Abhilasha Classes Sample Papers (2017-18) Class: IX By: P.S. Kushwah (M.Sc.; B.Ed)
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Abhilasha Classes M. M 80 Sample paper: -1 st Time- 3 h Section A (1 Mark each) 1. If x ab = 1, then find the value of a. 2. If p(x) = 2x 3 + 5x 2 3x - 2 is divided by x - 1, then find the remainder. 3. The distance of the point (0, -1) from the origin is. 4. If the vertical angle of an isosceles triangle is 100 0, then find the measures of its base angles. 5. The ratio of the whole surface area of a solid sphere and a solid hemisphere is. 6. There are 60 boys and 40 girls in a class. A student is selected at random. Find the probability that student is a girl. Section B (2 Marks each) 7. If p = 2 - a, then prove that a 3 + 6 ap + p 3 8 = 0. 8. In the adjoining figure 8, we have AB = BC, BX = BY. Show that AX = CY (Using appropriate Euclid s axiom) 9. If two opposite angles of a parallelogram are (63-3x) and (4x - 7). Find all the angles of the parallelogram. 10. Three Schools situated at P, Q and R in the figure are equidistant from each other as shown in the figure 10. Find QOR. 11. The diameter of the two right circular cones are equal if their slant heights are in the ratio 3 : 2, then what is the ratio of their curved surface areas? 12. A batsman in his 11 th innings makes a score of 68 runs and there by increases his average score by 2. What is his average score after the 11 th innings? Section C (3 Marks each) 13. Represent 10 on the number line. 14. Simplify: 73 73 73 + 27 27 27 73 73 73 27 + 27 27. 15. Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1 1 times its abscissa. 2 16. Locate the points (3, 0), (-2, 3), (2, -3), (-5, 4) and (-2, -4) in Cartesian plane. Also find the quadrant in which they lie. OR Observe the figure. 16, given below and answer the following: (i) The coordinates of B. (ii) The coordinates of C. (iii) The point identified by the coordinate (-3, -5). (iv) The abscissa of the point D. (v) The coordinates of H. (vi) The coordinates of origin 17. In figure 17, AC = AE, AB = AD and BAD = EAC. Show that BC = DE. OR AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that BAD = ABE and EPA = DPB. Show that (i) DAP EBP (ii) AD = BE 18. Show that the area of a rhombus is half the product of the lengths of its diagonals. 19. A, B, C and D are the four points on a circle. AC and BD intersect at point E such that BEC = 130 and ECD = 20. Find BAC. (Fig. 19) OR
Prove that equal chords of a circle subtend equal angles at the centre. 20. Sides of a triangle are in the ratio 12 : 17: 25 and its perimeter is 540 cm. Find its area. 21. The diameter of a garden roller is 14 m and it is 2 m long. How much area will it cover in 10 revolutions? OR The sum of height and radius of the base of a solid cylinder is 37cm. If the total surface area of the cylinder is 1628 cm 2, then find its volume. 22. Fifty seeds were selected at random from each 5 bags seeds and were kept under standardized conditions favorable to germination. After days, the number of seeds which had germinated in each collection were counted and recorded as follows: Bag 1 2 3 4 5 Number of seeds generated 40 48 42 39 38 What is the probability of germination of (i) More than 40 seeds in a bag (ii) 49 seeds in a bag (iii) More than 35 seeds in a bag Section D (4 Marks each) 23. If x = 6 32 2, then find the value of (x 3 + 1 x 3) - 6(x2 + 1 x 2) + (x + 1 ). OR x If x = 3+ 1 3 1, y = 3 1 3+1, find the value of x2 + xy y 2. 24. Determine the value of b for which the polynomial 5x 3 x 2 + 4x + b is divisible by 1-5x. 25. Draw the graph of two lines whose equations are x + y -6 =0 and x y -2 =0, on the same graph paper. Find the area of triangle formed by the two lines and y axis. OR The force exerted to pull a cart is directly proportional to the acceleration produced in the cart. Express the statement as a linear equation in two variables and draw the graph for the same by taking the constant mass equal to 6 kg. 26. In figure 26, the sides AB and AC of are produced to points E and D respectively. If bisectors BO and CO of CBE and BCD respectively meet at point O, then prove that BOC = 90 - - 1 2 BAC. 27. In the adjoining figure 27, P is the point in the interior of a parallelogram ABCD. Show that ar( APB) + ar( PCD) = ar ( gm ABCD). 28. Construct a right angled triangle whose base is 5 cm and sum of its hypotenuse and other side is 8 cm. 29. The floor of a rectangular hall has a perimeter 300cm. Let the cost of painting of four walls at the rate of Rs.12 per cm 2 is Rs. 24,000, then find the height of the hall. 30. The marks obtained (out of 100) by a class of 80 students are given below: Marks 10 20 20 30 30 50 50 70 70 100 No. of Student 6 17 15 16 26 Construct a histogram to represent the data above. Construct a frequency polygon for the following data: Age (in years) 0-2 2-4 4-6 6-8 8-10 Frequency 4 7 12 5 2 OR 1. a = 0 2. 2 3. 1 4. 40, 40 5. 4 : 3 6. 2 5 7. 0 8. 9. 33, 147. 10. Answers: 11. 3 : 2. 12. 48. 13. a 14. 100. 15. (2, 3) 16. 17. 18. 19. 110 20. 9000 cm 2 21. 88 m 2 OR 4620 cm 3 22. 0.4, 0, 1. 23. 0 Or 8 3 + 1. 24. b = 4 5
25. 16 sq units. 26. 27. 28. 29. 6.67 cm 2 Abhilasha Classes M. M 80 Sample paper: -2 nd Time- 3 h Section-A (1 Mark each) 1. Find the value of (64) 1 2 (125) 1 3. 2. If p(x) = x 3 3x 2 + 2x, then find the value of p (1). 3. Points A (8, 4) & B (-2, 4) lie on a line. AB is parallel to which axis. 4. If the graph of equation 2x + ky = 10k, intersect x-axis at point (5, 0). Find value of k. 5. Find the value of x from the adjacent figure 5. 6. Find the ratio of total surface area of a sphere and a solid hemisphere of same radius. Section-B (2 Marks each) 7. Factorise: 8a 3 + 27b 3. 8. Find the coordinates of the point where the graph of the equation 5x + 2y = 10 intersect both axes. 9. The sides of a triangle are 22 cm, 20 cm and 18 cm. Find its area. 10. The two consecutive class marks of a distribution are 52 & 57. Find the class limits. 11. A die is rolled 200 times & its outcomes are released as below: Out comes 1 2 3 4 5 6 Frequency 25 35 40 28 42 30 Find the probability of getting: (i) A multiple of 3. (ii) not a prime number. 12. Consider the following frequency distribution which gives the weights of 38 students of a class: Weights (kg) 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 Total No. of Students 9 5 14 3 1 2 2 2 38 (i) Find the probability that the weight of a student in the class lies between 36-45 kg. (ii) Give one event in this context having probability zero. Section C (3 Marks each) 13. If x = 5 2 6, find x 2 + 1 x 2. 14. Simplify: ( Xa X b)a b ( X b X c) b c ( Xc X a)c a. 15. Plot the points A (1, 1), B (-1, 5), C (7, 9) and D (9, 5). Name the type of figure ABCD. In which quadrant the point of intersection of diagonals lie? 16. In the given figure 16, Show that XY EF. 17. In the given figure 17, if AB = AC, BAD = CAE then prove that ADE is an isosceles triangle. 18. P, Q & R are respectively, the mid points of sides BC, CA & AB of a triangle ABC. PR & BQ meet at X. CR & PQ meet at Y. Prove that XY = 1 BC. (figure 18) 4 19. In the given figure 19, O is the centre of a circle. Prove that x + y = z. 20. Construct such that BC = 8cm, B = 45, AB AC = 3.5 cm. 21. If h, c and v respectively, are the height, the curved surface area and volume of a cone, prove that 3πvh 3 - c 2 h 2 + 9v 2 = 0. 22. The radius of a sphere is 10 cm. If the radius is increased by 1 cm. Then prove that volume of the sphere is increased by 33.1%. Section-D (4 Marks each)
23. Express 0.6 + 0.47 + 0.7 in the form p, where p and q are integers and q 0. q 24. Verify: a 3 + b 3 + c 3 3abc = 1 2 (a + b + c)[(a b)2 + (b c) 2 + (c a) 2 ]. 25. A pharmacist needs to strengthen a 15% alcohol solution to one of 32% alcohol. How much pure alcohol should be added to 800 m of 15% Solution? 26. In the figure two straight lines PQ & RS intersect each other at O. If POT = 75, find the values of a, b & c. 27. In the given figure, if AD = BD = CD. Prove that BAC is right angle. 28. In a parallelogram ABCD, E & F are the mid Points sides AB & CD respectively. Show that the line segment AF & EC trisect the diagonal BD. (Figure 28) 29. The residential colony has population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, a group of people decided for WATER HARVESTING. They constructed a water reservoir measuring 49m 27m 25m to collect the rain water. If this water reservoirs is full of water then for how many days it will last for the colony. 30. The Following table shows the life of LED bulbs. Life Time (in hours 300-400 400-500 500-600 600-700 700-800 800-900 900-1000 No. of Bulbs 14 56 60 86 74 62 48 (i) Represent the above information with the help of a histogram & frequency polygon. (ii) How many bulbs have a lifetime of 700 hours & more? ANSWERS 1. 40 2. 0 3. x-axis 4. K = 1 5. x = 18 6. 4 : 3 7. (2a + 3b)(4a 2 2 3ab + 3b 2 ) 8. A(2,0), B(0.5) 9. 120 2cm 2. 10. 52 = 49.5 54.5, 57= 54.5 59.5 11. 7 13. 98 20 200 38 14. 1 15. Plot the points on graph. Intersecting point of diagonals is in I-quadrant ABCD is a rectangle. 16. 17. 22. 33.1%. 23. 167 90 24. 25. 200 ml 26. 48. 27. 28. 29. 30. 184 Bulbs. 18. 19. 20. 21.
Abhilasha Classes M. M 80 Sample paper: - 3 rd Time- 3 h Section - A 1. Evaluate: (25) 1/3 (5) 1/3. Ans: 5 2. Find the total surface area of a cone whose radius is 2r and slant height is l/r. Ans: πr(l + 4r) 3. Find the radius of largest sphere that is curved out of the cube of side 8 cm. Ans: 4 4. An angle is 14 more than its complement. Find its measure. Ans: 52 5. Calculate the mean of first five multiples of 3. Ans : 9 6. If P(E)= 0.25 what is the value of P(not E). Ans:.75 Section - B 7. A, B and C are three points on a circle with centre O such that BOC = 30 and AOB = 60. If D is another point on the circle other than the arc ABC, find ADC. Ans: 45 0 8. For the following distribution, find the value of a and the frequencies of 30 and 70, if the mean of the distribution is 50. Ans: 5, 28, 24 x 10 90 30 70 50 f 17 19 5a + 3 7a 11 32 9. Some wooden crates, each measuring 1.5 m x 1.25 m x 0.5 m, have to be stored in a godown that measures 40 m x 25 m x 10 m. Find the maximum number of wooden that can be stored in the godown. Ans: 12800 10. Prove that equal chords of a circle subtends equal angles at the centre. 11. Prove that a diagonal of a parallelogram divide it into two congruent triangles. 12. In figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that: ROS = 1 ( QOS POS). 2 Section - C 13. Convert the given frequency distribution into a continuous grouped frequency distribution. Class intervals 150-153 154-157 158-161 162-165 166-169 170-173 Frequency 7 7 15 10 5 6 In which intervals would 153.5 and 157.5 be included? 14. The diagonals AC and BD of parallelogram ABCD intersect at the point O. If DAC = 34 and AOB = 75, then what is the measure of DBC? Ans: 41 0 15. Express 2.4178 in the form p/q. Ans: 12O77 4995 16. Factorise: (9x 1 5 )2 + (x + 1 3 )2 Ans: ( 120x 8 ) ( 150x 2 ) 17. If a, b, c are all non-zero and a + b + c = 0, prove that a2 bc + b2 ca + c2 ab = 3 18. A triangle ABC is right-angled at A. AL is drawn perpendicular to BC. Prove that BAL= ACB. 15 15
19. If x = 2 + 3then find the value of x 2 + 1 x2. Ans: 14 20. The volume of a rectangular block of stone is 10368 dm 3 and its dimensions are in the ratio of 3:2:1. (i) Find the dimensions (ii) Find the cost of polishing this rectangular block s entire surface at Rs. 2 per dm 2. 21. Construct a triangle ABC in which BC = 7cm, B = 75 and AB + AC = 9cm. Ans: 3168 dm 2,, 3168 Rs. 22. In the given figure, BC and CO are bisectors of DBC and ECB respectively. If BAC = 70 o and ABC = 40 o, find the measure of BOC. Ans: 55 0 Section - D 23. The diagonals of a quadrilateral ABCD are perpendicular to each other. Show that the quadrilateral formed by joining the mid-points of its sides is a rectangle 24. Without actual division, prove that (2x 4 6x 3 + 3x 2 + 3x 2) is exactly divisible by (x 2 3x +2). 25. AC and BD are chords of a circle that bisect each other. Prove that AC and BD are diameters and ABCD is a rectangle. 26. Three girls (Anita, Payal and Riya) are sitting at equal distance on the boundary of a circular bed of radius 2 m. Each of the three girls is having a toy telephone in their hands to talk to each other. Find the length of the string of each telephone. Ans: 2 3 27. Water in a canal, 30 dm wide and 12 dm deep is flowing with a velocity of 20 km per hour. How much area will it irrigate in 30 min, if 9 cm of standing water is desired? ( 10 dm = 1m) Ans: 0.4km 2 28. Factorise : 1 27 (2x + 5y)3 + ( 5 3 y + 3 4 z)3 - ( 3 4 z + 2 3 x)3 Ans: 1 144 (2x + 5y)( 20y + 9 z)(9z + 8y)
Abhilasha Classes M. M 80 Class IX Sample paper: -4 th Time- 3 h Section-A (1 Mark each) 1. If x 2 + kx + 6 = (x + 2)(x + 3) for all value of x then find value of K. 2. Write the zero of zero polynomial. 3. Write the distance of point (0, -3) from origin. 4. The parking charges of a car at Delhi Railway station is Rs.50 for first 3 hours and Rs.10 for subsequent hours. If for x hours parking charge is `y, then write a linear equation in two variables, which represent this information. 5. The radius and the lateral surface area of right circular cone are 8 cm and 220 cm 2 respectively. Find its slant height. 6. In figure 6, ABCD is a cyclic quadrilateral such that BAD = 63. Find value of x Section -B (2 Marks each) 7. Rationalise the denominator of 6 4 2 6+4 2. 8. Two lines AB and CD are intersected by a transversal l in the figure. Find the value of x and then show that the lines are not parallel. 9. Consider two postulates given below: (i) Given any two distinct points R and S, there exists a third point T which is in between R and S. (ii) There exist at least three points which are not in the same straight line and answer the following questions : (a) Do these postulates contain any undefined terms? (b) Do they follow from Euclid s postulates? Explain. (b) Both postulate are consistent as they do not oppose each other and refer to two different situation. These postulates do not follow from Euclid s postulates. They follow from the axiom, Given two distinct points, there is a unique line that passes through them. 10. An isosceles triangular field s perimeter is 250 m and each equal side is 100 m. Find the area of the field. (Use 15 = 3.87) 11. Plot the point (- 5, 1) and from it draw PM and PN perpendicular to x-axis and y-axis respectively. Write the co-ordinates of M and N. 12. A die is thrown 50 times and it showed the number of 1, 23 times. Find the probability of getting a number other than 1 in the next throw of the die. Section - C (3 Marks each) 13. The auto fare in a city are as follows: For the first kilometer it is Rs. 10 and for subsequent distance is Rs. 8 per km. Taking the distance as y km. and total fare as Rs. x, write a linear equation for this and draw the graph. Also find the fare of 15 km. 14. In 3x + 2y = 12, express y in terms of x. Find three solutions for this equation. Also find a point where it cuts the x-axis. 15. Draw a line segment QR = 5 cm. Construct perpendiculars at point Q and R respectively. Name them as QX and RY. Are they both parallel? 16. DEFG is a quadrilateral such that diagonal DF divides it into two parts of equal areas.
Prove that the diagonal DF bisects GE. (Fig. 16) 17. Along a path, 100 conical pillars are constructed. Each pillar has base radius 14 cm and height 18 cm. Find the total cost of painting these pillars at the rate of `120 per m 2. 18. Two coins are tossed simultaneously for 360 times. The number of times 2 Tails appeared was three times No. Tail appeared and number of times 1 tail appeared is double the number of times No Tail appeared. Find the probability of getting Two tails. 19. Find the values of a and b if 3 1 3+1 = a + b 3. 20. Factories: x 2 + 3 3 x + 6. 21. If x 2 + y 2 = 58 and x y = 10, then find the value of x 3 - y 3. 22. A quadrilateral park ABCD has C = 90, AB = 13 m, BC = 12 m, CD = 9 m and AD = 14 m. Find its area. OR The shape of cross-section of a canal is a trapezium. If the canal is 10 m wide at the top and 6 m wide at the bottom and the area of the cross-section is 72 m 2, find its depth. Section D (4 Marks each) 23. Simplify: 2 6 + 6 2-8 3. 2+ 3 6 + 3 6 + 2 24. If (x + 1) and (x + 2) are the factors of x 3 + 3x 2 3αx+ β, then find α and β. OR If (x 2-1) is a factor of ax 4 + bx 3 + cx 2 + d x + e, show that a + c + e = b + d = 0. 25. If z 2 + 1 z 2 = 14, find the value of if z3 + 1 z 3 taking only positive value of z + 1 z. 26. The following table shows the life of 400 neon lamps: Life time (in hrs) 300-400 400-500 500-600 600-700 700-800 800-900 900-1000 No. of Lambs 14 56 60 86 74 62 48 represent the following in histrogram. 27. Show that in aright triangle if one of the acute angle is double the other than prove that hypotenuse is double the shortest side. 28. Prove that sum of the two sides of triangle is greater than third. OR S is any point interior of triangle PQR, prove that PQ + PR > QS + RS. 29. In the figure 29, P, Q and R are the mid-points of sides BC, AC and AB of ABC. If BQ and PR intersect at X and CR and PQ intersect at Y, then show that XY = ¼ BC. 30. Construct ABC if AB = 2.1 cm, A = 110 and BC CA = 0.9 cm. OR Give reasons : (a) Construction of an angle of 22.50 is possible with the help of ruler and compass. (b) It is not possible to construct a ABC, given that BC = 7 cm, B = 45 and AB AC= 10 cm. (c) We can construct an angle of 67.5 using ruler and compass. (d) Construction of DEF, if EF = 5.5 cm, E = 75 and DE DF = 2 cm is possible.
Abhilasha Classes M. M 80 Class IX Sample paper: - 5 th Time- 3 h Section-A (1 Mark each) 1. Find the value of (625) 0.18 (625) 0.07. 2. Find the remainder when x 3 + 2x 2-3x 1 is divided by x + 1. 3. Write the coordinates of a point P where perpendicular distance from x-axis is 2 units and perpendicular distance from y-axis is 3 units P lies in III quadrant. 4. If AB CD EF and y : z = 3 : 7 then what will be the value of x? (Fig. 4) 5. If the radius & length of a cone are r & 2l respectively, what is its total surfa6ce area? 2 6. The probability of guessing the correct answer to certain question is x. If the probability of not guessing the 2 correct answer to the question is 2, then what is the value of x. 3 SECTION B (2 Marks each) 7. Find if (-2x -5) is a factor of the polynomial p(x) = 3x 4 + 5x 3 2x 2 4 or not. 8. In the adjacent figure 8, if x : y = 11 : 19 AD BE. Find DCE. 9. In the given figure 9, B < A and C < D. Show that AD < BC. 10. Show that opposite angles of parallelogram are equal. 11. Find area of a triangle whose two sides are 8cm & 11cm and its semi perimeter is 16cm. 12. The mean of first 8 observations is 18 & the mean of last 8 observations is 20. If mean of all 15 observations is 19. Find 8 th observation. SECTION C (3 Marks each) 13. Evaluate 13 + 4 10 7 2 10. 3+ 2 14. Find the values of a & b if = a + b 2. 3 2 15. Find the value of a if (1, -1) is the solution of the Equation 2x + ay = 5. Find the other two solutions of the Equation. 16. AD is a median of ABC and E is the midpoint of AD, BE, Produced meets AC in F. Prove that AF = 1 3 AC. 17. In the figure 17, L, M and N are mid-point of the side PQ, PR and QR respectively of PQR. If PQ = 4.4cm, QR = 5.6 cm and PR = 4.8 cm. Then find the perimeter of LMN. 18. Construct a STU, in which T = 150, TU = 3 cm & ST + US = 8cm. 19. 1.1 cm 3 of gold is drawn into the wire of 0.1 mm in diameter. Find the length of the wire in meter. 20. From the graph, write the co-ordinates of the points A, B, C, D & E. Is a ABCD, a rectangle on joining the points. If yes, write the name of the point where the diagonals meet. 21. The volume of a sphere is 4851 cm 3. How much should its radius be reduced so that its volume become 4312 cm 3? 22. 14 packets of Sugar, each marked 5kg, actually contained the following weights in Kg. 5.095, 4.995, 4.800, 5.120, 4.890. 5.000, 5.150, 5.000, 5.995, 5.995, 5.000, 4.900, 4.995, 5.000, 5.050. Find the probability of the following when a packet is chosen and it. (i) Contains more than 5 kg. Sugar. (ii) Contains correct weight. (iii) Contains weight less than 4.995 Kg. 3
1 1 + 1 1 + 1 3 8 8 7 7 6 6 5 Section D (4 Marks each) 23. Prove that = 5. 5 2 24. Without actually calculating the cubes, Find the value of ( 1) 3 + ( 2) 3 + ( 3) 3 + ( 4) 3 + 2(5 3 ). Write the identity used. 25. A man went to the Bank with Rs. 1000. He asked the cashier to give him Rs. 5 and 10 notes only in return. Write the linear equation in two variables. If number of 10 notes are 25, then find the number of 5 notes? Also represent it graphically? 26. In the adjacent figure 26. AB CD, DE FG. Find (i) PDE (ii) AFD (iii) DFG 27. In the figure 27, X and Y are the points on equal sides AB and AC of a ABC such that AX = AY. Prove that XC = YB. 28. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ABC is equal to half the difference of an angle subtended by the Chord AC and DE at the Centre. ABC = 1 [ DOE - AOC] 2 29. A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their height are the same with the same base. Find the ratio of their volumes. 30. Mean of a class of 35 students in a Mathematics class test was found to be 15. A chance was given to improve marks of those students who score less than 8 marks. Three students score 3, 5 & 6 marks respectively. A remedial class was taken by the teacher & then test was taken again. The three students score 7, 10, 12 marks respectively in improvement test. What will he the new mean of the class? What values of the teacher are depicted here? 1. 5 2. 3 3. ( 3, 2) 4. 126 5. πr(l + r 4 ) 6. 2 3 7. 361 16 8. 65 9. 10. 20. A(2,2),B(-1, -1),D(4, 0),C(3,3),E(1,1)Yes,E. 21. 23. a 22. 6, 4, 3. 24. 150 15 15 15 25. 150 29. V 1 : V 2 : V 3 : 42 33 11. 30. 15.7 ANSWERS 11. 8 30sq. cm 12. 19 13. 3 2 14. 11 7, 6 7 15. a = -3 26. 55, 55, 55 27. 28.. 16. a 17. 7.4 cm 18. 19. 140 m
Abhilasha Classes M. M 80 Class IX Sample paper: - 6 th Time- 3 h SECTION-A (1 Mark each) 1. Find two irrational numbers between 2017 and 2018. 2. Find the co-efficient of a 2 in (a - 1) (a 2 + 1). 3. If abscissa of a point is zero, on which axis do the point lies. 4. In the figure 4, for what value of x is l 1 l 2? 5. The diagonal of cube is 12 cm. What is length of its edge? 6. A & B are the only two outcomes of an event. Probability of P (A) = 0.72, then what will be the probability P(B). SECTION-B (2 Marks each) 7. Give possible expression for the length and the breadth of the rectangle, whose area is 6x 2 + x - 12. 8. If AB DE, BAC = 35 & CDE = 53, find DCE & DEC. (Fig. 8) 9. In the given figure 9, B < A and C < D. Show that AD < BC. 10. If two adjacent angles of a parallelogram PQRS are (10y - 9) & (8y - 45 ), Find all the four angles of parallelogram. 11. The longest side of a right angled triangle is 125 m and one of the remaining two sided is 100 m. Find its area using Heron's formula. 12. The numbers 2, 3, 4, 4, 3x - 1, 3x + 1, 7, 7, 8 are written in ascending order. If the median is 5, find x. SECTION - C (3 Marks each) 3+ 2 13. Find the values of a and b, if = a + b 2. 3 2 14. Factorise: (2x y - z) 3 + (2y z - x) 3 +(2z x y) 3. 15. Find three different solutions of 3m - 8n = 27. 16. Plot two points P(0, -4) & Q(0, 4) on the graph paper. Now plot R & S such that PQR & PQS are isosceles triangles. 17. ABCD is a rhombus with one diagonal equal to 18cm. & length of each side equal to 15 cm. Find the length of the other diagonal and area of rhombus. (Fig. 17) 18. In the figure 18, AP and BP are the bisectors of two adjacent angles A and B of quadrilateral ABCD. Prove that 2 APB = C + D. 19. Construct a triangle whose perimeter is 15cm and its two base angles are 90 and 30. 20. A Conical tent is 16m high and the diameter of its base is 24m. Find the cost of Canvas required to make the tent, if cost of 1m 2 Canvas is Rs.210. 21. A Hemispherical tank full of water is to he emptied by a pipe at the rate of 3 liters per minutes. How long will its take to empty the tank, if the diameter of the tank is 1 3 4 m? 22. The marks of 80 students (out of 80) in English speaking skills was recorded as follows: Marks 0 20 21 39 40 60 61 80 No. of Students 18 19 23 20 If the passing marks are 50% then find the probability that the student chosen at random: (i) Got the passing mark. (ii) Failed to get the passing marks. (iii) Got below 21 marks.
SECTION - D (4 Marks each) 23. Represent (1+ 9.5) on the number line. 24. x + 2 is a factor of polynomial ax 3 + bx 2 + x - 2 and the remainder 4 is obtained by dividing this polynomial by x - 2. Find the value of a and b. 25. Solve for x: 3x+2 7 + 4(x+1) 5 = 2 (2x + 1). 3 26. If two parallel lines are intersected by a transversal prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles. 27. In a square PQRS, diagonals PR and QS intersect at O. Show that POQ QOR ROS SOP. 28. In the given figure 28, O is the centre of the circle of radius 5 cm, OP CD, AB CD, AB = 6 cm and CD = 8cm, Determine PQ. 29. A right triangle having sides 6cm, 8cm and 10m is revolved about the side of length 6cm. Find the volume of solid so formed. 30. If the 26 English alphabets are taken such that A = 1, B = 2, C = 3, Z = 26 then find (i) The mean & median of the numbers corresponding to the vowels. (ii) Which alphabet corresponds to the median? ANSWERS 1. 2017.01010001, 2017.020020002. (other answers are also possible) 2. -1 3. y-axis 4. 47 5. 2 cm 6. 0.28 7. (2x + 3,(3x 4) 8. DCE = 90, DEC = 35 14. 3(2x y z)(2y z x)(2z x y) 15. Any 3 correct solutions 16. AC = 24 cm, Area = 216 cm 2 17. AC = 24 cm, Area = 216 cm 2 18. 19. 20. 158400 21. 7.8 hours (approx) 22. (i) 43 80 (ii) 37 80 (iii) 18 80 9. 10. 71, 119, 71, 119. 11. 3750 m 2 12. 2 23. 24. a = 0, b = 2 25. x = 4. 26. 27. 28. 1 cm 13. a = 11 7, b = 6 7. 29. 128 π cm 3 30. (i) Mean = 9.8, Median = 9 (ii) I