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
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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 |
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