section × length 1 Area of trapezium = 2 (a + b)h a cross section h length b Volume of cone = 1 r 2h 3 Curved surface area of cone = rl Volume of sphere = 4 r 3 3 Surface area of sphere = 4 r 2 r l h r In any triangle ABC b A Sine Rule a B c a sin A The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0‚ are given by C b
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Find the width of the room. 4. A rectangular park is 45 m long and 30 m width. A path 2‚5 m wide is constructed outside the park. Find the area of the path and the cost of constructing it at Rs. 125 per m2. 5. The area of a right angled triangle is 400 m2. If one of its legs measures 8 cm. Find the length of the other leg. 6. The diameter of the wheel of a car is 10 cm. How many revolutions will it make to travel 99 km? 7. A race track is in the form of a ring whose inner circumference
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Answers Chapter 1 c i No x-intercept‚ y = 4 iii y Pre-test 1 a 2x + 1 1 3 c x+ x= x 2 2 f 3x − 7 b 5(x − 1) 1 (x + 4) 3 -5ab -21x -4x + 4 3 ii 0 y=4 d 2x − 3 e a a a a 7x 8y 3x + 3 4m b b b b 6a 7 6 b 7 12 9 a 3 b -2 c 1 10 a y = 2x + 1 b y = -x + 5 c 4 7 d 19 72 Exercise 1A f 21 20 2 3 4 5 4 e 7 c c c c -5x 2 15a 2 -10x + 2x 2 a (0‚ 4) d g c 10 ii
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b)h h 2 b Volume of prism = area of cross section × length crosssection h lengt r 4 πr3 Volume of sphere = – 3 Surface area of sphere = 4 π r 2 1 Volume of cone = – π r2h l 3 h Curved surface area of cone = π rl r In any triangle ABC Area of triangle = 1 – 2 C ab sin C a b b a c Sine rule ––––– = ––––– = ––––– sin A sin B sin C A c B Cosine rule a2 = b2 + c2 – 2bc cos A The Quadratic Equation The solutions of ax2 + bx + c = 0‚ where a ≠ 0‚ are given by – b ± √ (b2 – 4ac)
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l3 in fig.‚ are parallel. The value of x is : [Marks:1] A. 50o B. 80o C. 40o D. 140o 6] [Marks:1] A. BC = EF B. AC = EF C. BC = DE D. AC = DE 7] The area of an equilateral triangle with perimeter 18x is: [Marks:1] A. B. C. D. 8] The area of triangle‚ whose sides are 15 cm‚ 25 cm and 14 cm is [Marks:1] A. B. C. D. 9] Simplify: . [Marks:2] 10] [Marks:2] 11] Without actually calculating the cubes‚ find the value
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Syntel Technical Interview Questions: 1.Difference between Virtual and Abstract Method ? 2.What is Runtime Polymorphism ? 3.What is Overiding ? 4.What is the use of a private constructor? 5.What design patterns you used in the project ? 6.What is an interface ? Is there any relation betweem interface and performance ? 7.what is an abstract class ? 8.What is the difference between DataSet and DataReader ? 9.What is CommandBuilder ? 10.What is the Difference between Application and Sesssion
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value is held constant. r as a Constant If we let the value of r be equal to 1‚ we can use that information to find the length of OP’ when OP=2‚ 3‚ and 4. The first thing one can deduce is that by using the points A‚ O‚ P’‚ and P two isosceles triangles can be formed; ∆AOP and ∆AOP’. To rationalize this assertion through an analytic approach it should first be understood that all line segments that connect the center of a circle to its perimeter‚ or circumference‚ is considered to be its radius
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INDEX CLASS - IX S.NO. SUBJECT NAME PAGE NO. CBSE TEST PAPERS 1. 2. 3. 4. 5. 6. 7. 8. 9. Test Paper # 1 (Mathematics) Test Paper # 2 (Mathematics) Test Paper # 2 (Science and Technology) Test Paper # 2 (Science and Technology) Test Paper # (Social Science) Test Paper # 2 (Social Science) Hints & Solutions # 1(Mathematics) Hints & Solutions # 2(Mathematics) Hints & Solutions # 1 (Science and Technology) 1-2 3-5 6-7 8-9 10 - 12 13 - 15 16 - 21 22 - 28 29 - 35 36 - 39 40 - 45 46 – 52
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The life and brutal death of Hypatia of Alexandria has been a topic of debatable discussion since the 4th century C.E. She lived Alexandria‚ Egypt (the center of ancient knowledge) and while it is assumed that she learned the study of mathematics from her father‚ “Theon of Alexandria” it is known that she was the head geometry teacher of the Neo-Platonist school (Belenky‚ 2010). Hypatia is regarded as one of the first women that contributed in many ways to the field of mathematical findings that
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“the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero‚ if the following number is always added to the previous as shown below‚ a triangular number will always be the outcome: 1 = 1 2 + 1 = 3 3 + (2 + 1) = 6 4 + (1 + 2 + 3) = 10 5 + (1 + 2 + 3 + 4) = 15 Moreover‚ triangular numbers can be seen in other mathematical theories‚ such as Pascal’s triangle‚ as shown in the diagram below. The triangular
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