2 = 2x.
Solution:
Gien parabola is y2 = x
Given circle is
x2 + y2 = 2x ⇒ (x – 1)2 + y2 = 1
The centre is at (1, 0) and radius is 1.
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(4)
Solving (1) and (2) we get
x2 + x = 2x ⇒ x2 – x = 0 ⇒ x(x – 1) = 0
⇒ x = 0, x = 1
When x = 0, y = 0 and when x = 1, y = 1.
Thus both the parabola and circle intersect at (0, 0) and (1, 1).
Required Area
CHSE Odisha Class 12 Math Solutions Chapter 10 Area Under Plane Curves Ex 10 Q.4(4.1)

CHSE Odisha Class 12 Invitation to English 1, 2, 3, 4 Book Solutions Answers Pdf

CHSE Odisha +2 2nd Year Invitation to English-1 2 3 4 Book Solutions Guide Question Answers Pdf Download

CHSE Class 12 Invitation to English 1 Solutions Answers Pdf

CHSE Class 12 Invitation to English 1 Answers Pdf (Prose and Poetry)

Unit-I Prose

Unit-II Poetry

CHSE Class 12 Invitation to English 2 Solutions Answers Pdf

CHSE Class 12 Invitation to English 2 Answers Pdf (Stories, Plays and Biographies)

Unit-III Non-Detailed Study

CHSE Class 12 Invitation to English 3 Solutions Answers Pdf

CHSE Class 12 Invitation to English 3 Answers Pdf (Steps to Writing)

Unit-IV Writing Skills

CHSE Class 12 Invitation to English 4 Solutions Answers Pdf

CHSE Class 12 Invitation to English 4 Answers Pdf (Grammar in Context and Translation)

Unit-V Grammar

CHSE Odisha Class 12 Invitation to English-1,2,3,4 Syllabus

CHSE Odisha Class 12 Invitation to English-1,2,3,4 Syllabus

CHSE Odisha Class 12 Invitation to English-1,2,3,4 Syllabus 1

Book Prescribed: Invitation to English – 1,2,3 & 4, Published by Odisha State Bureau of Text Book Preparation and Production, Bhubaneswar.

CHSE Odisha Class 12 Invitation to English Question Paper Pattern and Distribution of Marks

English +2, 2nd Year
Full Mark: 100, Time: 3 Hours

1. Reading Comprehension
(a) Prescribed Prose Pieces (10 marks)
(5 questions to be answered, each carrying 2 marks)
(b) Prescribed Poems (10 marks)
(5 questions to be answered each carrying 2 marks)
(c) Prescribed Extensive Reading Texts (10 marks)
(2 questions to be answered carrying 5 marks each; only global inferential and evaluative questions to be set on a passage of about 250 words)
(d) Unseen Prose passage (10 marks)
(5 questions including inferential ones, carrying 2 marks each)

2. Reading-related skills
(a) Vocabulary skills (to be tested on the unseen passage) (5 marks)
(b) Information Transfer (70 words) (5 marks)
(Converting non-Verbal information into verbal form)
(c) Dictionary/Reference skills (5 marks)

3. Writing Skills
(a) Report Writing (200 words) (10 marks)
(b) Guided Note making on a given passage (7 marks)
(c) Summarizing the same passage (8 marks)
(d) Essay writing (250 words on given outlines) (10 marks)

4. Grammar in Context (10 marks)

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha Class 12 History Book Solutions (+2 2nd Year)

CHSE Odisha 12th Class History Book Solutions (+ 2 2nd Year)

CHSE Odisha 12th Class History Book Solutions in English Medium

Unit 1 Sources of Indian History

Unit 2 Religious Movements of Sixth Century BC

Unit 3 Perceptions of Society through the Eyes of the Travellers (10th to 17th Centuries)

Unit 4 British Economic Policies in India (1757-1857 A.D.)

Unit 5 Colonial Cities

CHSE Odisha 12th Class History Book Solutions in Odia Medium

Chapter 1 ପ୍ରାଚୀନ ଭାରତ ଇତିହାସର ଉପାଦାନ

Chapter 2(a) ସିନ୍ଧୁ ସଭ୍ୟତା / ହରପ୍‌ପା ସଭ୍ୟତା

Chapter 2(b) ବୈଦିକ ଏବଂ ପରବର୍ତୀ ବୈଦିକ ଯୁଗ

Chapter 3 ଷୋଡ଼ଶ ମହାଜନପଦ

Chapter 4 ଖ୍ରୀ.ପୂ. ଷଷ୍ଠ ଶତାବ୍ଦୀର ଧର୍ମୀୟ ସଂସ୍କାର ଆନ୍ଦୋଳନ-ଜୈନଧର୍ମ, ବୌଦ୍ଧଧର୍ମ

Chapter 5 କଳିଙ୍ଗ ଯୁଦ୍ଧ, ମୌର୍ଯ୍ୟ ଶାସନ

Chapter 6 ଗୁପ୍ତଯୁଗର ସାଂସ୍କୃତିକ ବିକାଶ

Chapter 7 ପରିବ୍ରାଜକଙ୍କ ଚକ୍ଷୁରେ ଭାରତୀୟ ସମାଜ ସମ୍ପର୍କରେ ଧାରଣା

Chapter 8 ଦିଲ୍ଲୀରେ ସୁଲତାନୀ ରାଜତ୍ଵ

Chapter 9 ମୋଗଲ ଯୁଗର ସଂସ୍କୃତି

Chapter 10 ସୁଫି ଓ ଭକ୍ତି ଆନ୍ଦୋଳନ

Chapter 11 ଭାରତରେ ବ୍ରିଟିଶ୍ ଔପନିବେଶିକ ଅର୍ଥନୀତି (୧୭୫୭ ରୁ ୧୮୫୭)

Chapter 12 ବ୍ରିଟିଶ୍ ଔପନିବେଶିକ ବିରୁଦ୍ଧରେ ବିଦ୍ରୋହ ସନ୍ନ୍ୟାସୀ ବିଦ୍ରୋହ, ଖୋର୍ଦ୍ଧା ବିଦ୍ରୋହ (୧୮୧୭), ସାନ୍ତାଳ ବିଦ୍ରୋହ (୧୮୫୬-୫୬), ମହାନ୍ ଭାରତୀୟ ବିଦ୍ରୋହ (୧୮୫୭)

Chapter 13 ମହାତ୍ମା ଗାନ୍ଧି ଏବଂ ସ୍ଵାଧୀନତା ପାଇଁ ଜାତୀୟ ସଂଗ୍ରାମ

Chapter 14 ଔପନିବେଶିକ ସହରସମୂହ-ସହରୀକରଣ, ଯୋଜନା ଏବଂ କାରୁକାର୍ଯ୍ୟ

Chapter 15 ସ୍ଵତନ୍ତ୍ର ଓଡ଼ିଶା ପ୍ରଦେଶ ଗଠନ

Chapter 16 ଓଡ଼ିଶା ପ୍ରତି ଅବଦାନ : ମଧୁସୂଦନ ଦାସ, ଗୋପବନ୍ଧୁ ଦାସ, କୃଷ୍ଣଚନ୍ଦ୍ର ଗଜପତି, ସରଳା ଦେବୀ, ରମା ଦେବୀ ଓ ମାଳତୀ ଦେବୀ

Chapter 17 ଭାରତୀୟ ସମ୍ବିଧାନର ଗଠନ

CHSE Odisha Class 12 History Syllabus (+2 2nd Year)

2nd Year (Paper-II)
History of India

UNIT-1

  1. Sources of Indian History: Archaeological, Literary, Foreign Accounts and Archival
  2. Foundation of Indian Culture:
    a) Harappan culture: Discovery, Geographical extent, Town planning, Structures, Agriculture, Domestication of Animals, Technology and Craft, Trade, Contact with distant lands, Scripts, Weights, Measurement, Religious beliefs, and Seals.
    b) Rig Vedic and Later Vedic Age – Socio-Economic life, Political organization, Religious
    Beliefs, Position of Women.
  3. The Earliest states: Sixteen Mahajanapadas.

UNIT-II

  1. Religious Movements of Sixth Century B.C. – Jainism and Buddhism: A critical evaluation of the Teachings, Contribution to Indian culture.
  2. Kalinga War – Causes and Effects; Mauryan Administration.
  3. Cultural Attainments of the Gupta Age.

UNIT-III

  1. Perceptions of society through the eyes of the Travellers (10th to 17th centuries).
    (a) Al-Biruni, (b) Ibn Battuta, (c) Francois Bernier
  2. Delhi Sultanate: Nature of State, Social structure, Position of Women.
  3. Culture of Mughal Age: Social structure, Position of Women, Art and Architecture, Paintings, Din-i-Ilahi.
  4. Sufi and Bhakti Movements: Tenets, Impact on Indian Society.

UNIT-IV

  1. British Economic Policies in India (1757-1857 A.D.): Commercial Policy, Drain of Wealth, Development of means of Transport and Communication; Revenue Policy.
  2. Revolts against British Colonialism – Sanyasi Rebellion, Khurda Rebellion of 1817, Santal Rebellion (1855-56), The Great Indian Revolt of 1857.
  3. Mahatma Gandhi and National Struggle for Independence:
    a) Non-Cooperation Movement and its response in Odisha, b) Civil Disobedience Movement and its response in Odisha, c) Quit India Movement and its response in Odisha.

UNIT-V

  1. Colonial Cities – Urbanisation, Planning and Architecture:
    a) Towns and Cities in pre-colonial times, b) Changes in 18th century, c) Trends of changes in the 19th century, d) Ports, Forts and Centres for Services, e) A new urban milieu, f) The First Hill Stations, g) Social life in new cities, h) Colonial Architecture in Calcutta (Kolkata), Bombay (Mumbai) and Madras (Chennai).
  2. Formation of the Province of Odisha.
    a) Movement for Linguistic Identity, b) Events leading to the formation of the province
  3. Contributions of (a) Madhusudan Das, Gopabadhu Das, Krushna Chandra Gajapati, (b) Sarla Devi, Rama Devi and Malati Devi.
  4. Framing the Indian Constitution:
    a) Making of the Constituent Assembly, b) Vision of the Constitution, c) Salient features

BOOK PRESCRIBED:
Bureau’s Higher Secondary (+2) History, Published by Odisha State Bureau of Textbook Preparation & Production, Bhubaneswar.

CHSE Odisha Class 12 Text Book Solutions

CHSE Odisha MIL Sanskrit Class 12 Question Answer (+2 2nd Year)

+2 2nd Year MIL Sanskrit Book Solutions Pdf Download

गद्यभागः ଗଦ୍ୟଭାଗଃ

पद्यभागः ପଦ୍ୟଭାଗଃ

BSE Odisha Class 12 Sanskrit Grammar

CHSE Odisha Class 12 Sanskrit Question Pattern and Distribution of Marks

+2 M.I.L Sanskrit
Second Year

There shall be one piece of paper carrying 100 Marks. The duration of the Examination will be of three hours.

Course Structure

Classes Required Marks Allotted
(a) Reading Skill 20 20
(b) Writing Skill 25 40
(c) Literary Text 35 40
Total 80 Classes 100 Marks

 

Portions To Be Studied

(a) Prose – Sanskrutaprabha (Gadyabhagah)
संस्कृतभाषा (गद्यभागः)
The following proe pieces from the above mentioned book are to be studied
1. कपोतलुब्धककथा ( Kapotalubdhakakatha)
2. सुश्रुतस्य यन्त्रकर्मशस्त्रकर्माणि (Susrutasya Yantrakarmasastrakarmini)
3. गुणिगुणहीनविवेकः (Gunigunahinavivekah)
4. रामतपोवनभिगमनम् (Ramatapovanabhigamanam)

(b) Poetry – Samskrtaprabha (Podyabhagah)
संस्कृतभाषा (पद्यभागः)
The following poetry pieces from the above book are to be studied
1. दशवतारस्तुति: ( Dasavatarastutih)
2. गीतासौरभम् (Gitasourabham)
3. रघुवंशम् (Raghuvamsam)

(c) Grammar from the Prose and Poetry

1. कारक – विभक्ति (Karak Vibhakti)
2. सन्धि – सन्धिविच्छेद (Sandhi and Sandhi Viccheda)

(d) Topics from the Grammar text
1. शब्दरूप (Sabdarupa) (नर, फल, लता, मुनि, मति, वारि, नदी, पितृ, मातृ, गच्छत्, मनस्, आत्मन्, तद्, किम्, इदम् अस्मद् युष्मद्, द्वि, त्रि, चतुर)
2. धातुरूप (Dhaturupa) (भू, गम्, पठ्, कृ, अस्, लभ्, पूज्)
3. समास (Samasa)
4. स्त्री प्रत्यय (Stripratyaya)

(e) Translation and Comprehension

1. Comprehension – Sanskrit Passage from the comprehension pasages of संस्कृतभाषा, Part II.
2. Translation into Odia/English from Prose and Poetry, Translation from Odia/English to Sanskrit.

(f) Writing Skill
The art of writing – Textual Explanation, Textual long questions and Precis writing.

Distribution of Marks

1. Reading Skill (20 Marks)
(i) Multiple choice questions from Prose & Poetry (3 + 2) (1 × 5 = 5 Marks)
(ii) Very short questions from Prose & Poetry (2 + 3) (1 × 5 = 5 Marks)
(iii) Short questions from Prose & Poetry (1 + 1) (2 × 2 = 4 Marks)
(out of 4 questions)
(iv) Two questions from Prose & Poetry (1 + 1) (3 × 2 = 6 Marks)
(out of 4 questions)

2. Writing Skill (40 Marks)
(i) Very short questions from Grammar Text – 10 Marks (40 Marks)
(a) Sabdarupa (1 × 3 = 3 Marks)
(b) Dhaturupa (1 × 3 = 3 Marks)
(c) Samasa (1 × 2 = 2 Marks)
(d) Stripratyaya (1 × 22 Marks)
(ii) Translation of verse into Odia/English from Poetry Text (4 × 1 = 4 Marks)
(out of 2 verses)
iii) Translation of passage to Odia/English from Prose Text (6 × 1 = 6 Marks)
iv) Precis writing – 1/3 of an Unseen Passage (10 Marks)
v) Unseen Passage translation from Odia/English to Sanskrit (10 Marks)

3. Literary Text
(i) Grammar from Prose/Poetry Text (10 Marks)
Karaka – Vibhakti (2 × 3 = 6 Marks)
Sandhi and Sandhi-Vicchheda (1 × 4 = 4 Marks)
(ii) Explanation of Verse from Poetry text (one) (8 × 1 = 8 Marks)
(iii) Questions from Prose & Poetry (1 + 1) (6 × 2 = 12 Marks)
(out of 4 questions)
(iv) Comprehension of passage from the text (9 – 16) (2 × 5 = 10 Marks)

Note: Answers in Sanskrit are to be written either in Odia script or in Devanagari script.

CHSE Odisha Class 12 Psychology Unit 5 Questions and Answers

Odisha State Board CHSE Odisha Class 12 Psychology Solutions Unit 5 Questions and Answers.

CHSE Odisha 12th Class Psychology Unit 5 Questions and Answers

Objective Type Question and Answers

Question 1.
The measures of central tendency are:
(a) mean
(b) median
(c) mode
(d) all the above
Answer :
(d) all the above

Question 2.
_____is the middle score in a set of scores that have been ranked in numerical order.
(a) mode
(b) median
(c) range
(d) mean
Answer :
(b) median

Question 3.
_______is the best method of central tendency to use when describing skewed
data.
(a) mode
(b) median
(c) range
(d) mean
Answer :
(b) median

Question 4.
_____ is simply the most frequently occurring score in a data set.
(a) median
(b) range
(c) mean
(d) mode
Answer :
(d) mode

Question 5.
The two-mode are :
(a) binodal
(b) multimodal
(c) only (a)
(d) both (a) and (b)
Answer :
(d) both (a) and (b)

Question 6.
The informative measure of variability I_____.
(a) variance
(b) median
(c) only(b)
(d) none of the above
Answer :
(a) variance

Question 7.
______statistics is the name given to the procedure used to collect classify, summarize and present data.
(a) variance
(b) median
(c) descriptive
(d) only (a)
Answer :
(c) descriptive

Question 8.
The highest and lowest scores in a distribution and it founding by subtracting the lowest force him the highest score is called_____
(a) range
(b) mode
(c) median
(d) variance
Answer :
(a) range

Question 9.
Standard deviation is the root of _____.
(a) variance
(b) range
(c) mode
(d) none of the above
Answer :
(a) variance

Question 10.
The measures of variability used by researchers include the
(a) range
(b) variance
(c) standard deviation
(d) all the above
Answer :
(d) all the above

CHSE Odisha Class 12 Psychology Unit 5 Questions and Answers

Answer in single word / single sentence

Question 1.
Mode is simply the difference between the highest and lowest score in a distribution?
Answer :
True

Question 2.
Mode is useful as a rough guide to the variability demonstrated by a data set?
Answer :
False

Question 3.
The measures of variability used by researchers include the range the variance and standard deviation?
Answer :
True

Question 4.
Median is a good measure of central tendency?
Answer :
True

Question 5.
Mode is the middle score in a set of scores that have been ranked in numerical order?
Answer :
False

Question 6.
Mean is the arithmetic average of a set of scores?
Answer :
True

Question 7.
Methods of determining these central values are called measures of central tendency?
Answer :
True

Question 8.
Four main measures of central tendency?
Answer :
False

Question 9.
The mean can not affect by external scores?
Answer :
False

CHSE Odisha Class 12 Psychology Unit 5 Questions and Answers

Very Short Type Questions With Answer

Question 1.
What is Mean?
Answer :
When people talk about averages, they’re often referring to the mean, which is the arithmetic average of a set of scores. You have probably calculated the mean of a set of Psychology scores many times in the past. Every time you sum a set of scores and divide that sum by the total number of scores you have calculated the arithmetic mean of those scores.

Question 2.
What is the Median?
Answer :
The median is the middle score in a set of scores that have been ranked in numerical order. In cases where there are an even number of scores, the median lies between the two middle scores and is given the value of the midpoint between those scores. Of course, if the middle two scores in an even number of scores are the same, the median has the same value as the two scores themselves.

Question 3.
Range?
Answer :
The range is simply the difference between the highest and lowest scores in a distribution and is found by subtracting the lowest score from the highest score. This measure of variability gives the researcher only a limited amount of information, as data sets which are skewed towards a low score can have the same range as data sets which are skewed towards a high score, or those which cluster around some central score.

Question 4.
What is Variance?
Answer :
A more informative measure of variability is the variance, which represents the degree to which scores tend to vary from their mean. This tends to be more informative because, unlike the range, the variance takes into account every score in the data set. Technically speaking, the variance is the average of the squared deviations from the mean.
To calculate the variance for a set of quiz scores:

  • Find the mean score.
  • Find the deviation of each raw score from the mean. To do this,
  • Subtract the mean from each raw score. (Note that deviation scores will be negative for scores that are below the mean.) To check your calculations sum the deviation scores. This sum should be equal to zero.
  • Square the deviation scores: By squaring the scores, negative scores are made positive and extreme scores are given relatively more weight.
  • Find the sum of the squared deviation scores.
  • Divide the sum by the number of scores. This yields the average of the squared deviations from the mean, or the variance.

Question 5.
What is the Median?
Answer :
The median is the middle score in a set of scores that have been ranked in numerical order. In cases where their art an even number of scores, the median lies between the two middle scores and is given the value of the midpoint between those scores. Of course, if the middle two scores in an even number of scores are the same, the median has the same value as the two scores themselves.

There is no formula for quickly calculating the median Without doing some initial data analysis. Typically, when dealing with large data sets, researchers construct a frequency distribution representing all the scores in the data set. This allows time to use a formula to calculate each measure of central tendency using the information provided by the frequency distribution.

Unlike the mean, the median is a good measure of central tendency to use when describing a heavily skewed set of scores. Returning to our example from above, our student’s median test score would be 94%, which is a much better indication of the student’s overall performance.

Thus, the median is a better representation of the scores within a skewed data set than is the mean. In fact, the median is the best method of central tendency to use when describing skewed data.

CHSE Odisha Class 12 Psychology Unit 5 Questions and Answers

Long Questions With Answers

Question 1.
What statistical use for psychology?
Answer :
Much of psychological research involves measuring observations of particular characteristics of either a population or a sample taken from a population. These measurements yield a set of values or scores, and this set represents the findings of the research or data. Often, it is impractical to completely measure, the characteristics of a given population, known as parameters, directly.

Thus, psychologists often focus on the characteristics of samples taken from a population. These characteristics are called statistics. The psychologist then uses these sample statistics to make inferences about population parameters.

In this section, we will focus on a type of statistics known as descriptive statistics. We will begin with an examination of three methods of describing a set of data using scores that seem to be typical of those found in the set. We will then look at three methods of describing how scores within the set vary from these typical scores.

Question 2.
Measures of Central Tendency.
Answer :
Often, data tends to group itself around some central value. This value may, in turn, be used to describe or represent the data set as a whole. Methods of determining these central values are called measures of central tendency. There are three main measures of central tendency used by psychologists. They are the mean, the median, and the mode.

Mean :
When people talk about averages, they’re often referring to the mean, which is the arithmetic average of a set of scores. You have probably calculated the mean of a set of Psychology scores many times in the past. Every time you sum a set of scores and divide that sum by the total number of scores you have calculated the arithmetic mean of those scores.

As you probably know from experience, the mean can be affected by extreme scores. For example, if a student were to receive five test marks over 90% and one test mark less than 20%, (let us say marks of 98%, 96%, 94%, 94%, 92%, and 18%), the mean of – 497 – the test scores would be (98 + 96 + 94 + 94 + 92 +18) / 6 = 82.

Obviously, the mean, in this case, has been pulled in the direction of the score of under 20%. For this reason, the mean can be a very, misleading description of a set of scores with a heavily skewed distribution.

Median :
The median is the middle score in a set of scores that have been ranked in numerical order. In cases where there are an even number of scores, the median lies between the two middle scores and is given the value of the midpoint between those scores. Of course, if the middle two scores in an even number of scores are the same, the median has the same value as the two scores themselves.

There is no, the formula for quickly calculating the median without doing some initial data analysis. Typically, when dealing with large data sets, researchers construct a frequency distribution representing all the scores in the data set. This allows them to use a formula to calculate each measure of central tendency using the information provided by the frequency distribution.

Unlike the mean, the median is a good measure of central tendency to use when describing a heavily skewed set of scores. Returning to our example from above, our student’s median test score would be 94%, which is a much better indication of the student’s overall performance. Thus, the median is a better representation of the scores within a skewed data set than is the mean. In fact, the median is the best method of central tendency to use when describing skewed data.

Mode :
The mode is simply the most frequently occurring score in a data set. Returning once again to the test scores of our sample student, the mode for this data set is would be 94%, as it occurs twice within the data set. If two scores occur equally often within a data set, the set has two modes and is termed bimodal. Any data set that has two or more modes can be referred to as multimodal.

Like the median, there is no formula for calculating the mode without conducting at least some preliminary data analysis. For small data sets the mode may simply be determined by comparing the number of times the most popular scores appear in the set.
Measures of Variability
Almost all data sets demonstrate Some degree of variability. In other words, data sets usually contain scores that differ from one another. Only under very rare circumstances to researchers encounter data sets that have no variability.

Needless to $ say, of the few sets of data that demonstrate no variability, fewer still will be of any interest to psychological researchers. The truly interesting observations are those of characteristics that vary within a population or sample. This variability cannot be captured or shown by measures of central tendency.

For. example, if two data sets have the same mean, there is no guarantee that the two – 498 – sets are very similar at all. What is needed are measures of variability which allow the researcher to determine the degree of variation within a population or sample, and thus to determine just how representative a particular score is of the data set as a whole.

This in turn allows the researcher to determine the scope and validity of any generalizations he or she wishes to make based on his or her observations. The measures of variability used by | researchers include the range, the variance, and the standard deviation.

Question 3.
What is Range?
Answer :
The range is simply the difference between the highest and lowest scores in a
distribution, and is found by subtracting the lowest score from the highest score. This measure of variability gives the researcher only a limited amount of information, as data sets which are skewed towards a low score can have the same range as data sets which are skewed towards a high score, or those which cluster around some central score.

The range is, however, useful as a rough guide to the variability demonstrated by a data set, as it tells the researcher how a particular score compares to the highest and lowest scores within a data set. For example, a student might find it useful to know whether his or her score was near the best or worst on an exam.

CHSE Odisha Class 12 Psychology Unit 5 Questions and Answers

Question 4.
What is Variance?
Answer :
A more informative measure of variability is the variance, which represents the degree to which scores tend to vary from their mean. This tends to be more informative because, unlike the range, the variance takes into account every score in the data set. Technically speaking, the variance is the average of the squared deviations from the mean.
To calculate the variance for a set of quiz scores:

  • Find the mean score.
  • Find the deviation of each raw score from the mean. To do this,
  • Subtract the mean from each raw score. (Note that deviation scores will be negative for scores that are below the mean.) To check your calculations sum the deviation scores. This sum should be equal to zero.
  • Square the deviation scores. By squaring the scores, negative scores are made positive and extreme scores are given relatively more weight.
  • Find the sum of the squared deviation scores.
  • Divide the sum by the number of scores. This yields the average of the squared deviations from the mean, or the variance.

Question 5.
What is Standard Deviation?
Answer:
More informative still is the standard deviation, which is simply the square root of the variance. You may be asking yourself why not simply use the variance ?’ One reason is that, unlike the variance, the standard deviation is in the same units as the raw scores themselves. This is what makes the standard deviation more meaningful. For example, it would make more sense to discuss the variability of a. set of IQ scores in IQ points than in squared IQ points.

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