NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2

Get the comprehensive Chapter 8 Ex 8.2 Class 10 Maths NCERT Solutions from here and score good marks in CBSE Class 10 Board Examinations

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 8 Introduction to Trigonometry Class 10 NCERT Solutions Ex 8.2.

BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 8
Chapter NameIntroduction to Trigonometry
ExerciseEx 8.2
Number of Questions Solved4
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2

NCERT Solutions for Class 10 Maths

Page No: 187

Question 1. Evaluate the following :
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan245° + cos230° – sin260°
(iii) \(\frac { cos45^{ 0 } }{ sec{ 30 }^{ 0 }+cosec{ 30 }^{ 0 } } \)
(iv) \(\frac { sin{ 30 }^{ 0 }+tan45^{ 0 }-cosec{ 60 }^{ 0 } }{ sec{ 30 }^{ 0 }+cosec{ 60^{ 0 } }+cot{ 45 }^{ 0 } } \)
(v) \(\frac { 5cos^{ 2 }{ 60 }^{ 0 }+4sec^{ 2 }{ 30 }^{ 0 }-tan^{ 2 }{ 45 }^{ 0 } }{ sin^{ 2 }{ 30 }^{ 0 }+cos^{ 2 }{ 30 }^{ 0 } } \)

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 16

Question 2. Choose the correct option and justify your choice :
(i) \(\frac { 2tan{ 30 }^{ 0 } }{ 1+tan^{ 2 }{ 30 }^{ 0 } } =\)
(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°

(ii) \(\frac { 1-tan{ ^{ 2 }45 }^{ 0 } }{ 1+tan{ ^{ 2 }45 }^{ 0 } } =\)
(A) tan 90° (B) 1 (C) sin 45° (D) 0

(iii) sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°

(iv) \(\frac { 2tan{ 30 }^{ 0 } }{ 1-tan{ ^{ 2 }30 }^{ 0 } } =\)
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 17
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 18

Question 3. If tan (A + B) = √3 and tan (A – B) = 1/√3; 0° < A + B ≤ 90°; A > B, find A and B.

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 19

Question 4. State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 20

 

We hope the NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3

NCERT Maths Solutions for Ex 2.3 class 10 Polynomials is the perfect guide to boost up your preparation during CBSE 10th Class Maths Examination.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 2 Polynomials Class 10 NCERT Solutions Ex 2.3. 

BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 2
Chapter NamePolynomials
ExerciseEx 2.3
Number of Questions Solved5
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3

Page No: 36

Question 1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 15

Solution:

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 16
Quotient = x – 3
Remainder = 7x – 9

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 18
Quotient = x2 + x – 3
Remainder = 8

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 19
Quotient = -x2 – 2
Remainder = -5x + 10

Concept Insight: While dividing one polynomial by another, first arrange the polynomial in descending powers of the variable. In the process of division, be careful about the signs of the coefficients of the terms of the polynomials. After performing division, one can check his/her answer obtained by the division algorithm which is as below:
Dividend = Divisor x Quotient + Remainder
Also, remember that the quotient obtained is a polynomial only.

Question 2. Check whether the first polynomial is a factor of the second polynomial by dividing the
second polynomial by the first polynomial:
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 20

Solution:
The polynomial 2t4 + 3t3 – 2t2 – 9t – 12  can be divided by the polynomial t2 – 3 = t2 + 0.t – 3 as follows:

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 21
Since the remainder is 0, t² – 3 is a factor of 2t4 + 3t3 – 2t2 – 9t – 12 .
(ii) The polynomial 3x4 + 5x3 – 7x2 + 2x + 2 can be divided by the polynomial x2 + 3x + 1 as follows:
Since the remainder is 0, x² + 3x + 1 is a factor of 3x4 + 5x3 – 7x2 + 2x + 2
(iii) The polynomial x5 – 4x3 + x2 + 3x + 1 can be divided by the  polynomial x3 – 3x + 1 as follows:
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 22
Since the remainder is not equal to 0, x3 – 3x + 1 is not a factor of x5 – 4x3 + x2 + 3x + 1.

Concept Insight: A polynomial g(x) is a factor of another polynomial p(x) if the remainder obtained on dividing p(x) by g(x) is zero and not just a constant. While changing the sign, make sure you do not change the sign of the terms which were not involved in the previous operation. For example in the first step of (iii), do not change the sign of 3x + 1.

Question 3. Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and – √(5/3).

Solution:
Let p(x) = 3x4 + 6x3 – 2x2 – 10x -5
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 23
Now, x² + 2x + 1 = (x + 1)2
So, the two zeroes of  x² + 2x + 1 are -1 and -1.
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 24

Concept Insight:  Remember that if (x – a) and (x – b) are factors of a polynomial, then (x – a)(x – b) will also be a factor of that polynomial. Also, if a is a zero of a polynomial p(x), where degree of p(x) is greater than 1, then (x – a) will be a factor of p(x), that is when p(x) is divided by (x – a), then the remainder obtained will be 0 and the quotient will be a factor of the polynomial p(x). To cross check your answer number of zeroes of the polynomial will be less than or equal to the degree of the polynomial.

Question 4. On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and
-2x + 4, respectively. Find g(x).

Solution:
Divided, p(x) = x3 – 3x2 + x + 2
Quotient = (x – 2)
Remainder = (-2x + 4)
Let g(x) be the divisor.
According to the division algorithm,
Dividend = Divisor x Quotient + Remainder
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 25

Concept Insight: When a polynomial is divided by any other non-zero polynomial, then it satisfies the division algorithm which is as below:
Dividend = Divisor x Quotient + Remainder
Divisor x Quotient = Dividend – Remainder
So, from this relation, the divisor can be obtained by dividing the result of (Dividend – Remainder) by the quotient.

Question 5. Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0

Solution:
According to the division algorithm, if p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that
p(x) = g(x) x q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).

(i)  Degree of quotient will be equal to degree of dividend when divisor is constant.
Let us consider the division of 18x2 + 3x + 9  by 3.
Here, p(x) = 18x2 + 3x + 9  and g(x) = 3
q(x) = 6x2 + x + 3  and r(x) = 0
Here, degree of p(x) and q(x) is the same which is 2.
Checking:
p(x) = g(x) x q(x) + r(x)
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 26
Thus, the division algorithm is satisfied.

(ii)  Let us consider the division of 2x4 + 2x by 2x3,
Here, p(x) = 2x4 + 2x and g(x) = 2x3
q(x) = x and r(x) = 2x
Clearly, the degree of q(x) and r(x) is the same which is 1.
Checking,
p(x) = g(x) x q(x) + r(x)
2x4 + 2x =  (2x3 ) x x  + 2x
2x4 + 2x = 2x4 + 2x
Thus, the division algorithm is satisfied.

(iii)    Degree of remainder will be 0 when remainder obtained on division is a constant.
Let us consider the division of 10x3 + 3 by 5x2.
Here, p(x) = 10x3 + 3 and g(x) = 5x2
q(x) = 2x and r(x) = 3
Clearly, the degree of r(x) is 0.
Checking:
p(x) = g(x) x q(x) + r(x)
10x3 + 3 = (5x2 ) x 2x  +  3
10x3 + 3 = 10x3 + 3
Thus, the division algorithm is satisfied.

Concept Insight: In order to answer such type of questions, one should remember the division algorithm. Also, remember the condition on the remainder polynomial r(x). The polynomial r(x) is either 0 or its degree is strictly less than g(x). The answer may not be unique in all the cases because there can be multiple polynomials which satisfy the given conditions.

 

We hope the NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3, drop a comment below and we will get back to you at the earliest.

Maharashtra SSC Time Table 2020 (Exams Postponed) | Download Maharashtra Class 10 Date Sheet

Maharashtra SSC Class 10 Date Sheet

Maharashtra SSC Board Exam Time Table 2020: Maharashtra officials have released a time table for class 10 students for the year 2020. Previously, the provisional Maharashtra 10th Time Table 2020 was announced. The students now can download the final SSC Time Table 2020 Maharashtra Board. It is accessible online on the official website mahahsscboard.maharashtra.gov.in. A direct link to download the time table is also provided on this page below.

Latest Update: Maharashtra SSC Board Exams has been postponed due to the spread of COVID-19.

Depending on the Maharashtra SSC Time Table for Class 10, the board exams will commence from March 03, 2020. Post 22 days, the exams will conclude on March 23, 2020. The exams will be conducted in the morning including the evening slot. Students will have to appear for the exams according to the opted subjects. Furthermore, details of Maharashtra SSC Time Table for Class 10 are provided in the content below.

Maharashtra SSC Board Time Table 2020 Overview

In compliance with the timetable 2020, the board exams for Class 10 will start from 3rd March to 23rd March 2020. The exams will be conducted in two slots, that is morning and evening. The morning slot will be conducted from 11:00 AM to 2:00 PM. The evening slot will be held from 3:00 PM to 6:00 PM. In this article, we will give you all the information regarding 10th Time table 2020 Maharashtra board. Maharashtra SSC Time Table For Class 10 PDF link is given below.

The time table has been announced for 9 divisions including Pune, Konkan, Nagpur, Latur, Aurangabad, Nashik, Mumbai, Amaravati, and Kolhapuri. The time table for the last year was very concise and the students were not having the required time to revise. We will offer you all the information considering the 10th exam time table 2020 Maharashtra. Read on to find more about the 10th SSC time table 2020.

Maharashtra SSC Time TableOverview
The Exams will Begin From03 March 2020
The Last Date of the Exams23 March 2020
Mode Of The ExaminationOffline
Exam TimingsMorning: 11:00 AM to 2:00 PM
Evening: 3:00 PM to 6:00 PM
CategoryMaharashtra SSC Time Table For Class 10
Official Websitemahahsscboard.maharashtra.gov.in

Download Maharashtra SSC Time Table 2020 PDF 

Maharashtra SSC Exam Time Table 2020

DateSubjectShift/Time
03rd March 2020First Language

  • Marathi (01)
  • Hindi (02)
  • Urdu (04)
  • Gujarati (05)
  • Kannada (06)
  • Tamil (07)
  • Telugu (08)
  • Malayalam (09)
  • Sindhi (10)
  • Bengali (11)
  • Punjabi (12)
11:00 AM to 2:00 PM
Second Language: German (34) or
Third Language: French (35)
3:00 PM to 600 PM
04th March 2020Second/Third Language

  • Marathi (16)
  • Kannada (20)
  • Tamil (21)
  • Telugu (22)
  • Malayalam (23)
  • Sindhi (24)
  • Bengali (25)
  • Punjabi (26)
11:00 AM to 2:00 PM
Second/Third Language
Marathi (Composite)
11:00 AM to 1:00 PM
06th March 2020Second or Third Language: Hindi (15)
Second or Third Language: Hindi (Composite) anusha
11:00 AM to 2:00 PM
11:00 AM to 1:00 PM
07th March 2020Second/Third Language

  • Urdu (18)
  • Gujarati (19)
  • Sanskrit (27)
  • Pali (28)
  • Ardhamagadhi (29)
  • Persian (30)
  • Arabic (31)
  • Avesta (32)
  • Pahlavi (33)
  • Russian (36)
11:00 AM to 2:00 PM
09th March 2020First Language: English11:00 AM to 2:00 PM
Third Language: English anusha11:00 AM to 2:00 PM
12th March 2020Mathematics Part – I : (Algebra)11:00 AM to 1:00 PM
Arithmetic (For Blind, Deaf, Spastics, Autism, Learning Disabled & other eligible Divyang Candidates)11:00 AM to 1:00 PM
14th March 2020Mathematics Part –II
Geometry
11:00 AM to 1:00 PM
16th March 2020Science and Technology Part-I11:00 AM to 1:00 PM
Physiology Hygiene & Home Science (For Special needs Divyang-Blind, Deaf, Spastics, Autism & Learning disabled, etc., Candidates)11:00 AM to 1:30 PM
18th March 2020Science and Technology Part-II11:00 AM to 1:00 PM
21st March 2020Social Sciences Paper-I
History and Political Sciences
11:00 AM to 1:00 PM
23rd March 2020Social Sciences Paper-II
Geography
11:00 AM to 1:00 PM

How To Download Maharashtra SSC Class 10 Date Sheet 2020

Applicants can look out for Maharashtra SSC Time Table for Class 10 from the official website according to the steps as below:

  • Open official website: mahahsscboard.maharashtra.gov.in.
  • Below “Latest Notification”, click on the link “SSC March-20 Time Table (Revised Course)”.

Maharashtra State Board of Secondary Education

  • The page will be taken to Maharastra State Board SSC Time Table 2020 in PDF format.
  • View/download Maharastra SSC Time Table for Class 10 for further reference.

Details Mentioned on Maharashtra SSC Time Table 2020

In the content of the time table, you will get some data. You can go through it form the steps given below

  • Board’s Name
  • Name of the Subjects
  • Class Name
  • The Date for the Exam
  • Time
  • Day for the Exams
  • Some Other Instructions

Maharashtra SSC Board Exam – Preparation Tips

  • Organize your Study (Place & Plan): The students must first know to start the study plan. The candidates should make a proper plan for the exams. Make sure the study place must be peaceful and clean. Place and the plan for the studies is the most significant factor.
  • Proper Revision is needed: After planning for the studies, you should prepare according to it strictly. By doing this, the students will be able to remember the learning effectively. Once, you learn a topic, the revision is a compulsory step. The revision is the mandatory factor for the students.
  • Practice the Previous Year’s Model Question Papers: Once, you will feel that your revision has been finished then you are needed to solve the question papers of the previous years’. Solving the question papers will aid the perfectness in your preparations.
  • Don’t get diverted: There are many social networking sites which help the students. Students get involved with WhatsApp, Facebook, Instagram etc for distraction. So, you should focus on the studies ignoring these distractions.

Board Exam Time Table 2020

Odisha HSC/10th Exam Time Table 2020 (Released) | Download Odisha 10th Exam Time Table from Here

Odisha 10th Exam Time Table

Odisha 10th Exam Time Table 2020: Board of Secondary Education of Odisha Class 10th Time Table for the year 2019 has to be announced soon and the exam will be conducted in the month of February 2019. BSE Odisha Class 10th Exam has been organized and regulated in the state of Odisha, India. Odisha (BSE), is a board of education for both public and private schools, under the state government of Odisha. It started functioning since 1955 and is managing and controlling all the secondary education in Odisha. Its center is located in Cuttack, Odisha (India). 2020 Matric Exam Date Odisha is 19th February 2020.

Odisha Board Time Table of Class 10th will be available on its official website. The exam for Odisha Class 10th Board, according to previous data, usually starts in the month of February and ends in the month of March. The class 10th timetable will help students to prepare well for the upcoming examination. Here, in this article, you will get to know everything about Odisha 10th Board Exam Time Table 2020.

BSE Odisha 10th Exam Time Table 2020 Dates

Odisha 10th Time Table 2020Important Dates
Availability of Time Table24th December 2019
10th Exam Date 2020 Odisha19th February 2020
End of the examination02nd March 2020

Odisha 10th Time Table 2020

Date and DaySubject
19th February
Wednesday
Odia Language
22nd February
Saturday
English
24th February
Monday
Sanskrit/ Hindi
26th February
Wed
Mathematics
28th February
Friday
General Science
02nd March
Monday
Social Studies

Odisha 10th Board Exam Time Table 2020 PDF

How To Download Odisha 10th Exam Time Table 2020?

To help the students of Odisha Board HSC/Class 10 we are providing here easy steps to find and download the Odisha HSC/10th Exam Time Table. Please follow these simple steps given below;

  • Firstly, students need to visit the official website of Board of Secondary Education, Odisha i.e. bseodisha.nic.in
  • Then click on “View all news” in the “Latest News” section.
  • Now you have to click on the link provided for Odisha HSC/10th
  • Once you click on the link, the Orisha 10th Exam Time Table will be displayed to you in the form of a PDF file.
  • Download and take out the print out of the timetable.
  • Keep it for future use.

Details Mentioned on Odisha Class 10 Time Table 2020

  • Name of Examination
  • Name of Board
  • Exam Date and Day
  • Subject list
  • Subjects Code
  • Exam Timings
  • Important Instructions

Odisha Class 10 – List of Subjects

Below are the lists of subjects which will be covered for Class 10th Odisha Board

  • First Language: First Language Bengali (FLB), First Language English (FLE), First Language Hindi (FLH), First Language Odiya (FLO), First Language Tamil (FLT), First Language Urdu (FLU)
  • Second Language: SLE (English), SLH (Hindi), SEP (Environment and Population Education)
  • Third Language: TLH, TLS, TLP, TLV, TLO (Theory)
  • MTH (Mathematics)
  • TLV (Practical)
  • GSC (Science)
  • SSC (Social Science)

Odisha Class 10th Admit Card

Admit card for BSE Odisha Class 10th will be released on its official website. Students need to download the admit card online, as it is not available offline to any candidate. Admit card is mandatory to produce in the examination hall to the invigilator, else candidates will not be allowed to give their exams. After the Odisha Class 10th timetable is release, it is expected that the Admit Card will be released in the month of February.

Admit card of Odisha Class 10th Exam contains the following information.

  • Name of Candidate
  • Enrollment Number
  • Exam Date
  • Center Of Exam
  • Center Code
  • Signature Of Candidate
  • Authority Signature

As candidates have got all the details related to Odisha Class-10th Exam Time Table, subjects to cover and also about the admit card, they should start preparing themselves for the exams to score well. Odisha Board Class-10th Exam decides your career path. Some students go for further studies by opting for their subject of interest and some choose to do the jobs. To prepare well for the exam, Odisha Board Class 10th  students should know their syllabus in a systematic manner, should solve previous years’ papers, should plan their studies according to the subjects and apart from all these, they should take good care of their health.

Get Updated Board Exam Time Table 2020 for Class 10 and 12.