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Exercise 13 C Question 1 Write down the following products. (i) (y+2)(y-2) (ii) (p+1)(p-1) (iii) (x-4)(x+4) (iv) (3b+7)(3b-7) (v) (9a+10b)(9a-10b) (vi) (5p2-7q)(5p2+7q) (vii) (a2+b2)(a2-b2) (viii) (ab-c)(ab+c) (ix) (x) (a2b3-x3y4)(a2b3+x3y4) Question 2 Find the following products (i) (x+y+z)(x+y-z) (ii) (l+m+n)(l-m+n) Question 3 Simplify : (i) (x+y)(x-y)(x2+y2) (ii) (2-x)(2+x)(4+x2)  Question 4 Simplify : (a+b)(a-b)+(b+c)(b-c)+(c+a)(c-a) Question 5 Find …

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Exercise 13 B Expand the following : Question 1 (i) (x+5)2 (ii) (3x+4)2 (iii) (3x+5y)2 (iv) (1+10mn)2 Question 2 (i) (7y-8)2 (ii) (p-2q)2 (iii) (5y-3z)2 (iv) (6a-11b)2 Question 3 (i) (a2+1)2 (ii) (3a2+b2)2 (iii) (xy-4z)2 (iv) (5a2-7b2)2 Question 4 (i) (ii) Question 5 (i) (1.5p+2q)2 (ii) (iii) (3.2d-5f)2 (iv) Question 6 Simplify : (i) (x+3y)2+ …

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Exercise 13 A Multiply mentally and write only the products for each of the following . Question 1 (x+4)(x+2) Sol :   Question 2 (a+1)(a+8) Question 3 (c+3)(c+2) Question 4 (b-2)(b-5) Question 5 (n-1)(n-6) Question 6 (3-x)(5-x) Question 7 (y-7)(y+3) Question 8 (m+3)(m-2) Question 9 (x-4)(x+6) Question 10 (p+10)(p-9) Question 11 (xy+6)(xy-5) Question 12 (5-xy)(3+xy) …

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Exercise 1 E Question 1 The product of two rational numbers is -26 . If one of the numbers is -3, find the other. Sol : Let x be the other rational number A.T.Q ⇒x × (-3) = -26 On transposing ⇒ Question 2 Divide the sum of by the reciprocal of Sol : First …

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Exercise 1 D Question 1 Find a rational number between a and b, if (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : Question 2 Find the two rational numbers between -2 and 2 . Sol : Two rational numbers are 0 , 1 Question 3 Find the three rational numbers between …

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Exercise 1 C Question 1 Answer True (T) or False (F) (i) Sol : F (ii) Addition distributes over multiplication in rational numbers . Sol : F (iii) The reciprocal of -8 is Sol : F (iv) is a rational numbers . Sol : T (v) implies that 0 is the multiplicative identity for rational …

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Exercise 1 B Question 1 Answer True (T) or False (F) (i) Subtraction is commutative for rational numbers. F (ii) To subtract , we add the additive inverse of . F (iii) 0 is its own additive inverse . T (iv) The additive inverse of . T (v) While subtracting three or more rational numbers …

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PS Verma Biology Class 9 Chapter 6 Natural Resources Text Book Solutions – P.S.Verma and V.K.Agarwal – Biology CBSE Class 9 Chapter 6 Natural Resources PS Verma and V.K. Agarwal Biology Class 9 Page No – 356. Solution SAQ – 1 Air is composed of a mixture of gases such as nitrogen, oxygen and carbon …

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PS Verma Biology Class 9 Chapter 5 Why Do We Fall Ill ? Text Book Solutions – P.S.Verma and V.K.Agarwal – Biology CBSE Class 9 Chapter 5 Why Do We Fall Ill ? PS Verma and V.K. Agarwal Biology Class 9 Page No – 300. Solution SAQ – 1: Healthy: 1. It is a state …

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PS Verma Biology Class 9 Chapter 1 – Improvements In Food Resources Text Book Solutions – P.S.Verma and V.K.Agarwal – Biology PS Verma and V.K. Agarwal Biology Class 9 Page No – 253. CBSE Class 9 Chapter 4 Diversity In Living Organisms Solution SAQ – 1 (a) Point Diversity – This is a diversity present …

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PS Verma Biology Class 9 Chapter 3 Tissues Text Book Solutions – P.S.Verma and V.K.Agarwal – Biology CBSE Class 9 Chapter 3 Tissues PS Verma and V.K. Agarwal Biology Class 9 Page No – 165. Solution 1: Importance of tissues- (i) Formations of tissues have brought about a division of labour in multicellular organisms. (ii) …

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PS Verma Biology Class 9 Chapter 2 – The Fundamental Unit Of Life – Cell Text Book Solutions – P.S.Verma and V.K.Agarwal – Biology CBSE Class 9 Chapter 2 – The Fundamental Unit Of Life – Cell PS Verma and V.K. Agarwal Biology Class 9 Page No – 116. Solution SAQ – 1: Prokaryotic Cell: …

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PS Verma Biology Class 9 Chapter 1 – Improvements In Food Resources Text Book Solutions – P.S.Verma and V.K.Agarwal – Biology CBSE Class 9 Chapter 1 – Improvements In Food Resources PS Verma and V.K. Agarwal Biology Class 9 Page No – 63. Solution 01: Micronutrients (i) They are required in very small quantities. (ii) …

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Lakhmir Singh Chemistry Class 9 Solutions Chapter 3 Atoms and Molecules Text Book Solutions – Lakhmir Singh and Manjit Kaur – Chemistry Lakhmir Singh Class 9 CBSE Chemistry Text Book PAGE No 128 Solution 01 International Union of Pure and Applied Chemistry Solution 02 (a) Law of conservation of mass – Antonie Lavoisier (b) Law …

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Lakhmir Singh Chemistry Class 9 Solutions Structure of The Atom Text Book Solutions – Lakhmir Singh and Manjit Kaur – Chemistry Lakhmir Singh Class 9 CBSE Chemistry Text Book PAGE No 191 Answers Solution 01 Neutron is not present in ordinary hydrogen atom. Solution 02 J. J. Thomson Solution 03 Maximum of 2 e- can …

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Lakhmir Singh Physics Class 9 Solutions Motion Lakhmir Singh Physics Class 9 Solutions Page No:19 Question 1: Is displacement a scalar quantity ? Solution : No, displacement is a vector quantity. Question 2: State whether distance is a scalar or a vector quantity. Solution : Distance is a scalar quantity. Question 3: Change the speed …

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Exercise 1 A Question 1 Fill in the blanks (i) , expressed as a rational number with denominator Sol : Denominator can not be negative ⇒ On dividing and multiplying by 6 ⇒ (ii) (>,<,=) Sol : L.C.M of 7 and 11 is 77 ⇒..(i) Denominator can not be negative ⇒ ⇒..(ii) From (i) and …

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EXERCISE 12 D QUESTION 1 Divide (i) 28a3b2c by 7ab (ii) 48a4b5c6 by – 16a2c2 (iii) $-\dfrac{4}{5}a^2b^2c^4 \text{ by } -\dfrac{6}{15}abc^2$ QUESTION 2 Divide : (i) 16pr2-8pr3-4p2r2 by -4pr2 (ii) 6×7-8×6+4×5-10×4+6×3 by -2×3 (iii) 7x4y2-14x3y3+35x2y4-56x7y5+21y6 by 7x2y2 (iv) $\dfrac{3}{5}abc-\dfrac{2}{5}a^2bc^2+\dfrac{1}{7}ab^2 \text{ by } \dfrac{1}{3}abc$ QUESTION 3 Divide : (i) (x2+8x+15) by (x+3) (ii) (2×2+7x+6) by (x+2) …

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EXERCISE 12 C QUESTION 1 Multiply : (i) 12xy by -8×2 (ii) -16a2b2 by -5ab2 (iii) $\left(\dfrac{3}{5}a^2b^2\right) \text{ by } \left(\dfrac{10}{27}ab^4\right)$ (iv) $\left(-\dfrac{11}{8}xy^3\right)\text{ by } \left(-\dfrac{24}{55}x^4\right)$ QUESTION 2 Multiply : (i) (6x-5) by -3x (ii) (12x^2-4x+5) by 8×3 (iii) (3a^3x^3-4ay^2+7a^2y) by -4x2ya2 QUESTION 3 Find the product : (i) (x+6)(x+11) (ii) (2a+5)(3a-6) (iii) (5x+2b)(5x-2b) (iv) …

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EXERCISE 12 B QUESTION 1 Add the following expressions (i) 2ab + 3b and 5ab + 7b Sol:  2ab + 3b + 5ab + 7b   (ii) 2×2 + 3xy and 6xy – 4×2 (iii) 5×2 – 11z + 7 and 10z2 -18 + 7z (iv) y2 – 3y2 + 7y – 17 and 2y^2 …

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EXERCISE 10 B Question 1 The pressure P of an enclosed gas , held at a constant temperature , is inversely proportional to the volume V of the gas . Express P in terms of V and the constant of variations K . Calculate (i) The value of K when P = 500 and V …

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EXERCISE 10 C Question 1 4 mens can make 4 cupboards in 4 days ; how many cupboards can 14 mens make in 14 days ? Sol : As number of men ∝ number of cupboards or Number of days In 4 days 4 mens make 4 cupboards ∴ In 1 day 4 mens make …

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EXERCISE 7 (B) Question 1 What percent of a day is the time duration of 3 hours? Sol : Total hours in a day = 24 hours Given hours = 3 hours in percentage Hence , of a day represent 3 hours   Question 2 About 67% of a human body’s total weight is water.If …

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EXERCISE 4 (B)   Number Cube Cube Root 1 1 1.000 2 8 1.260 3 27 1.442 4 64 1.587 5 125 1.710 6 216 1.817 7 343 1.913 8 512 2.000 9 729 2.080 10 1000 2.154 11 1331 2.224 12 1728 2.289 13 2197 2.351 14 2744 2.410 15 3375 2.466 16 4096 …

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Exercise 3 (D)   NUMBER SQUARE SQUARE ROOT 1 1 1.000 2 4 1.414 3 9 1.732 4 16 2.000 5 25 2.236 6 36 2.449 7 49 2.646 8 64 2.828 9 81 3.000 10 100 3.162 11 121 3.317 12 144 3.464 13 169 3.606 14 196 3.742 15 225 3.873 16 256 …

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Exercise 3 (C)   Question 1  Find the square root of each of the following numbers. (i) 152.7696 (ii) 49.7025 (iii) 64.0324 (iv) 291.7264 (v) 81.108036 (vi) 0.000036 (vii) 0.00002809 (viii) 0.00033124 Question 2 The area of a square field is 577.4409 square meters. Find the length of one side of the field. Question 13 Find the square root of the following …

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Exercise 3 (B)   Question 1 Find the square root of each of the following numbers by division method. (i) 3249 (ii) 6889 (iii) 15129 (iv) 75625 (v) 166464 (vi) ​9548100 Sol : (vii) ​ (viii) ​​​​ (ix)  Sol : (x) ​​ Sol : Question 2 Find the perimeter of a square field whose area is 13689 m2 Sol : Question 3 What should …

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EXERCISE 30 Question 1  A die is rolled once. What is the probability of rolling. (i) 3 Sol : (ii) 7 Sol : (iii) an even number Sol : (iv) a prime number ? Sol : Question 2  Ramesh chooses a date at random in April for a party. Calculate the probability that he chooses. …

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EXERCISE 29 B 1.Represent the following distribution of ages (in years) of 35 teachers in a school by means of a histogram. <div style=”overflow: auto;”> <table style=”border-collapse: collapse;” border=”1″> <tr><th>Age(in years)</th><td>25-30</td><td>30-35</td><td>35-40</td><td>40-45</td><td>45-50</td></tr> <tr><th>Number of teachers</th><td>12</td><td>11</td><td>8</td><td>1</td><td>3</td></tr> </table> </div> Draw histrograms for the following frequency distributions. 2. <div style=”overflow: auto;”> <table style=”border-collapse: collapse;” border=”1″> <tr><th>Size</th><td>0-10</td><td>10-20</td><td>20-30</td><td>30-40</td><td>50-60</td></tr> <tr><th>Frequency</th><td>5</td><td>10</td><td>20</td><td>25</td><td>20</td><td>10</td></tr> </table> </div> …

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EXERCISE 29 A 1.The following table shows the number of students in a school playing five different games. <div style=”overflow: auto;”> <table style=”border-collapse;” border=”1″> <tr><th>Games</th><td>Football</td><td>Hockey</td><td>Cricket</td><td>Tennis</td><td>Squash</td></tr> <tr><th>Number of students</th><td>200</td><td>175</td><td>250</td><td>75</td><td>50</td></tr> </table> </div> Present this information on a bar graph 2.The following table shows how a student spends his pocket money during the course of a month <div …

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EXERCISE 28 C Find the median of the following. 1. 7,32,15,28,43,29 2. 22,22,38,73,42,64,28,54 3.What is the median score achieved by a student who recorded the following scores on 10 math quizes ? 4.Determine the mode(s) for each of the following sets of data (i) 2,8,7,3,2,7,6,7 (ii) 14,16,18,14,10,14,16,12,16,10 (iii) 21,38,80,26,55,80,53,68,80,51 (iv) 26,32,26,21,83,26,83,67,53,83,85 5.Find the mode of …

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EXERCISE 28 B 1.Fill in the blanks: (i) The difference between the maximum and the minimum observations in a data is called the ___ of the data. (ii) The number of observations in a particular class interval is called the ___ of the class interval. 2.Find: (i) Lower limit of the class interval 46 – …

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EXERCISE 28 A 1.Write (T) for true or (F) for false. Use the following frequency table. <div style=”overflow: auto;”> <table> <tr><th>Age</th><td>13</td><td>14</td><td>15</td><td>16</td><td>17</td><td>18</td><td>19</td></tr> <tr><th>Frequency</th><td>3</td><td>2</td><td>7</td><td>2</td><td>3</td><td>2</td><td>1</td></tr> </table></div> (i) The frequency of 19 is 1 (ii) The frequency of 14 is 3 (iii) 17 has the lowest frequency (iv) 16 has a frequency of 2 (v) 15 has the highest …

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EXERCISE 27 C 1.Find the volume of each of the following cylinders whose: (i) Radius of base = 10cm Height = 14 cm (ii) Radius of base = 21cm Height = 30 cm (iii) Radius of base = 10.5cm Height = 35 cm 2.The area of the base of a circular cylinder is 35 cm^2 …

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EXERCISE 27 B 1.Copy and complete the given table for a cylinder (use pi=22/7) <div style=”overflow: auto;”> <table style=”border-collapse: collapse;” border=”1″> <tr><th></th><th>Radius</th><th>Height</th><th>Curved Surface Area</th><th>Area of Base</th><th>Total Surface Area</th></tr> <tr><td>(i)</td><td>14cm</td><td>20cm</td><td></td><td></td><td></td></tr> <tr><td>(ii)</td><td>0.28cm</td><td>45cm</td><td></td><td></td><td></td></tr> <tr><td>(iii)</td><td>5.6cm</td><td>13.2cm</td><td></td><td></td><td></td></tr> </table> </div> 2.Find the radius of a sylinder whose height is 42cm and whose curved surface area is 8448 cm^2. 3.The total surface area …

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EXERCISE 27 A 1.Find the surface area and volume of cuboid whose dimensions are : (i) 3m , 5m and 7m (ii) 4.8m , 80cm and 50cm (iii) 2.4cm , 16cm , 4mm 2.Find the surface area and volume of a cube whose side is : (i) 6cm (ii) 1.2cm (iii) $\dfrac{1}{8}~cm$ 3.Find the volume …

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EXERCISE 26 1.Find the circumference and area of each of the following circles given: (i) radius=14cm (ii) radius=4.2cm (iii) diameter=56cm (iv) diameter=16.1cm 2.Find the diameter of the circle whose (i) Circumference is 308cm (ii) Area=962.5cm^2 3.Two wire circles of diameters 28cm and 35cm are cut and then joined to form a big circle of radius …

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EXERCISE 25 E Find the areas of the following polygons 1. 2. 3. 4. 5.A school croosing sign has the dimensions as shown in the figure. (i) What is the area of the sign boards ? (ii) If the 4 such sign boards are cut from the rectangular metal sheet 350cm long and 320cm wide, …

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EXERICSE 25 D 1.Find the area of the following trapezium whose dimensions are: (i) Height=10cm Parallel sides=6cm and 8cm (ii) Height=4cm Parallel sides=6.4cm and 4.6cm (iii) Height=8.4cm Parallel sides=15cm and 9.2cm (iv) Height=7cm Parallel sides=12cm and 16cm 2.Find the height of a trapezium. whose sum of the lengths of the bases is 31 cm and …

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EXERCISE 25 C 1.Find the area of each of the following parallelogram whose base=340mm , height=17cm. 2.The adjacent sides of a parallelogram are 8m and 5m .The distance between the longer sides is 4m. What is the distance between the shorter sides ? 3.The area of a parallelogram is 98cm^2 and its altitude is twice …

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EXERCISE 25 B 1.Find the area of each of the following triangles: (i) (ii) (iii) 2.The base of a triangle measures 32 cm and its altitude is 45 cm. Find the area of the triangle in square metres. 3.Find the height of a triangle, if its area is 24 cm^2 and its base is 15 …

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EXERICSE 25 A 1.(i) Find the perimeter and area of a square whose one side is 6.5cm long. (ii) Find the area of a square whose perimeter is 124 cm. (iii) Find the perimetr and diagonal of a square whose area is 64 cm^2 2.Find in hectares the area of a square-shaped field 14km long. …

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EXERCISE 24 B Calculate the angles marked with letters. O is the center of the circle wherever given. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.(i) If angleAOb=126deg , what is angleAPB ? (ii) If angleOAB=29 deg , what is angleAPB ? (iii) If angleAPB=62 deg , …

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EXERCISE 24 A   1. Calculate the length marked by x In each oi the following diagrams. the unit of length being cm. (O is the centre in each diagram) (i) (ii) (iii) 2.In a circle with centre O and radius 13cm , AB is a chord. If OMperpendicularAB and OM=5cm , what is the …

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EXERCISE 23 D 1.Match each graph with the correct description. (i) (ii) (iii) (iv) (a) (b) (c) (d) 2.The graph shows an aeroplane’s f‌light. (i) What does 1 small square represent (a) horizontally ? (b) vertically? (ii) For how long was the aeroplane climbing ? (iii) What was the aeroplane’s speed whilst climbing? (iv) How …

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EXERCISE 23 C 1.From a table of values showing the coordinates of the points highlighted on each of the graphs given below and hence write the equation showing the relationship between x and y. (i) (ii) (iii) (iv) 2.Copy and complete the table of values for each equation. Hence,draw the respective graphs. (i) y=x+5 (ii) …

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EXERCISE 23 B 1.Fill in the blanks: (i) The graph of x=1 is a line parallel to the ____ axis (ii) The graph of y=1 is a line parallel to the ____ axis (iii) The equation ax+by+c=0 (where a and b are not both zero) is called a ___ equation. (iv) The graph of 2x=1 …

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EXERCISE 23 A 1.Draw your own set of axes on a graph paper and plot the following points (i) A (5, 3) (ii) B (—4, 6) (iii) C (—3, -7) (iv) D (6, —5) (v) E (6, 6) (vi) F (-6, 3) (vii) G(-8,-6) (viii) H(-1,8) 2.Write down the coordinates of: (i) The vertices P, …

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EXERCISE 22 C 1.State the co-ordinates of image of each of the following points: (i) P(5,8) , Q(-7,11) , R(10,-6) , T(-15,-7) after reflection in x-axis (ii) A(11,14) , B(-10,15) , C(17,-12) , D(-6,-8) after reflection in y-axis 2.Write down the coordinates of image of each the points E(-7,-13) and F(16,-21) when (i) reflected in …

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EXERCISE 22 D 1.Which of the following shapes have rotationary symmetry of order more than 1 ? Also state the order for each figure. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) 2.Name any four geometric figure which have same number lines of symmetry and order of rotational symmetry. 3.What is the angle of rotation …

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EXERCISE 22 B 1.Copy the figure and show the images which result from reflection in the line m (i) (ii) (iii) 2.Complete the given shapes after drawing the images of the given portions in the mirror line. Name the complete shape so formed. Example. The first one is a kite (i) (ii) (iii) (iv)

EXERCISE 22 A 1.Examine the following shapes and tell which of these have a line or lines of symmetry and which do not have any line of symmetry ? (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) 2.Draw the lines of symmetry in each of the following figures: (i) (ii) (iii) (iv) (v) (vi) (vii) …

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EXERCISE 21 1.The adjoining net is made up of two equilateral triangles and three rectangles (i) Name the solid it represents (ii) How many faces,edges and vertices does this solid have ? 2.For each solid, count the numebr of faces , vertices and edges. Check if the Euler’s rule is true for each one. (i) …

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EXERCISE 20 B I.Construct a rectangle ABCD given: 1.AB=7cm , BC=6cm 2.AB=6.9cm , BC=3.7cm 3.AB=8.2cm , BC=7.1cm 4.AB=8cm , BC=5.8cm 5.AB=8cm , BD=10cm 6.AB=12cm , AC=13cm 7.Constrcut a rectangle WXYZ where WX=5cm and WY=7cm II. Constrcut a square ABCD 1.Of side 2.3cm 2.Of side 6.2cm 3.AB=3.8cm 4.One diagonal=6.2cm 5.One diagonal=8cm 6.BD=5.9cm III.Constrcut a parallelogram ABCD …

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EXERCISE 20 A Comnstruct a quadrilateral: 1.(i) ABCD in which AB=4cm , BC=6cm, CD=5.5cm,AD=5cm and AC=8cm (ii) PQRS in which PQ=3.5cm,QR=5.5cm , RS=4.5cm, PS=5cm and PR=7cm 2.(i) PQRS in which PQ=4cm , QR=3cm , PS=2.5cm , PR=4.5cm and QS=4cm (ii) Is it possible to construct a quadrilateral ABCD in which AB=1.5cm , AD=3cm ,CD=2cm , …

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EXERCISE 19 E 1.Find the number of sides of a regular polygon in which each interior angle is 162°. 2.How many sides has a polygon the sum of whose interior angles is 1980deg ? 3.The angles of a quadrilateral taken in order are 2x , 3x , 7x ,8x. Find x and prove that two …

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EXERCISE 19 D 1.EFGH is a rhombus. Find a , b , c 2.PQRS is a rectangle whose diagonals intersect at point O. IF OP=4x-1 and OS=2x+7. Find the value of x. 3.The diagonals of a rectangle ABCD intersect at O. If angleAOB=114 deg , find angleACD and angleADB . 4.ABCD is a rhombus with …

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EXERCISE 19 C 1.For each of the statements given below, indicate if it is true(T) or false(F): (i) A rectagle is a parallelogram (ii) A square is a rectangle (iii) A parallelogram is a rhombus (iv) A square is a rhombus (v) A rectangle is a square (vi) A square is a parallelogram 2.What kind …

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EXERCISE 19 B 1.In a parallelogram PQRS, angleS=75deg . Determine the measures of angleP and angleQ. 2.The measures of two adjacent angles of a parallelogram are in the ratio 2:7. Find the measure of each of the parallelogrm. 3.Two opposite angles of a parallelogram are 6x-17deg and x+63 deg. Find the measure of each angle …

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EXERCISE 19 A 1.What would you call a figure having four sides out of which two opposite sides are parallel ? 2.What would you call a figure having four sides, the opposite sides parallel and the angles at the corner right angles ? 3.What would you call a figure having four equal sides, the opposite …

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EXERCISE 18 1.The three angles of a quadrilaterals are 110 deg , 71 deg and 70 deg. Find its fourth angle. 2.In a quadrilateral PQRS, angleP=120 deg and angleQ=angleR=angleS, find angleQ , angleR and anglesS 3.In the adjoining figure, P is a point in the interior of angleAOB and angleAOB=40 deg. If Pmperpendicular 4.Find the …

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EXERCISE 17 B 1.Two sides begin , calculate the third side marked by letter in each right angled triangle: (i) (ii) (iii) (iv) 2.Calculate the length of the ramp fig 3.Calculate the length of the wire fig 4.Look at the figure at the right. If you walk at the speed of 8 m/sec , how …

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EXERCISE 17 C 1.Can the following side lengths form a triangle? Explain. (i) 3,5,6 (ii) 6,9,12 (iii) 5,7,13 (iv) 7,8,13 (v) 10,15,25 2.P is a point in the interior of deltaABC. State which of the following statements are true (T) or false (F). (i) AP+PB<AB (ii) AP+PC>AC (iii) BP+PC=BC 3.in the f‌igure, state which path …

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EXERCISE 17 D 1.In the given figure , AX bisects angleCAB and angleBDC. Show that deltaABDsimilaritydeltaACD. 2.In the figure, ABC is a triangle with BD and CE perpendicular to AC and AB respectively, such that BD = CE. Prove that deltaBCDsimilaritydeltaCBE 3.In the given figure, AB = AC and D , E and F are …

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EXERCISE 17 A 1.The three angles of a triangle measures (2x-10degree) , (x+31deg) and (5x+7deg) . Find the value of x and hence all the angles of the triangle 2.One of the exterior angles of a triangle is 153 deg and the interior opposite angles are in the ratio 5 : 4 . Find the …

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EXERCISE 16 B 1. 2. 3. 4. 5. 6.

EXERCISE 16 A 1. 2. 3. 4. 5. 6. 7. 8.

EXERCISE 15 B Question 1 The sum of three consecutive odd natural numbers is 87. What are the three numbers ? Sol : Let the three consecutive odd numbers be (2x+1) , (2x+3) and (2x+5) A.T.Q ⇒(2x+1)+(2x+3)+(2x+5)=87 ⇒2x+1+2x+3+2x+5=87 ⇒6x+9=87 ⇒6x=87-9 ⇒6x=78 ⇒ ⇒x=13 Hence , the consecutive numbers are ⇒2x+1=2×13+1=27 , ⇒2x+3=2×13+3=29 and ⇒2x+5=2×13+5=31   …

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EXERCISE 15 A Solve the following equations: Question 1 3(x+1) + 4x = 24 Sol : ⇒ 3x+3+4x=24 ⇒ 7x=24-3 ⇒ 7x=21 ⇒ ⇒   Question 2 16-2(3y+5) = 4(y-2) Sol: ⇒16-6y-10=4y-8 ⇒16-10+8=4y+6y ⇒24-10=10y ⇒14=10y ⇒ ⇒y=1.4   Question 3 3(z+1)+4(z+0.3) = 20z + 0.98 Sol: ⇒3z+3+4z+1.2=20z+0.98 ⇒7z+4=20z+0.98 ⇒4-0.98=20z-7z ⇒3.02=13z ⇒ ⇒z=0.23   Question 4 …

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EXERCISE 14 H Factorise: 1. 2x^2 + 7x + 5 2. 4x^2 + 15x + 14 3. 4x^2 + 28x + 13 4. 3x^2 + 13x + 14 5. 4x^2 + 8x – 5 6. 2x^2 – 5x -12 7. 13a^2 + 37a – 6 8. 40a^2 + a -6 9. 4a^2 – 16a + …

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EXERCISE 14 G 1. a^2 + 7a +12 2. x^2 + 8x + 15 3. x^2 + 13x + 42 4. x^2 – 17x + 72 5. s^2 + 9s – 36 6. x^2 + 5x – 50 7. a^2 – 10a + 16 8. x^2 – 4x – 5 9. a^2 + 2a – …

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EXERCISE 14 F 1. (a+b)^2 – 1 2. (3x-2y)^2 – 9z^2 3. 1-(x-y)^2 4. 4x^2 – 9(2x-y)^2 5. 16(x+y)^2 – 25(x-y)^2 6. ab^2 – ac^2 7. 36x^3 – x 8. 3 – 12b^2 9. 18ax^2 – 98ay^2 10. 2x^2 – \dfrac{1}{2} [Hint: Given Exp=2\left(x^2-\dfrac{1}{4}\right)] 11. x^4 – y^4 12. x^4 – 625 13. 16y^4 – …

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EXERCISE 14 E 1. x^2 – 9 2. x^2 – 4 3. a^2 – 25 4. p^2 – 1 5. 16a^2 – 121 6. 16x^2 – 25y^2 7. 36m^2 – 169n^2 8. -64 + 25x^2 9. x^2y^2 – a^2 10. x^4 – 9 11. a^8 – 36 12. x^6 – 16 13. 1 – 4c^12 …

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EXERCISE 14 D 1. x^2 + 4x + 4 2. x^2 + 6x + 9 3. x^2 – 10x + 25 4. 4x^2 – 4x + 1 5. a^2 + 10ab + 25b^2 6. x^2 – 8xy + 16y^2 7. 4x^2 + 20xy + 25y^2 8. 64x^2 – 80xy + 25y^2 9. x^4 + 6x^2 …

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Exercise 14 C 1. x(m+n) + ym + yn 2. px + py + x(x+y) 3. ax + ay + 8x + 8y 4. m(m+4) – 8m – 32 5. 3x + 3y + px + py 6. ax + bx + 7a + 7b 7. xy – zx -2y + 2z 8. x^2 + …

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Exercise 14 B Factorise: 1. (x+3)x + (x+3)y 2. (a+1)x + (a+1)y 3. a(m+n) + b(m+n) 4. 2(x-a)^2 + (x-y) 5. a(a+b) – b(b+a) 6. (p+q)^2 + 3(p+q) 7. (x+y)^2 + (x+y) 8. 21(4p-5q)^3 + 14(4p-5q)^2 9. a(x-y) – b(x-y)^2 10. a(x+y+z) + b(x+y+z) + c(x+y+z) 11. (a+b)^3 – 3ab(a+b) 12. a(a-2c) + b(a-2c) + …

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Exercise 14 A Factorize completely by removing a monomial factor. Question 1  3y – 9 Sol : = 3(y) + 3( -3) The common factor is 3 , dividing each term by 3 we obtain other factor ( y – 3 ) = 3(y-3)   Question 12  5x + 10 Sol : = 5(x) + …

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EXERCISE 6 (A) 1.State which of the following sets are finite and which are infinite. (i) {The men who have orbited the Earth}. (ii) {The men who have landed on the moon}. (iii) {The integers between -5 and +5} (iv) {} (v) {The infants in your class}. (vi)  (vii) {The sets of atoms in Earth} (viii) …

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EXERCISE 5 C Question 1 Replace each letter W the correct numeral. (i) (ii) (iii) (iv) Question 2 What should come in place of the question mark(?) in the following number series ? (i) 563 , 582 , 620 , 677 , 753 , 848 ? (ii) 17 , 17 , 51 , 255 , …

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EXERCISE 5 (B) Question 1 Which of the following numbers are divisible by 2 ? 57, 4, 60, 93, 126, 365, 80, 992 Sol: A numbers is divisible by 2 , if their unit digit is even (0 , 2 , 4 , 6 , 8) . So , the answer is 34 , 60 …

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EXERCISE 2 Question 1 Evaluate: (i) 2-3 Sol : Using property ⇒ ⇒ (ii) 60 Sol : Using property: a0=1 ⇒60=1 (iii) (-3)-2 Sol : Using property ⇒ ⇒ (iv) 85 . 8-5 Sol : Using property am×an=a(m+n) ⇒85 . 8-5 or ⇒85 × 8-5  ⇒8(5-5) (v) Sol : Using property ⇒2(-2)×-1 ⇒22 ⇒4 (vi) …

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EXERCISE 24 C 1.Find the area of the following graphical figures (i) fig (ii) (iii) 2. Find the area of a rectangle whose (i) Length = 18 cm and breadth = 13 cm (ii) Length = 12 cm and breadth = 7.5 cm (iii) Length $=3\dfrac{1}{4}~m$ and breadth $=1\dfrac{1}{2}~m$ (iv) Length = 5 m 60 …

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EXERCISE 24 B 1. An equilateral triangle with one side measuring (i) 9 cm (ii) 30 cm (iii) 45 mm (iv) 100 mm 2. A regular hexagon with one side measuring  (i) 15 cm (ii) 55 mm (iii) 80 mm (iv) 0.7 m 3. Find the length of one side of a regular hexagon, if …

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EXERCISE 24 A 1. Find the perimeter of a square whose one side is of length (i) 6 cm (ii) 16 mm (iii) 1.8 m (iv) 2.7 m (v) 14 cm 2. Find the perimeter of a rectangle whose length and breadth are  (i) 8 cm , 5 cm (ii) 20 cm , 25 cm …

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EXERCISE 25 C 1. Convert: (i) 7 cm3 to mm3 (ii) 60000 mm3 to cm3 (iii) 0.0086 m3 to cm3 (iv) 5000 cm3 to m3 2. Express in cm3: (i) 36 litre (ii) 0.73 litre (iii) 0.0068 litre 3. Express in litres : (i) 8000 cm (ii) 2000 cm3 (iii) 3500 cm3 4. Express in …

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EXERCISE 25 B 1.Work out the volume of each cuboid. (i) fig (ii) fig (iii) fig 2. Complete the following table. (Measurements are in cm) (i) (ii) (iii) (iv) (v) (vi) Length 4 2 7 ? 16 ? Breadth 3 6 3 9 ? 28 Height 5 8 4 12 18 24 Volume ? ? …

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EXERCISE 25 A 1. Find the surface area of each of the cuboids whose dimensions are given below (i) (ii) (iii) (iv) (v) l 9 cm 5 cm 12 cm  5 cm  $5\dfrac{1}{2}$ b 4 cm 5 cm 10 cm  1.5 cm  4cm h 3 cm 10 cm 4 cm 2.4 cm $10\dfrac{1}{2}$   2. …

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अमृतं संस्कृतम (क) विश्वस्य उपलब्धासु भाषासु संस्कृतभाषा प्राचीनतमा भाषास्ति। भाषेयं अनेकाषां भाषाणां जननी मता। प्राचीनयो: ज्ञानविज्ञानयो: निधि: अस्यां सुरक्षित:। संस्कृतस्य महत्त्वविषये केनापि कथितम्‌ – “भारतस्य प्रतिष्ठे द्वे संस्कृतं संस्कृतिस्तथा “।   सरलार्थ – संसार की प्रपत भाषाओं में संस्कृत भाषा प्राचीन (पुरानी) भाषा है । यह भाषा अनेक भाषाओं की माता मानी गई हैं । …

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विश्वबन्धुत्वम् (क) उत्सवे, व्यसने, दुर्भिक्षे, राष्ट्रविप्लवे, दैनन्दिनव्यवहारे च य: सहायतां करोति सः बन्धु: भवति। यदि विश्वे सर्वत्र एतादृश: भाव: भवेत्‌ तदा विश्वबन्धुत्व सम्भवति। परन्तु अधुना निखिले संसारे कलहस्य अशान्ते: च वातावरणम्‌ अस्ति। मानवा: परस्परं न विश्वसन्ति। ते परस्य कष्टं स्वकीयं कष्टं न गणयन्ति। अपि च समर्था: देशा: असमर्थान्‌ देशान्‌ प्रति उपेक्षाभावं प्रदर्शयन्ति, तेषाम्‌ उपरि स्वकीयं …

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EXERCISE 2 D QUESTION 1 Fill In the blanks to make each of the following a true statement, using properties of multiplication . Also name the property used in each of them.  (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x)   QUESTION 2 QUESTION 3 QUESTION 4 QUESTION 5 QUESTION 6  

EXERCISE 2 C QUESTION 1 Perform the following subtractions and check your result by corresponding addition. (i) 456 – 215 Sol :   (ii) 15795 – 9784 Sol :   (iii) 20000 – 9999 Sol :   QUESTION 2 Complete : (i) 1340 – ___ = 990 Sol :   (ii) 5245 – ___ = …

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EXERCISE 2 B QUESTION 1  

EXERCISE 2 A QUESTION 1 Fill in the blanks. (i) The successor of the smallest whole number is ___ (ii) The predecessor of the smallest natural number is ___ (iii) Every whole number is not a ___ number. (iv) Every whole number on the number line is ___ than every whole number on its left. …

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EXERCISE 1 F QUESTION 1 Answer the following by estimating. The headline read ‘A MILLION VOTED TODAY’ Actually 90,018 people voted each hour for 12 hours . Did the newspaper give a sensible account of the number of votes cast in the election . QUESTION 2 Choose the most suitable estimate from the possible answers …

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EXERCISE 1 F QUESTION 1 Estimate first, then write the sum or difference. Find the sum to check your work. (i) 51 + 47 Sol :   (ii) 528 + 62 Sol :   (iii) 2314 + 372 Sol :   (iv) 1521 + 6325 Sol :   (v) 43278 + 2902 Sol :   …

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EXERCISE 1 E QUESTION 1 Round off the following to the nearest ten. (i) 52 Sol :   (ii) 17 Sol :   (iii) 95 Sol :   (iv) 93 Sol :   (v) 253 Sol :   (vi) 166 Sol :   (vii) 892 Sol :   (viii) 578 Sol :   (ix) 875 …

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EXERCISE 1 D QUESTION 1 Find the sum    QUESTION 2 Subtract:   QUESTION 3 Multiply: (i) 28845 by 6502 Sol : (ii) 659675 by 928 Sol :   QUESTION 4 Divide : (i) 13443003 by 567  Sol :   (ii) 23890764 by 1985 Sol :   QUESTION 5 A toy factory produced 1,56,935 toy …

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EXERCISE 1 C QUESTION 1 Read the following numbers in the International system of numeration and write in words (i) 53,673 Sol :   (ii) 430,057 Sol :   (iii) 78,823,761 Sol :   (iv) 600,003 Sol :   (v) 1,369,864,005 Sol :   (vi) 80,112,005,459 Sol :   QUESTION 2 Write the numerals for …

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EXERCISE 1 B QUESTION 1 Read and write down in words , the following numbers in the Indian system of numeration. (i) 6,80,453 Sol :   (ii) 12,36,748 Sol :   (iii) 8,30,09,007 Sol :   (iv) 10,00,30,004 Sol :   (v) 33,04,05,078 Sol :   QUESTION 2 Write the following in figures . (i) …

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EXERCISE 1 A QUESTION 1 Write the following numbers in words and expanded form (i) 60802 Sol :   (ii) 70045 Sol :   (iii) 32001 Sol :   (iv) 89316 Sol :   QUESTION 2 Write the following numbers in standard form  (i) Sixty thousand nine hundred forty Sol :   (ii) Fifty-eight thousand …

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EXERCISE 17 C Question 1 (i) Using the inner scale of the protector , find the measure of (a) x (b) y (c) z (d) w (e) AOC (f) BOD (g) AOD (h) COE (ii) Using the outer scale of the protector , find the measure of (a) (b) (c) (d) (e) (f) (g) (h) …

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Exercise 17 B Question 1 In the given fig. Q1 , which setting will the pointer face after it turns  (i) 45º clockwise from normal ? Sol : A circle consist of total angle of 360º  . Now lets find the angle between two options . And to do so , we take = 45º …

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EXERCISE 12 A QUESTION 1 Which of the following expressions are not polynomials ? (i) Sol : Yes , its a polynomial   (ii) Sol :   [∴ ] No , its not a polynomial since it contains negative exponent(power)   (iii) Sol : Yes , it is a polynomial   (iv) Sol : No …

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 EXERCISE 11 Question 1 A can do of the work in 12 days . In how many days can he complete of the work ? Sol : ⇒A can do of work in 12 days ⇒ A can do 1 work in days And  [Mutiplying both side by 3/4] ⇒ A can do work in …

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EXERCISE 10 A Question 1 Given that y is directly proportional to x and y = 40 , when x = 200 . Find the value of (i) y , when x = 15 Sol: (i) y ∝ x ⇒ , where k is the constant of variation Given , ⇒ k = Also , …

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EXERCISE 9 C Question 1 What total amount will Ravi get in 3 years if he invest 5000 at 5% per annum , compounded annually ? Sol : Principal(P) = 5000 , Rate(R) = 5% and Time period(n) = 3 years = 5×1157.625 = 5788.125 = 5788.13 (approx)   Question 2 A person borrowed 7500 …

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PERCENTAGE EXERCISE 7 (A) QUESTION 1 Write each of these percentages as a fraction and a decimal. (i) 15% Sol : = 0.15 (ii) 84% Sol : = 0.84 (iii) 12.5% Sol : = 0.125 (iv) 120% Sol : = 1.2 (v) Sol : = 0.33 QUESTION 2 Write each of the following as percentages. …

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Exercise 3 (A)   Question 1 Find the square of the following numbers : (i) 15 (ii) 48 (iii) ​​ (iv) ​​ (v) ​​ (vi) 0.9 (vii) 1.1 (viii) 0.018 Sol : Question  Determine whether square of the following numbers will be even or odd.(Do not find the square) Note : Square of even number are even Square of odd number is odd …

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