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Class-IX Math Chapter : Area of Parallelogram and Triangles
Points to Remember - Solved Theorem and some examples to illustrate the use of these theorem Points to Remember : 1. Two congruent figures must have equal areas. However, two figures having equal areas need not to be congruent. 2. Two figures are said to be on the same base and between the same parallels, if they have a common base and the vertices (or the vertex) opposite to the common base of each figure lie on a line parallel to the base. 3. Parallelograms on the same base and between the same parallels are equal in area. 4. Area of parallelogram = Base × corresponding height. 5. Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels. 6. Two triangles on the same base (or equal bases) and between the same parallels are equal in area. 7. Two triangles having the same base (or equal bases) and equal areas lie betwen the same parallels. 8. Area of Triangle = 1/2× Base × corresponding height. 9. Area of a Rhombus= 1/2× product of diagonals. 10. Area of a Trapezium= 1/2× (sum of the parallel sides) × (distance between them). 11. A median of a triangle divides it into two triangles of equal area. 12. The diagonals of a parallelogram divides it into four triangles of equal area Activity related to Area of parallelogram and triangle NCERT Solutions Topper learning Area of Parallelogram and Triangle Test paper IX Chapter-15 : PROBABILITY - NCERT solution - Key points CCE Test papers Solved Theorem and Illustrated examples
Points to Remember : 1. An activity which gives a result is called an experiment. 2. An experiment which can be repeated a number of times under the same set of conditions, and the outcomes are not predictable is called a Random Experiment. 3. Performing an experiment is called a trial. 4. Any outcome of an experiment is known as an event. 5. In n trials of a random experiments, if an event E happens m times, then the probability of happening of E is given by, P (E)= Number of outcomes favour to E /Total number of possible outcomes 6. For any event E, which is associated to an experiment, we have 0 lessthan and equal P(E) greater and equalto 1. 7. If E1, E2, E3, ....., En are n elemantary events associated to a random experiment, then P(E1) + P(E2) + P(E3) + ........... + P(En) = 1 PRACTICE EXERCISE 1. A number is chosen from 1 to 20. Find the probability that the number chosen is : (i) a prime number (ii) a composite number (iii) a square number (iv) an odd number (v) an even number (vi) number between 7 and 14 2. A bag contains 9 red and 6 blue balls. Find the probability that a ball drawn from a bag at random is (i) Red ball (ii) blue ball 3. In a sample of 500 items, 120 are found to be defective. Find the probability that the item selected at random is (i) defective (ii) non-defective 4. In a school of 1800 students, there are 875 girls. Find the probability that a student chosen at random is (i) a boy (ii) a girl 5. In a cricket match, a batsman hit a boundary 12 times out 45 balls he plays. Find the probability that hedid not hit a boundary. 6. A coin is tossed 700 times and we get head : 385 times; tail : 315 times. When a coin is tossed at random,what is the probability of getting : (i) a head? (ii) a tail? 7. Two coins are tossed 600 times and we get two heads : 138 times, one head : 192 times ; no head : 270 times. When two coins are tossed at random, what is the probability of getting : (i) 2 heads? (ii) 1 head? (iii) no head? 8. Three coins are tossed 250 times and we get: 3 heads : 46 times; 2 heads : 56 times; 1 head : 70 times; 0 head : 78 times. When three coins are tossed at random, what is the probability of getting : (i) 3 heads ? (ii) 2 heads? (iii) atleast 2 heads? (iv) atmost 2 heads? 9. Find the probability that a leap year, selected at random will have 53 sundays 10. A bag contains 10 white balls and x black balls. If the probability of drawing a black ball is double that of a white ball, find X Sample- Paper- Class – X Subject –Physics Light: Reflection and Refraction
Very short Answer 1. What is radius of plane mirror? 2. What is angle of reflection for a ray falling normally on a plane mirror? 3. Why do we use convex surface for side view mirror? 4. Can a virtual image be photographed? 5. What is the power of a plane mirror? 6. When the angle of incidence is 90 deg., what is the angle of refraction? 7. What is the value of refractive index of air? 8. What is the magnification produced by a plane mirror? 9. Define power. Give its S.I unit? 10. What is power of sunglass? Download full paper: Reflection_and_refraction_test_paper-1 You may also like 10th Light – Reflection and Refraction Key concepts and terms X Physics Reflection and Refraction Solved questions 10th_physics_ch._light__reflection_and_refraction_ncert_solution GIST OF THE CHAPTER Light Refraction and Refraction
1. The first theory of light was put forward by Newton. This theory treats light as a particle called corpuscle. 2. We can say that light propagates as a wave and is emitted and absorbed as a particle. 3. One may regard light as having dual nature. 4. Maxwell proved that light has wave nature; it is an electromagnetic transverse wave, which does not require medium to propagate. 5. The speed of light in air is a universal constant. It has a value of 3x108m/s. 6. Light gets reflected when it falls on polished surface; like mirror. 7. Light suffers refraction when it travels from one medium to another. 8. There is a change in the wavelength of light when it moves from one medium to another. 9. The image is unmagnified, virtual and erect in a plane mirror. 10 Focal length of a plane mirror is infinity. 11. Power of a plane mirror is zero.' 12. It should be noted that, if the spherical lenses are surrounded by a material with a refractive index greater than that of the lens, the convex lens gets converted into a concave lens or vice-versa. FORMULAE f = R/2 1 / v + 1 / u = 1 / f = 2 /R M = h2 /h1 = -v/u n = c/v 1n2 = 1/2n1 1n2 = n2/n1= sin i/sin r a n w = x/y 1/v –1/u = 1/f m =I/O = h2 /h1 = v/u P= 1/f metre P = p1 + p2 + p3 + ……. VERY SHORT QUESTIONS CARRYING 1 MARK EACH. 1. Out of convex mirror and concave mirror, whose focus is situated behind the mirror? Ans: The focus of convex mirror is situated behind it. 2. For what position of an object, a concave mirror forms an enlarged virtual image? Ans: Object between pole (P) and focus (F) of the concave mirror. 3. If the focal length of a concave mirror is 25cm. What is its radius of curvature? Ans: Focal length = Radius of curvature / 2 25 = R / 2 R = 25 X 2 = 50cm. 4. A ray of light falls on a mirror normally. What are the values of angle of incidence and the angle of reflection? Ans: Both angle of incidence and the angle of reflection are zero. 5. What is the focal length of a plane mirror? Ans: Infinite. 6. Which spherical mirror is called a divergent mirror? Ans: A convex mirror is called a divergent mirror. 7. What is the angle of incidence, when a ray of light falls on the spherical mirror from its centre of curvature? Ans: The angle of incidence is zero, when a ray of light falls on the spherical mirror from its centre of curvature. 8. Name the type of mirror that always forms a virtual image for a real object? Ans: Convex Mirror. 9. State the relation between radius of curvature and focal length of spherical mirrors. Ans: Radius of curvature = 2 X focal length. R = 2f. 10. Which of the two is a diverging lens? Convex lens (or) Concave lens. Ans: Concave lens. 11. If an object is placed at a distance of 10cm in front of a plane mirror, how far would it be from its image? Ans: The object would be at a distance of 20cm from its image. 12. Name the physical quantity which remains the same when light goes from one medium to another? Ans: Frequency of light. 13. Define power of a lens. Ans: The reciprocal of the focal length of the lens is called power of a lens. P = 1/f 14. Calculate the power of a convex lens of focal length 25cm? Ans: Focal length f = 25cm. Power = 1/.25 = 100/25 = +4D. 15. Name the phenomenon responsible for the following affect. Ans: When we sit in front of a plane mirror and write with our right hand, it appears in the mirror that we are writing with the left hand.Ans: Lateral Inversion 16. Define Refractive Index Ans: It is the ratio of speed of light in vacuum to the speed of light in medium is called Refractive index. 17. Why is the convex lens also known as a converging lens? Ans: A convex lens is also known as a converging lens because it converges a parallel beam of light raying passing through it. 18. Give the ratio of velocities of two light waves travelling is vacuum and having wave lengths 4000A and 8000A. Ans: In Vacuum, light of all the wave lengths travel with the same velocity i.e. 3 X 108 m/sec. 19. For what angle of incidence, the lateral shift produced by parallel sided glass plate is zero? Ans: For i = 0. 20. What are the factors on which the lateral shift depends? Ans: Thickness of the refracting medium, angle of incidence and its refractive index. 21. What is the power of a plane glass plate? Ans: Zero. 22. An object is placed at the focus of a concave lens. Where will its image be formed? Ans: The rays will appear to come from infinity. Therefore, a virtual image will be formed at infinity. 23. What is the unit of power of a lens? Ans: Dioptre. 24. Why the stars appear to twinkle? Ans: The twinkling of a star is due to the atmospheric refraction of star’s light. 25. What is the value of refractive index of air? Ans: One More study material visit : 10th Science - Light Refraction and Refraction10th Light – Reflection and Refraction Key concepts and terms X Physics Reflection and Refraction Solved questions-1 |
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