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Maths ·Class 9 Maths

Ganita Manjari Class 9 Solutions

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RBSEGuide
· Jul 02, 2026 · Reviewed & updated Sep 17, 2026 · 32 min read

Ganit Manjari Class 9 Solutions

Class 9 Ganit Manjari Solution

Class 9 Ganita Manjari Solutions - Ganita Manjari Class 9 Answer Key

Ganita Manjari Class 9 Part 1 Solutions

Chapter 1 Orienting Yourself The Use of Coordinates Class 9 Solutions

  1. Let us examine Fig. 1.1 to understand the layout of the room. Notice that this only shows the map Class 9
  2. Fig. 1.3 shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked Class 9
  3. What are the standard widths for a room door? Look around your home and in school. Class 9
  4. For example, in Fig. 1.4, point S (3, –5) is in Quadrant IV, the x-coordinate is 3 units and the y-coordinate Class 9
  5. What is the x-coordinate of a point on the y-axis? Class 9
  6. If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true? Class 9
  7. Place Reiaan's rectangular study table with three of its feet at the points (8, 9), (11,9) and (11,7). Class 9
  8. If the bathroom door has a hinge at Bi and opens into the bedroom, will it hit the wardrobe? Class 9
  9. Look at Reiaan's bathroom. i. What are the coordinates of the four comers O, F, R, and P Class 9
  10. Other rooms in the house i. Reiaan's room door leads from the dining room which has the length Class 9
  11. In moving from A (3, 4) to D (7, 1), what distance has been covered along the x-axis Class 9
  12. In distance formula, what if, x1, x2, y1, y2 take negative values? Class 9
  13. With reference to the given figure, what has remained the same and what has changed with the reflection? Class 9
  14. Would these observations be the same if AADM is reflected in the x-axis (instead of the y-axis)? Class 9
  15. Point W has x-coordinate equal to -5. Can you predict the coordinates of point H which Class 9
  16. Plot point Z (5, –6) on the Cartesian plane. Construct a right-angled triangle IZN and find Class 9
  17. Are the points M (-3, -4), A (0, 0) and G (6,8) on the same straight line? Suggest a method Class 9
  18. Use your method (from Problem 6) to check if the points R(-5,-1), B(-2,-5) and C(4, -12) Class 9
  19. Using the origin as one vertex, plot the vertices of Class 9
  20. The following table shows the coordinates of points S, M and T. In each case, state whether M Class 9
  21. Use the connection you found to find the coordinates of B given that M(-7, 1) is the midpoint Class 9
  22. Let P, Q be points of trisection of AB, with P closer to A, and Q closer to B. Using your knowledge Class 9
  23. Given the points A (1, -8), B (-4, 7) and C(-7, -4), show that they lie on a circle K Class 9
  24. The midpoints of the sides of triangle ABC are the points D, E, and F. Given that Class 9
  25. A city has two main roads which cross each other at the centre of the city. These two roads Class 9
  26. A computer graphics program displays images on a rectangular screen whose coordinate system Class 9
  27. Plot the points A(2,1), B(-1, 2), C(-2, -1) and D(1, -2) in the coordinate plane. Is ABCD Class 9

Chapter 2 Introduction to Linear Polynomials Class 9 Solutions

  1. Can you identify the terms, variables and coefficients of this algebraic expression Class 9
  2. A wire of length 20 cm is bent in different ways to form rectangles. For example Class 9
  3. Can you identify the terms, variables and coefficients of this algebraic expression? Class 9
  4. Find the degrees of the following polynomials: Class 9
  5. Write polynomials of degrees 1, 2 and 3. Class 9
  6. What is the coefficient of z in the polynomial 4z³ + 5z² - 11 ? Class 9
  7. Find the perimeter of squares with sides 1 cm, 1.5 cm, 2 cm, 2.5 cm and 3 cm. What will happen Class 9
  8. If a player paid ₹ 750, how many matches did he play? Class 9
  9. We have learnt that to evaluate the value of an algebraic expression, we substitute a value of the variable Class 9
  10. Find the value of the quadratic polynomial 7s² - 4s + 6 if: Class 9
  11. The present age of Salil's mother is three times Salil's present age. After 5 years, their ages Class 9
  12. The difference between two positive integers is 63. The ratio of the two integers is 2 : 5. Find the two integers. Class 9
  13. Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total Class 9
  14. A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times Class 9
  15. If the length of a rectangle is three more j than twice its width and its perimeter is 24 cm Class 9
  16. Predict the number of squares in the next three stages of the pattern and write the sequence Class 9
  17. Using the expression 2n - 1 can you find out how many tiles will be there in the 15th stage Class 9
  18. Bela has ₹100 for pocket money. She spends ₹5 every day. What amount will be left Class 9
  19. An auto-rikshaw fare starts at ₹25 and remains the same for the initial 2 km. Then it increases Class 9
  20. A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. Class 9
  21. A rally starts with 120 members. Each hour, 9 members drop out of the group. Class 9
  22. Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm Class 9
  23. Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if the height Class 9
  24. Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages class 9
  25. Rohan has a box of 60 chocolates. He eats 4 chocolates every day. Find the number of chocolates Class 9
  26. The cost of a journey is given by the linear function C(d) = 100 + 60 d, where C indicates total cost Class 9
  27. Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month. Class 9
  28. A mobile phone is bought for ₹ 10,000. Its value decreases by ₹ 800 every year. Class 9
  29. The initial population of a village is 750. Every year, 50 people move from a nearby city to the village. Class 9
  30. A telecom company charges ₹ 600 for a certain recharge scheme. This prepaid balance is reduced Class 9
  31. A telecom company charges a fixed monthly fee and an additional cost per GB of the internet data used Class 9
  32. Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent? Class 9
  33. A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. Class 9
  34. Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F) Class 9
  35. Identify other points on the line y = 2x + 1 by completing the following table Class 9
  36. Let us plot the points (- 3, 6), (- 2, 4), (0, 0), (1, - 2), (2, - 4), (3, - 6) in the coordinate plane on a graph paper Class 9
  37. In order to graph y = 1/2 x, we could take the points (0, 0) and (4, 2). Class 9
  38. Draw the graphs of y = 1/2 x, y = x, y = 2x Class 9
  39. Draw the graphs of y = -1/3 x, y = -x, y = -3x on the same axes. Does this help Class 9
  40. Draw the graph of y = 2x - 1, y = 2x + 1 and y = 2x + 5 on the same axes. Class 9
  41. Draw the graphs of the following sets of lines. In each case, reflect on the role of 'a' and 'b'. Class 9
  42. Write a polynomial of degree 3 in the variable x, in which the coefficient of the x² term is - 7. Class 9
  43. If we multiply a number by 5/2 and add 2/3 to the product, we get -7/12. Find the number. Class 9
  44. If you have ₹ 800 and you save ₹ 250 every month, find the amount you have after (i) 6 months (ii) 2 years Class 9
  45. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number Class 9
  46. Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates Class 9
  47. If the temperature of a liquid can be measured in Kelvin units as x K and in Fahrenheit Class 9
  48. The work done by a body on the application of a constant force is the product of the constant force Class 9
  49. The graph of a linear polynomial p(x) passes through the points (1, 5) and (3, 11). Class 9
  50. Let p(x) = ax + b and q(x) = cx + d be two linear polynomials such that: Class 9
  51. Look at the first three stages of a growing pattern of hexagons made using matchsticks. Class 9
  52. Let p(x) = ax + b and q(x) = cx + d be two linear polynomials such that: Class 9
  53. What do all linear functions of the form f(x) = ax + a, a > 0, have in common? Class 9

Chapter 3 The World of Numbers Class 9 Solutions

  1. A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. Class 9
  2. We know that Natural Numbers are closed under addition the sum of any two natural numbers Class 9
  3. Why does a negative times a negative equal a positive? Think of it in terms of action and debt. Class 9
  4. A spice trader takes a loan (debt) of ₹ 850. The next day, he makes a profit fortune Class 9
  5. Explain, using a real-world example of debt, why subtracting a negative number is the same as adding Class 9
  6. While adding or subtracting two rational numbers having different denominators Class 9
  7. Prove that the following rational numbers are equal: i. 2/3 and 4/6 ii. 5/4 and 10/8 Class 9
  8. Find the sum: i. -2/5 + 3/10 ii. 7/12 + 5/8 iii. -4/7 + 3/13 Class 9
  9. Find the difference: i. 5/6 - 1/4 ii. 11/18 - 3/4 Class 9
  10. Find the product: i. 2/3 × 3/10 ii. 7/11 × 5/8 iii. -4/7 × 5/14 Class 9
  11. Show that: 1/2 + 3/4 × 8/3 = 1/2 × 8/3 + 3/4 × 8/3 Class 9
  12. Find the rational number x such that: 5/6x + 3/5x = 5/3x + 1/2 Class 9
  13. Represent the rational numbersand 2/5, -5/4 and 11/2 on a single number line. Class 9
  14. Simplify the expression: -1/4 + 5/12. Class 9
  15. Find three rational numbers between 3.1415 and 3.1416. Class 9
  16. Can 2 be written as a rational number p/q ? Class 9
  17. Try to prove the irrationality of 3 using the approach of proof by contradiction. Class 9
  18. We have seen how to obtain a line whose length is a rational number. How do we obtain lines Class 9
  19. Locate 2 on the number line. Class 9
  20. Try to extend this method for constructing line segments of lengths 3 and 5 Class 9
  21. Try to find the decimal expansions of 10/3 and 11/12. What do you observe about the repetition Class 9
  22. Without performing long division, determine which of the following rational numbers will have terminating decimals Class 9
  23. Perform the long division for 1/13. Identify the repeating block of digits. Does it show cyclic properties Class 9
  24. Classify the following numbers as rational or irrational: Class 9
  25. The number 0.9 (which means 0.99999 ...) is a rational number. Using algebra let x = 0.9, multiply by 10 Class 9
  26. Consider this puzzle: What is the square root of -1? Class 9
  27. Prove that 5 is an irrational number. Class 9
  28. Convert the following decimal numbers in the form of p/q. Class 9
  29. Locate the following rational numbers on the number line. Class 9
  30. Find 6 rational numbers between 3 and 4. Class 9
  31. Find 5 rational numbers between 1/6 and 2/5. Class 9
  32. Let a and b be two non-zero rational numbers such that a + 1/b = 0. Without assigning any numerical values Class 9
  33. Without performing division, determine whether the decimal expansion of 18/125 is terminating Class 9
  34. Let a = 1/12 and b = 5/6. Express both a and b in the form Class 9
  35. Three rational numbers x, y, z satisfy x + y + z = 0 and xy + yz + zx = 0. Show that all the rational numbers Class 9
  36. Show that the rational number a+b/2 lies between the rational numbers a and b. Class 9
  37. Find the lengths of the hypotenuses of all the right triangles in the given figure which is referred to as the square root spiral. Class 9

Chapter 4 Exploring Algebraic Identities Class 9 Solutions

  1. Try and find other patterns like this one. For example, you could consider 4 consecutive squares Class 9
  2. If a = 10 and b = 2, what are the values of (a + b)² and a² + b²? (a + b)² = (10 + 2)² = 12² = 144 Class 9
  3. What can you say about a and b if (a + b)² > a² + b²? Class 9
  4. Using the identity (a + b)² = a² + 2ab + b², expand the following: Class 9
  5. Using the same identity, find the values of the following: Class 9
  6. What if we replace b by - b in (a + b)² = a² + 2ab + b²? Class 9
  7. Factor completely: i. 9x² + 24xy + 16y² ii. 4s² + 20st + 25t² iii. 49x² + 28xy + 4y² Class 9
  8. Find the values of the following using the identity (a - b)² = a² - 2ab + b². Class 9
  9. Label the squares and rectangles in Fig 4.4 so that it represents the identity Class 9
  10. Find the following squares using one of the above identities. Determine which of these identities Class 9
  11. Factor using suitable identities: i. 16y² - 24y + 9 Class 9
  12. Expand the following using the identity (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca: Class 9
  13. Look at the following figure. Justify the identity a² = (a + b)(a - b) + b² for yourself. Class 9
  14. Try to evaluate the following using a suitable identity: Class 9
  15. Observe the two rows of figures below. They represent an algebraic identity. Try to identify it. Class 9
  16. Suppose 7x is split as 2x + 5x; can a similar rectangular arrangement be formed? Consider other possibilities Class 9
  17. Algebra tiles can be used to represent products and find factors. Class 9
  18. Consider the case where we have a rectangle of side lengths 2x + 3 and 3x + 1, as shown in the figure. Class 9
  19. Fill in the blanks to complete the following identities: Class 9
  20. Select and use the identity that will help you to find the following products without multiplying directly: Class 9
  21. Factor the following: i. 9a² + b² + 4c² - 6ab +12ac - 4bc ii. 16s² + 25t² - 40st Class 9
  22. James and Reshma were talking about algebraic identities they learnt in school. James Class 9
  23. Verify (x - y) (x² + xy + y²) = x^3 - y^3 by choosing different values of x and y. Class 9
  24. We already know that x² - y² = (x - y) (x + y). Further, we have verified that x^3 - y^3 = (x - y) (x² + xy + y²). Class 9
  25. Try to simplify the following rational expression: Class 9
  26. Simplify the following rational expressions assuming that the expressions in the denominators are not equal to zero: Class 9
  27. Use suitable identities to find the following products: Class 9
  28. Find the values using suitable identities: Class 9
  29. Factor the following algebraic expressions: Class 9
  30. Simplify the following: Class 9
  31. Find possible expressions for the length and breadth of each of the following rectangles Class 9
  32. Find possible expressions for the length, breadth, and heights of each of the following cuboids Class 9
  33. The village playground is shaped as a square of side 40 metres. A path of width Class 9
  34. If a number plus its reciprocal equals 10/3, find the number. Class 9
  35. A rectangular pool has area 2x² + 7x + 3 square hastas. If its width is 2x + 1 hastas find its length Class 9
  36. If both x - 2 and x - 1/2 are factors of px² + 5x + r, show that p = r. Class 9
  37. If a + b + c = 5 and ab + bc + ca = 10, then prove that a³ + b³ + c³ - 3abc = - 25. Class 9
  38. By factoring the expression, check that n³ - n is always divisible by 6 for all natural Class 9
  39. Find the value of i. x³ + y³ - 12xy + 64, when x + y = - 4 Class 9

Chapter 5 I’m Up and Down and Round and Round Class 9 Solutions

  1. Can you recognise the origin of the shapes in the given figure? Class 9
  2. What are the rotational symmetries of a square? How many lines of reflection symmetry Class 9
  3. The locus of points at a given distance from a given point is a circle. What can we say about Class 9
  4. Are there circles of all possible radii passing through A and B? What is the radius of the smallest Class 9
  5. You are given two points A and B on plane. How many squares can you draw on the same plane Class 9
  6. Draw ∆ABC with AB = 5 cm, ∠A = 100°, ∠C = 4 cm. Draw the circumcircle of ∆ABC. Class 9
  7. What is the least possible radius of a circle through two points A and B? Class 9
  8. The circumcircle of a given ∆ABC is drawn. Can there be other triangles congruent to ∆ABC Class 9
  9. Show that if two such isosceles triangles occurring in the previous question have equal base length Class 9
  10. Do we get something special when we draw a line segment from the centre of a circle to the midpoint Class 9
  11. Can you explain why the converse to Theorem 4 is true, i.e., why does the perpendicular from the centre Class 9
  12. An isosceles triangle ABC is inscribed in a circle, with AB AC. Show that the altitude from A to BC Class 9
  13. Two parallel chords of lengths 6 cm and 8 cm are on opposite sides of the centre of a circle. Class 9
  14. Activity: Take a paper circle. Fold the circle from the boundary, inwards. Open the fold The crease Class 9
  15. Use the Baudhayana-Pythagoras theorem to show why Theorem 6 must be true. Class 9
  16. Consider the given fig. 5.15. If CE is perpendicular to AB, CH is perpendicular to GH, and CE = CH Class 9
  17. Solve the previous question using the Baudhayana’s-Pythagoras theorem. Class 9
  18. Find the length of the chord of a circle where the radius is 7cm and perpendicular distance is 6 cm. Class 9
  19. Explain why the following statement is true: If the perpendicular distance of a chord from the centre Class 9
  20. In a circle, if the distance of chord AB from the centre is twice the distance of another chord CD Class 9
  21. Exercise: A circle with centre O is drawn, and A, B, C, D are points on the circle Class 9
  22. In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm Class 9
  23. Let A and B be two points on a circle with centre O. Are there points X, Y on the circle Class 9
  24. Find x in the given fig. 5.26. Class 9
  25. In a circle, a chord is 5 cm away from the centre. If the radius of the circle is 13 cm, what is the length Class 9
  26. An arc of a circle subtends an angle of 70° at the centre. What is the measure of the angle subtended Class 9
  27. A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle Class 9
  28. Prove that the perpendicular bisector of a chord passes through the centre of the circle. Class 9
  29. The diameter of a circle is AB. Point C is on the circumference. What is the measure of the ∠ACB Class 9
  30. Quadrilateral PQRS is inscribed in a circle. If ∠P = (2x + 10)° and ∠R = (3x - 20)°, find the value of x Class 9
  31. The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle. Class 9
  32. A cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area. Class 9
  33. Consider a cyclic quadrilateral. Without drawing its circumcircle, how can we find out whether the centre Class 9
  34. Draw a circle in which a chord of 6 cm length stands at a distance of 3 cm from the centre. Class 9
  35. Show that rectangle is the only parallelogram that can be inscribed in a circle. Class 9
  36. Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals Class 9
  37. Consider all chords of a circle of a fixed length. What is the shape formed by the midpoints Class 9
  38. In a circle with centre O, chords AB and AC are congruent. Explain why this statement is true Class 9
  39. Two parallel chords of lengths 10 cm and 24 cm are on the same side of the centre of a circle. Class 9
  40. A regular hexagon is inscribed in a circle of radius r. Find the length of the sides of the hexagon Class 9
  41. A quadrilateral MNOP is inscribed in a circle. If MN is a diameter, what can you say about ∠MOP and ∠MNP Class 9
  42. "There is no chord of a circle that is longer than its diameter." How do you justify this statement? Class 9
  43. Let A be any point within a given circle with centre O. Show that the shortest chord of the circle that passes Class 9
  44. How would you use the following figure to justify the statement that the angle in a semicircle is 90°? Class 9
  45. In a circle, two chords CC' and DD' are drawn perpendicular to a diameter AB. Prove that the segment Class 9
  46. How would you use the following figure to justify the statement that the sum of the opposite angles of a cyclic Class 9

Chapter 6 Measuring Space Perimeter and Area Class 9 Solutions

  1. In Fig. 6.1, you see athletes assembled at the start of a 4 x 100 m relay race. The tracks are laid out Class 9
  2. In my school, the playground is too small to have a 400 m track, so the school constructed Class 9
  3. What is the connection between the question about finding what the perimeter Class 9
  4. What happens to the perimeter of a square if we double its side? Class 9
  5. What about a circle? What is its perimeter (usually called the circumference) in terms of its diameter? Class 9
  6. What will be the length of a quarter circle with the same radius (Refer given Figure)? Class 9
  7. A Closer Look at a 400 m Athletics Track Class 9
  8. What is the difference in radius between the first and second lanes? Class 9
  9. Two circles of equal radius are located such that each circle passes through the centre Class 9
  10. In above figure we see points P and Q, and two paths connecting them. Class 9
  11. Unless stated otherwise, use the approximation 22/7 for π. Class 9
  12. Calculate the length of the arc of a circle if: i. the radius is 3.5 cm and the angle at the centre is 60°
  13. Find the perimeter of a sector (i.e., the curved portion as well as the two straight portions) of a circle Class 9
  14. Find the perimeters of the following shapes taking the arcs to be quarter or half or three-quarters Class 9
  15. If the diameter of a car tyre is 56 cm, then: How far does the car need to travel for the tyre Class 9
  16. Find the total perimeter of all the petals in each of the given flowers. Class 9
  17. The ratio of the perimeters of two circles is 5 : 4. What is the ratio of their radii? Class 9
  18. What happens if the parallelogram is "thin" (Fig. 6.18) and the foot of the perpendicular from C to AD Class 9
  19. The area of a rectangle can be found when we know the lengths of its sides. Is the same true Class 9
  20. Since ∆ABD and ∆ACD have equal area, you may wonder - Can we divide ∆ABD using straight cuts Class 9
  21. Think of various rectangles with perimeter 40 units (the sides do not have to be integers). Class 9
  22. What procedure would you use to square a given triangle? Here, the task is to construct a square Class 9
  23. Find the area of triangle ADE in given figure Class 9
  24. The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal Class 9
  25. Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm. Class 9
  26. The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300 m. Find its area. Class 9
  27. One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm² Class 9
  28. ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area Class 9
  29. O is any point on the diagonal PR of a parallelogram PQRS. Prove that the areas of triangles Class 9
  30. If the mid-points of the sides of a 4-gon also known as a quadrilateral, but we prefer to call it a '4-gon' Class 9
  31. In ∆ABC, the midpoint of BC is D. Median AD is drawn. P is any point on AD. Show that area (∆ABP) Class 9
  32. Given a square ABCD, let P be a point within it. Join PA, PB, PC, PD. What is the ratio of the areas Class 9
  33. In ∆ABC, D is the midpoint of AB. P is any point on BC, and Q is a point on AB such that CQ || PD. Class 9
  34. Why were human beings so fond of using circular shapes? Was this only for practical reasons Class 9
  35. Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°. Class 9
  36. The length of the minute hand of a clock is 7 cm. Find the area swept by the minute hand in 10 minutes. Class 9
  37. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre of the circle. Find the areas Class 9
  38. A car has two wipers which do not overlap. Each wiper has a blade of length 28 cm and sweeps Class 9
  39. A chord of a circle of radius r subtends an angle of 60° at the centre of the circle. Show that the area Class 9
  40. An equilateral triangle is inscribed in a circle of radius r. Show that the ratio of the area of the triangle Class 9
  41. A square is inscribed in a circle of radius r. Show that the ratio of the area of the square to the area of the circle Class 9
  42. A hexagon is inscribed in a circle of radius r. Show that the ratio of the area of the hexagon to the area Class 9
  43. Identities in algebra can sometimes be shown as area relationships. For example: Class 9
  44. An isosceles triangle has perimeter 40 cm; the equal sides are 15 cm each. Find the area of the triangle. Class 9
  45. An isosceles triangle has base 10 cm, and its area is 60 cm². What are the lengths of the equal sides? Class 9
  46. The area of a right-angled triangle is 54 sq. cm. One of its legs has length 12 cm. Find its perimeter. Class 9
  47. The sides of a triangle are in the ratio 2 : 3 : 4, and its perimeter is 45 cm. Find its area. Class 9
  48. The sides of a triangle have lengths 7 cm, 24 cm, 25 cm. Find the area of the triangle in two different ways. Class 9
  49. If the wheel of a bicycle has a diameter of 60 cm, find how far a cyclist will have travelled after the wheel Class 9
  50. The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete Class 9
  51. You know that the area of a parallelogram is base × height. Using this and the figure, show that the area Class 9
  52. By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied Class 9
  53. Show how we can use two identical copies of a trapezium to make a parallelogram. Class 9
  54. Show that the area of a kite is half the product of its diagonals. Class 9
  55. Three problems about fitting congruent shapes together: Class 9
  56. Let ∆ABC be the triangle, D divides side AB into two parts and E and F divides AC into three equal parts. Class 9
  57. Three equal circles fit exactly inside the rectangle, touching each other and the sides of the rectangle. Class 9
  58. Use the above to make a conjecture about the area occupied by circles fitted into a rectangle Class 9
  59. The figure shows nine identical rectangles fitted together to make a large rectangle whose area is 72 cm² Class 9
  60. Show that the areas of the shaded blue triangle and the shaded red triangle are equal. Class 9
  61. The figure shows a quarter circle in a square. Its centre is at one vertex, and it passes through two Class 9
  62. In given Fig. 6.50, four semicircles have been drawn within the given square whose side is 2 units. Class 9
  63. In Fig. 6.51 we see two concentric circles with a common centre O. A chord BC of the larger circle Class 9
  64. In Fig. 6.52, semicircles have been drawn on all the sides of a right-angled triangle as shown. Class 9
  65. Fig. 6.53 shows two circles passing through each other's centres. Find the area of the region Class 9
  66. In Fig. 6.54, we see three triangles within a rectangle. The areas of the triangles are A, B, C, as marked. Class 9
  67. In the figure we see two shaded regions formed by a quarter circle, a semicircle, and a triangle. Class 9

Chapter 7 The Mathematics of Maybe Introduction to Probability Class 9 Solutions

  1. Unpredictability can be useful sometimes! For example, in a cricket match, the fact that a coin is tossed Class 9
  2. Rank the following events on a scale from 0 (Impossible) to 1 (Certain). Label each event: Impossible Class 9
  3. A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. Class 9
  4. A survey is conducted at a school where a random sample of 40 students is asked about their favourite Club. Class 9
  5. Toss a coin 20 times and record the result each time (heads or tails). Class 9
  6. Toss a paper cup into the air 100 times. After each toss record whether the cup lands on its bottom Class 9
  7. What is the probability of getting an even number when rolling a fair 6-sided die? Class 9
  8. Suppose you roll a 6-sided die 12 times and get a '3' three times. Class 9
  9. When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space? Class 9
  10. In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks Class 9
  11. There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B Class 9
  12. Let us say that you have a box containing 3 red pens, 4 black pens and 2 green pens. Class 9
  13. Fill in the blanks. i. The probability of an impossible event is Class 9
  14. Which of the following experiments have equally likely outcomes? Explain. Class 9
  15. Write the sample space and calculate the probability based on the given information. Class 9
  16. A bag has 3 candies: strawberry, lemon, and mint. One is picked at random. What is the probability Class 9
  17. A child has 2 shirts (one red and one blue) and 3 types of pants (jeans, khakis, and shorts). Class 9
  18. A tyre company records distances before replacement in 1000 cases. Class 9
  19. The letters of the word 'PEACE' are placed on cards. Leela draws a card without looking. Class 9
  20. A game of chance consists of spinning an arrow (see Figure) which comes to rest pointing at one of the numbers Class 9
  21. A basket contains 4 red balls and 5 blue balls. One ball is drawn and laid aside, and a second ball is drawn. Class 9
  22. I throw a pair of 6-sided dice. Write down an event that has a probability of 0 and an outcome Class 9
  23. Write the sample space and calculate the probability based on the given information. Class 9
  24. A box contains 4 balls numbered 1 to 4. Record a sample space using a tree diagram for the following experiments: Class 9
  25. List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card Class 9
  26. Suppose you drop a dye at random on the rectangular region shown in the figure. Class 9

Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions Class 9 Solutions

  1. Can you describe the pattern in each of the above sequences? Can you predict the next few numbers Class 9
  2. Consider the sequence 1, 4, 7, 10, 13, ....... Can you predict the next four terms? Can you derive the first Class 9
  3. Can you write t5, t6 t7 and t8 for the sequence of triangular numbers? Class 9
  4. Why is it useful to have an explicit formula for the nth term of a sequence? Class 9
  5. Can you find the rule describing the nth term of the sequence of square numbers? Class 9
  6. Find the first five terms of the sequence in which the Mth term is given by Class 9
  7. Find the 10th and 15th terms of the sequence tn = 5n - 3 for n ≥ 1. Class 9
  8. Which term of the sequence tn = 5n - 3 for n ≥ 1 is 607? Class 9
  9. A sequence is given by the recursive rule t1 = - 5, tn+1 = tn + 3 for n ≥ 1.
  10. Let T1 = 1, T2 = 2, T3 = 4, and Tn = Tn-1 + Tn-2 + Tn-3 for n ≥ 4. Class 9
  11. Can you predict the number of squares in Stages 5 and 6 of the sequence ? In Stages 10, 11 and 12 Class 9
  12. Consider all the sequences we have discussed so far in this chapter. Which ones are arithmetic progressions Class 9
  13. Verify that the following sequences are arithmetic progressions and write their nth terms.
  14. Using the formula tn = a + (n -1) × d, find the nth term of the following arithmetic progressions. Class 9
  15. Find recursive rules for the APs in the previous exercises. Class 9
  16. Can you use this formula to find S20, S50 and S1000? Class 9
  17. Find the 10th and 26th terms of the AP: 3, 8, 13, 18, ...... Class 9
  18. Which term of the AP: 21, 18, 15, ... is - 81? Also, is 0 a term of this AP? Give reasons for your answer. Class 9
  19. Find the nth term of the AP: 11, 8, 5, 2 ... Write the recursive rule for this AP. Class 9
  20. An AP consists of 50 terms in which the 3rd term is 12 and the last term is 106. Find the 29th term. Class 9
  21. How many 2-digit numbers are divisible by 3? What is the sum of all these 2-digit numbers? Class 9
  22. Harish started work at an annual salary of ₹ 5,00,000 and received an increment of ₹ 20,000 each year. Class 9
  23. Can you predict the number of squares in Stages 5 and 6 of the pattern? In Stages 10,11 and 12? Class 9
  24. Check whether the following sequences are geometric progressions and find their nth terms, Class 9
  25. Can you find a recursive rule for the formula tn = 3 × 10n-1 that generates the geometric progression Class 9
  26. Observe the Sierpiriski triangle and try to answer the following questions a. How many black triangles Class 9
  27. Find the 12th term of a GP with common ratio 2, whose 8th term is 192. Class 9
  28. A sequence is given by the recursive rule t1 = 2, tn+1 = 3tn-2 for n ≥ 1. Which term of the sequence Class 9
  29. A ball is dropped from a height of 80 metres. After hitting the ground, it bounces back to 60% of the height Class 9
  30. Which term of the sequence 2, 2√2, 4,... is 128? Class 9
  31. The given figure shows Stages 0 to 3 of the Sierpinski square carpet. Stage 0 of this fractal Class 9
  32. Find the 31st term of an AP whose 11th term is 38 and 16th term is 73. Class 9
  33. Determine the AP whose third term is 16 and whose 7th term exceeds the 5th term by 12. Class 9
  34. How many three-digit numbers are divisible by 7? Class 9
  35. How many multiples of 4 lie between 10 and 250? Class 9
  36. Find a GP for which the sum of the first two terms is - 4 and the fifth term is 4 times the third term. Class 9
  37. Find all possible ways of expressing 100 as the sum of consecutive natural numbers. Class 9
  38. The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria Class 9
  39. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms Class 9
  40. Find the smallest value of n such that the sum of the first n natural numbers is greater than 1,000. Class 9
  41. Which term of the GP: 2, 8, 32, ... is 131072? Write the explicit formula as well as the recursive formula Class 9
  42. The sum of the first three terms of a GP 13/12 is and their product is - 1. Find the common ratio Class 9
  43. If the 4th, 10th and 16th terms of a GP are x, y and z respectively prove that x, y, z are in GP. Class 9
  44. The sum of the first three terms of a geometric progression is 26, and the sum of their squares is 364. Class 9
  45. Suppose P1 = 1, P2 = 2 and for n > 2, Pn = P1 + P2 + ... + Pn-1 + 1. Find the values of P1, P2, ..., P8. Class 9
  46. Suppose W1 = 1, W2 = 2 and for n > 2, Wn = W1 + W2 + ... + Wn-2 + 2. Find the values of W1, W2,..., W8. Class 9