JSUNIL TUTORIAL CBSE MATHS & SCIENCE
Let us be friend !
  • HOME
    • STUDY ZONE
    • Think Zone
    • Board Papers Solutions
    • CBSE Board Date Sheet
    • Study Material
    • Syllabus for Class I to XII
  • CLASS 10
    • 10th Science Term-I >
      • X Chemical Reaction and Equation
      • X Acid Base and Salt
      • X Metals and Non Metals
      • X Electricity
      • X Magnetic Effects of Currents
      • X Source Of Energy
      • X Biology Term-1 >
        • 10th Life Process
        • 10th Control and coordination
    • 10th science Term II >
      • Carbon and Its Compounds
      • Periodic Classification of Elements
      • Light - Reflection and Refraction
      • The Human Eye and the Colourful World
      • X Biology Term-II >
        • How Do Organisms Reproduce ?
        • Heredity and Evolution
        • Our Environment
        • Management of Natural Resource
    • 10th Maths Term I >
      • X Real Numbers
      • X Linear Equations in Two Variables
      • X Polynomials
      • X Similar Triangles
      • X Trigonometry and Identities
      • X Statics(Mean,median and Mode)
    • 10th Maths Term II >
      • 10th Quadratic Equations
      • 10th Arithmetic Progressions
      • 10th Co-Ordinate Geometry
      • 10th Height and Distance
      • 10th Circles
      • 10th Area Related to Circles
      • 10th Surface Areas and Volumes
      • 10th Probability
      • 10th Constructions
    • 10th Social Science >
      • 10th History and Geography
      • 10th Civics and Economics
    • 10th CBSE English
    • 10th Solved Assignments
  • CLASS 9
    • 9th Science term I >
      • IX Motion and Rest
      • IX Force and Laws of motions
      • IX Gravitation
      • IX Matter in our surrounding
      • IX Is Matter around Us Pure
      • IX Biology Term-1 >
        • Cell structure n function class9
        • Tissue class9
        • Improvement in food resources class9
    • 9th Science term II >
      • Atoms and Molecules
      • Structure of the Atom
      • Thrust and Pressure
      • Work and Energy
      • Sound
      • IX Biology Term-2 >
        • Diversity in Living Organisms
        • Natural Resources
        • Why Do We Fall ill ?
    • 9th Maths term I >
      • IX Number system
      • IX Polynomials
      • IX Introduction to Euclid Geometry
      • IX Lines and Angles
      • IX Triangles
      • IX Coordinate geometry
      • IX Area of triangles by Heron's formula
    • 9th Maths term II >
      • Linear equations in two variables
      • Quadrilaterals
      • Area of Parallelogram and Triangle
      • Circle
      • Surface Areas and Volumes
      • Constructions
      • Statistics
      • Probability
    • IX Social Science >
      • 9th Social Science Term-1
      • 9th Social Science Term-2
    • IX English and Hindi
    • CBSE ASL Corner
  • IX Sample Papers
    • 9th Mid Term Papers
    • 9th Final Exam papers
    • 9th Sample Paper 2018
    • IX Sample Papers SA-I >
      • 9 Mathematics SA1
      • 9 Science SA1
      • 9 Social Science SA1
      • 9 English and Hindi SA1
    • IX Sample Paper SA-II >
      • Mathematics
      • Science
      • Social Science
      • English Hindi Sanskrit
    • IX Practical skill Science
  • X Sample Papers
    • 10th Mid Term Papers
    • 10th Board Exam Papers
    • 10th Sample Paper 2018
    • X Sample Paper SA-I >
      • X Mathematics SA1
      • X Science SA1
      • X Social Science SA1
      • 10th English sa-1 paper
      • 10th Hindiand sanskrit sa-1 paper
    • X Sample Paper SA-II >
      • Mathematics
      • Science
      • Science Practicals MCQ
      • Social Science
      • Hindi English and Sanskrit
  • CLASS 8
    • 8th Science >
      • Class 8 Physics >
        • Force Pressure and Frictions
        • Sound
        • Chemical Effects of Electric Current
        • Refraction of Light and Our Eyes
        • Some Natural Phenomenon
        • Stars and the Solar System
      • Class 8 Chemistry >
        • Synthetic fibre and Plastics
        • Metals and Non-Metals
        • Combustion ,Flame and Fuel
        • Coal Petroleum, Natural Gases
        • Air and Water Pollution
      • Class 8 Biology >
        • Crop Production and Management
        • Microorganisms friend and foe
        • Cell structure and functions
        • Reproduction in animals
        • Reaching the Age of Adolescence
        • Conservation of plants and animals
    • Class 8 Mathematics >
      • Algebra >
        • Rational Number
        • Square and Square Roots
        • Algebraic Expression
        • Factorization
        • Exponent and Power
        • Linear Equations
      • Commercial math >
        • Unitary Methods
        • Percentage
        • Profit and Loss
        • Discounts & Sales Tax
        • Compound Interest
      • Geometry/Mensuration >
        • Quadrilateral
        • Practical Geometry
        • Perimeter and Area
        • Data Handling
        • Introduction of Graphs
    • Class 8 Sample papers >
      • 8th Question paper sa1
      • 8th Question paper sa2
  • CLASS 07
    • class 7 Science >
      • class 7 Physics
      • class 7 chemistry
      • class 7 Biology
      • 7th Science Test Papers
      • 7th Science Solved Papers
    • class 7th Maths >
      • Class 07 Maths Tem-I
      • Class 07 Maths Tem-II
  • Class 06
    • 6th Maths
    • 6th science >
      • 6th Science Term-1
      • 6th Science Term-2
  • NCERT Solutions
    • X Science and Maths
    • IX Science and Maths
  • Class 11 - 12
    • 12th Sample paper
    • 11th Study Material >
      • 11th Physics
      • 11th Chemistry
      • 11th Maths
    • 12th Study Material
  • NTSE
    • NTSE SAMPLE PAPER

9th Mid term 2019-20 Maths original Paper

14/9/2019

1 Comment

 
Class9 Mid Term Examination Paper DAV Bihar Zone 14 sep 2019
Picture
Picture
Picture
Fore more question papers click on given link :  Class-9 Mid Term Question papers 2019-20
1 Comment

properties of arithmetic mean class9

2/10/2018

0 Comments

 
Picture
Picture
Picture
Picture
Picture
Link for further study:
​9th maths Ch- Statics - assignments                                
9th chapter Statics CBSE Test Paper solved New         
9th Mean Median and Mode Test Paper-1                          
9th Mean Median and Mode Test Paper-2       Download File
0 Comments

9th Maths Holly mission Half yearly SA1 paper2019

21/9/2018

0 Comments

 
Picture
Picture
Picture
0 Comments

9th (IX) INTRODUCTION TO EUCLID’S GEOMETRY

27/8/2018

1 Comment

 
Picture
EUCLID’S Postulates
1. A straight line may be drawn from any point to any other point.
2. A terminated line (line segment) can be produced indefinitely.
3. A circle may be described with any centre and any radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side of it, taken 
together less than two right angles, then the the two straight lines if produced indefinitely, meet on 
that side on which the sum of angles is taken together less than two right angles.
Euclid used the term postulate for the assumptions that were specific to geometry and otherwise 
called axioms. A theorem is a mathematical statement whose truth has been logically established.

Visit Page Link to download solved Questions and Guess test Paper  
CBSE Class IX  Introduction to Euclid's  geometry  
1 Comment

class IX Factor and reminder theorem :Polynomial

27/8/2018

1 Comment

 
Picture
Proof of this factor theorem
Let p(x) be a polynomial of degree greater than or equal to one and a be areal number such that p(a) = 0. 
Then, we have to show that (x – a) is a factor of p(x).Let q(x) be the quotient when p(x) is divided by (x – a).
By remainder theorem
Dividend = Divisor x Quotient + Remainder
p(x) = (x – a) x q(x) + p(a) [Remainder theorem]
⇒ p(x) = (x – a) x q(x) [p(a) = 0]⇒ (x – a) is a factor of p(x)
Conversely, let (x – a) be a factor of p(x). 
Then we have to prove that p(a) = 0
Now,     (x – a) is a factor of p(x)⇒ p(x), 
when divided by (x – a) gives remainder zero. 
But, by the remainder theorem, p(x) when divided by (x – a) gives the remainder equal to p(a).                 ∴ p(a) = 0
Proof of remainder theorem.
Let q(x) be the quotient and r(x) be the remainder obtained when the polynomial p(x) is divided by (x–a).
Then, p(x) = (x–a) q(x) + r(x), where r(x) = 0 or some constant.
Let r(x) = c, where c is some constant. 
Then p (x) = (x–a) q(x) + c
Putting x = a in p(x) = (x–a) q(x) + c, 
we getp(a) = (a–a) q(a) + c  ⇒ p(a) = 0 x q(a) + c  
⇒ p(a) = c
This shows that the remainder is p(a) when p(x) is divided by (x–a).1.   [a is –8.]
​Download study material for polynomial
1 Comment

Euclid’s Geometry 9th CBSE Final exam study material

27/8/2018

0 Comments

 
Picture
Thales is the first mathematician credited with giving the first known proof “a circle is bisected by its diameter.  

One of Thales’ most famous pupils was Pythagoras and his group discovered many geometric properties and developed the theory of geometry to a great extent.  

 At that time Euclid, a teacher of mathematics at Alexandria in Egypt, collected all the known work and arranged it in his famous treatise, called ‘Elements’. He divided the ‘Elements’ into thirteen chapters, each called a book.

Some definitions from book -1 of Elements are: 

1. A point is that which has no part.

2. A line is breathless length.

3. The ends of a line are points.

4. A straight line is a line which lies evenly with the points on itself.

5. A surface is that which has length and breadth only.

6. The edges of a surface are lines.

7. A plane surface is a surface which lies evenly with the straight lines on itself.

Þ  An axiom or a postulate is a mathematical statement which is assumed to be true without proof. These assumptions are actually obvious universal truths.

Þ   Theorems are statements which are proved, using definitions, axioms, previously proved statements and deductive reasoning.

Þ Some of the Euclid’s axioms are:

(i) Things which are equal to same thing are equal to one another.

 (ii) If equals are added to equals, the wholes are equal.

(iii) If equals are subtracted from equals, the remainders are equals.

(iv)  Things which coincide with one another are equal to one another.

(v) The whole is greater than the part.

(vi)  Things which are double of the same thing are equal to one another.

(vii) Things which are halves of the same thing are equal to one another.

Þ  Euclid’s five postulates are: 

(i) A straight line may be drawn from any point to any other point. 

(ii) A terminated line can be produced indefinitely. 

(iii) A circle can be drawn with any centre and any radius. 

(iv)  All right angles are equal to one another. 

(v) If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

A system of axioms is called consistent, if it is impossible to deduce from these axioms a statement that contradicts any axioms or previously proved statement. 

 Euclid’s first postulate can also be stated as below:  Given two distinct points, there is a unique line that passes through them. 

Two distinct lines cannot have more than one point in common. 

Playfair’s Axiom: For every line l and for every point P not lying on l, there exists a unique line m, passing through P and parallel to l. [~ 5th Postulate]

Two distinct intersecting lines cannot be parallel to the same line. 


CBSE Class IX  Introduction to Euclid's  geometry  full study 

9th Introduction to Euclid Geometry NCERT SOLUTION
File Size: 226 kb
File Type: pdf
Download File

0 Comments

Class IX, Math Chapter 3, Coordinate Geometry Questions

27/8/2018

6 Comments

 
Picture
9th Coordinate Geometry:   Key concepts

ÞCoordinate Geometry: The branch of mathematics in which geometric problems are solved through algebra by using the coordinate system is known as coordinate geometry.

Þ Coordinate axes: The position of a point in a plane is determined with reference to two fixed mutually perpendicular lines, called the coordinate axes.

Þ Coordinate System, position of a point is described by ordered pair of two numbers.

Þ Ordered pair: A pair of numbers a and b listed in a specific order with 'a' at the first place and 'b' at the second place is called an ordered pair (a, b). Note that (a, b) ¹ (b , a) and (x, y) = (y, x), if x = y.

Þ P(a,b) be any point in the plane. 'a' the first number denotes the distance of point from Y-axis and 'b' the second number denotes the distance of point from X-axis.

Þ The coordinates of origin are (0,0)

Þ Every point on the x-axis is at a distance o unit from the X-axis. So its ordinate is 0.

Þ Every point on the y-axis is at a distance of 0 unit from the Y-axis. So, its abscissa is 0.                            

Þ  The coordinates of a point on the x-axis are of the  form (x, 0) and that of a point on the y-axis are (0, y).

Þ A point in the first quadrant will be of the form (+, +). Similarly, a point in the second, third and fourth quadrants will be of the form (–, +), (–, –) and (+, –) respectively.
Download links 
IX  Co -Ordinate geometry Test Paper-1
IX Co -Ordinate geometry Test Paper-2
IX Co -Ordinate geometry Test Paper-3
IX Co -Ordinate geometry Test Paper-4
Assignment- IX Co -Ordinate geometry -5

Download above  File
6 Comments

9th Congruence of triangle question paper for Periodic Test2

27/8/2018

1 Comment

 
Picture
 1. AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

2.  In DABC , ∠Q > ∠R, PA is the bisector of ∠QPR and PM ^QR. Prove that <∠APM = 1/2(∠< Q – ∠<R).

3. D ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle.

4. In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side.

6. Example 5. If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.

7. A triangle ABC is right angled at A. L is a point on BC such that AL ^  BC. Prove that ∠ < BAL = ∠ < ACB

8. Q is a point on the side SR of a Δ PSR such that PQ = PR. Prove that PS > PQ. 

9. S is any point on side QR of a Δ PQR. Show that: PQ + QR + RP > 2 PS.

10. D is any point on side AC of a Δ ABC with AB = AC. Show that CD < BD. 

11. l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively. 


12. Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC =∠ABC.

13. Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC. 

14. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. {Produce QS to intersect PR at T}

15. Prove that in a right triangle, hypotenuse is the longest (or largest) side.

Related posts: PDF Download CLICK HERE

CBSE Sample Questions Papers Maths Ch: Triangle

IX Mathematics Congruence of Triangle CBSE Examination Question 2012-13

CBSE Test sample paper- IX Mathematics (Congruent triangle)

CBSE TEST PAPER CLASS - IX Mathematics (Congruent triangle)

1 Comment

Practice paper IX Herons formula

27/8/2018

2 Comments

 
Picture
1. The area of a triangle is 30 cm2. Find the base if the altitude exceeds the base by 7 cm.[ 5 cm , 12 cm.]

2. From a point in the interior of an equilateral triangle, perpendiculars drawn to the three sides are 8 cm, 10 cm and 11 cm respectively. Find the area of the triangle. [486.1 cm2]

3. The difference between the sides at right angles in a right-angled triangle is 14 cm. The area of the triangle is 120 cm2. Calculate the perimeter of the triangle. [24 cm, 10 cm, 60 cm.]

4. Find the percentage increase in the area of a triangle if its each side is doubled? [300%]

5. Calculate the area of the triangle whose sides are 18 cm, 24 cm and 30 cm in length. Also, find the length of the altitude corresponding to the smallest side of the triangle.

6. The sides of a triangle are 10 cm, 24 cm and 26 cm. Find its area and the longest altitude.

7. Two sides of a triangular field are 85 m and 154 m in length, and its perimeter is 324 cm. Find (i) the area of the field, and (ii) the length of the perpendicular from the opposite vertex on the side measuring 154 cm.

8. The sides of a triangular field are 165 cm, 143 cm and 154 cm. Find the cost of ploughing it at 12 paise per sq. m.

9. The base of an isosceles triangle measures 80 cm and its area is 360 cm2. Find the perimeter of the triangle.

10. The perimeter of an isosceles triangle is 42 cm and its base is 11/2  times each of the equal sides. Find (i) the length of each side of the triangle, (ii) the area of the triangle, and (iii) the height of the triangle.

11. The perimeter of a right angle triangle is 40 cm. Its hypotenuse is 17 cm. Find the sides containing the right angle. Also find the area of the triangle.

2 Comments

CBSE Sep 2015 class 9 Maths Question paper new

30/9/2015

2 Comments

 
New addition of question paper sa1 for 2015-16
Picture
Picture
Picture
Picture
Picture
Picture
Picture
Picture
Picture
2 Comments
<<Previous

    Stay Updated. Enter E-Mail:

    Delivered by FeedBurner

    Blog Posts Categories

    All
    10th Biology
    10th English Term 1
    10th English Term 2
    10th Maths Term 01
    10th Maths Term 02
    10th Question Paper Sa1
    10th Sample Paper 2020
    10th Sample Paper Exam 2019
    10th Sample Paper SA2
    10th Science Study Term 02
    10th Science Term 01
    10th Social Science Sa1
    10th Social Science SA 2
    10th Social Science SA-2
    12th Sample Paper
    6th Maths And Science
    6th Science
    7th Maths
    7th Maths And Science
    7th Sample Paper
    7th Science
    8th Mathematics
    8th Question Papers
    8th Science
    9th Mathematics Term 01
    9th Mathematics Term 02
    9th Midterm Exam Papers
    9th PSA Study Material
    9th Sample Paper Exam 2018
    9th Sample Paper Exam 2019
    9th Sample Paper SA2
    9th Sample Paper SA I
    9th Science Term 01
    9th Science Term 02
    9th Social Science SA 1
    9th Social Science SA 2
    Board Paper Solutions
    CBSE 10 [Old Post]
    CBSE 11th And 12th
    CBSE News Updates
    Class 12 Study Materials
    CPS And SDV Updates
    NCERT Solutions
    Olympiad-NTSE
    Science-maths Practicals
    Study Material

          Join Us For Update

                Author

    I am a school teacher and serving CBSE students community since 1995.

    Archives

    September 2019
    July 2019
    March 2019
    February 2019
    January 2019
    December 2018
    November 2018
    October 2018
    September 2018
    August 2018
    June 2018
    April 2018
    March 2018
    February 2018
    January 2018
    December 2017
    October 2017
    September 2017
    August 2017
    July 2017
    June 2017
    May 2017
    March 2017
    February 2017
    January 2017
    December 2016
    November 2016
    September 2016
    August 2016
    July 2016
    June 2016
    May 2016
    April 2016
    March 2016
    February 2016
    January 2016
    December 2015
    November 2015
    October 2015
    September 2015
    August 2015
    July 2015
    June 2015
    May 2015
    April 2015
    March 2015
    February 2015
    January 2015
    December 2014
    November 2014
    October 2014
    September 2014
    August 2014
    July 2014
    June 2014
    May 2014
    April 2014
    March 2014
    February 2014
    January 2014
    December 2013
    November 2013
    October 2013
    September 2013
    August 2013
    July 2013
    June 2013
    May 2013
    April 2013
    March 2013
    February 2013
    January 2013
    December 2012
    November 2012
    October 2012
    September 2012
    August 2012
    July 2012
    June 2012
    May 2012
    April 2012
    March 2012
    February 2012
    January 2012
    December 2011
    November 2011
    October 2011
    September 2011
    August 2011
    July 2011

      Comment & Submit Papers

      [object Object]
      Max file size: 20MB
    Submit
Powered by Create your own unique website with customizable templates.