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ICSE Class X Board Exam 2024 : Mathematics

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ST. JOSEPH S COLLEGE, PRAYAGRAJ MATHEMATICS CLASS: X Maximum Marks: 80 Time allowed: Two and a half hours Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. _______________________________________________________________________ Attempt all questions from Section A and any four questions from Section B All working, including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ] Mathematical tables are provided. SECTION A (Attempt all questions from this Section) Question 1. Choose the correct answers to the questions from the given options. [15] (Do not copy the questions, write the correct answer only) 7 i. If A = [5 2] and B = [ ], which of the following operation is/are possible 11 1. A B 2. A + B 3. AB 4. BA a. Only 3 b. Both 1 and 2 c. Only 4 d. Both 3 and 4 e. None of these 2 ii. If + 28 = ( 7)( + 4) for all values of , then the value of is a. 11 b, 3 c. 3 d. 11 e. None of these iii. A retailer purchased an item for 2500 from a wholesaler and sells it to a customer at 12% profit. The sales are intrastate and the rate of GST is 18%. The amount of tax paid by the customer to the central government is a. 252.00 b. 504.00 c. 27.00 d. 54.00 e. None of these iv. If the roots of the quadratic equation 2 + 12 = 0 are real and different, then the values of are a. > 36 b. > 36 c. < 36 d. < 36 e. None of these v. Which of the following is/are an Arithmetic Progression (A.P.)? 1. 8, 1, 6, 13, .. 2. 5, 5, 5, 5, . 3. 3, 12, 27, 48, a. Only 1 b. Only 1 and 2 c. Only 2 d. All 1, 2 and 3 e. None of these vi. The table shows the values of & , where is proportional to M 12 4 9 18 N MTHS_CLS_X_PREBOARD1_PG1/8 What are the values of M and N? a. M = 6 and N = 9 b. M = 9 and N = 6 d. M = 6 and N = 6 vii. c. M = 9 and N = 9 e. None of these In the given figure, ABC ~ PQR and = 5 . The ratio of 11 Perimeter( ):Perimeter( ) is a. 11 : 5 b. 5 : 6 c. 5 : 11 d. 6 : 11 e. None of these viii. A cylindrical vessel of diameter 4cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8cm. The diameter of each ball is a. 0.8cm b. 0.4cm c. 0.5cm d. 0.2cm e. None of these ix. Choose the equation whose graph is shown in the given figure a. + 2 = 0 b. 2 = 0 d. 2 3 + 6 = 0 e. None of these x. c. 2 + 3 6 = 0 Two chords AB and CD of a circle cut each other when produced outside the circle at P. AD and BC are joined. If = 30 and = 45 , then find a. 105 b. 115 c. 125 d. 135 e. None of these xi. An electrician has to repair an electric fault on a pole of height 5m. He has to reach a point 1.3m below the top of the pole to undertake the repair work. How far from the foot of the pole should he place the foot of the ladder? (Take 3 = 1.732) MTHS_CLS_X_PREBOARD1_PG2/8 a. xii. 1. 2. 3. a. xiii. 3.14m b. 2.14m c. 2.26m d. 3.16m Which of the following is a better investment? 10% 50 shares quoted at 80 5% 100 shares at a discount of 20 15% 30 shares at par Only 1 b. Only 2 c. Only 3 d. Both 1 and 2 e. None of these A ( 3, 4), B ( 3, 2) and C (1, 2) are the vertices of a right angled triangle. Find the coordinates of its orthocentre. a. ( 3, 4) b. ( 3, 2) c. (1, 2) d. ( 1, 1) e. None of these xiv. A point A ( , ) is invariant when reflected about a line = , the coordinates of the reflected point is a. ( , ) b. ( , ) c. ( , ) d. ( , ) e. None of these xv. For the given 49 variables 1 , 2 , 3 , . . 49 Assertion (A) : To find median of the given data, the variable needs to be arranged in ascending or descending order Reason (R) : The median is the central most term of the arranged data a. A is true, R is false b. A is false, R is true c. Both A and R are true d. Both A and R are false. Question 2. i. The adjoining figure shows a model of a toy, which has a hemispherical base surmounted by a cylinder and a cone. If the height of the cylindrical part is 7cm, and the total height of the toy is 14cm. Find [4] a. Volume of the toy to the nearest 3 MTHS_CLS_X_PREBOARD1_PG3/8 b. Surface area of the toy. c. If the scale factor is 1 : 20, find the volume of the toy in 3 . [Take = 3.1] ii. In a recurring deposit account for 2 years, the total amount deposited by Arsh is 14400. If the interest earned is three-eighth of his total deposit. Find [4] a. The interest he earns b. His monthly deposit c. The rate of interest iii. Find: [4] a. b. 1 1+cos 1+cos 1 cos c. Using the above results prove the following trigonometric identity 1 cos 1+cos + 1+cos 1 cos = 2 Question 3. i. If is the mean proportion between and , prove that [4] 2 2 2 ( 4 + 4 + 4 ) = 2 ( 4 + 4 + 4 ) ii. The adjoining figure shows a circle circumscribing a pentagon in which AB = BC = CD and = 132 . Calculate the value of [4] Use graph paper for this question. Take 2 cm = 1 unit on both axes [5] Plot the points A( 3, 0), B(1, 3), C(1,1), D(3, 1), E(3, 3) and F(7, 0) Reflect the points B, C, D and E about the x-axis and name them as , , respectively. c. From the above points (A to F) name the invariant point(s) after reflection about xaxis. d. Give the geometrical name of the closed figure by joining the points in order. e. Name a line of symmetry. a. b. c. d. iii. a. b. MTHS_CLS_X_PREBOARD1_PG4/8 SECTION B (Attempt any four questions from this section) Question 4. i. ii. iii. 3 4 4 For two matrices A and B, 2A + B = [ ] and A 2B = [ 2 7 1 3 ], find AB. 1 [3] 2 Solve the given equation 2 9 6 = 0 and express your answer correct to one place of decimal. (You may use mathematical tables for this question) [3] In the given figure ABCD is a parallelogram, E is a point on AB, CE intersects the diagonal BD at O and EF || BC. If AE : EB = 2 : 3, find [4] a. EF : AD b. ar( ): ( . ) c. Prove that: ~ d. ar( ): ( ) Question 5. i. Use step-deviation methos to find the mean of monthly wages of the following distribution. [3] Monthly Wages 90 110 (in 1000) Number of Men 4 ii. 130 150 150 170 170 190 6 4 8 18 DTDC has three types of courier service for its premium clients. An industrial house has given following orders. Find the amount of the bill. [3] Types of Services Number of Services Cost of each service (in ) Discount (%) GST iii. 110 130 Plus 45 Gold 18 Platinum 16 150 200 300 Net 12% 10% 18% 20% 28% In the given figure ABCD is a cyclic quadrilateral, = 135 . Sides BA and CD are produced to meet at P, sides AD and BC are produced to meet at Q, if = 2 1, find: [4] MTHS_CLS_X_PREBOARD1_PG5/8 a. b. c. Question 6. i. Find the geometric progression whose 5th term is 48 and 8th term is 384. [3] ii. The following table shows the expenditure of 60 boys on books [3] Expenditure (in ) 20 25 25 30 30 35 35 40 40 45 45 50 No. of Students 14 7 12 6 3 18 Use graph sheet for this question. Take 2 cm = 5 on one axis and 2cm = 2 students on another axis. a. Draw a histogram representing the above distribution b. Find the mode of their expenditure. iii. Two spheres of radii 3cm and 5cm are kept one on the other and then covered by a cone as shown in the figure. Find the height of the cone. [4] MTHS_CLS_X_PREBOARD1_PG6/8 Question 7. i. From the figure, find the equations of [5] a. b. c. ii. Altitude AD Median BM Line AX. The angle of depression of two cars A and B on the opposite side of a skyscraper of height 100m are respectively 42 and 54 . The line joining the two cars passes through the floor of the skyscraper. Find the distance between the two cars A and B, give your answer correct to the nearest whole number. [5] Question 8. i. Solve the following inequation, write the solution set and represent it on the real number line. [3] 2 +1 2 2 3 > 3 5 A man has some shares of 100 at par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% 50 shares at a premium of 10. This transaction decreases his annual income from dividend by 120. Find [3] a. The number of shares before transaction b. The number of shares he sold c. His initial annual income from shares. iii. The length of a rectangular garden is 12m more than its breadth. The numerical value of its area is equal to four times the numerical value of its perimeter. Assuming the breadth of the garden to be . Write [4] a. The expression for the area b. The expression for the perimeter c. Frame the equation in terms of d. Find the dimension of the rectangular garden. Question 9. i. Using properties of proportion, solve for : [3] ii. 1+ + 2 1 + 2 ii. = 13(1+ ) 14(1 ) Each of the letter of the word HOUSEWARMING is written on cards and put in a bag. If a card is drawn at random from the bag after shuffling, what is the probability that the letter on the card is: [3] MTHS_CLS_X_PREBOARD1_PG7/8 a. b. c. iii. A vowel One of the letters of the word SEWING Not a letter from the word WEAR Construct two concentric circles of radii 3cm and 5cm. Taking a point P on the outer circle, construct the pair of tangents to the other circle. Measure and record the length of a tangent. [4] Question 10. i. The distribution of height (in cm) of 96 children is given below: a. b. c. d. e. ii. Height 124 128 132 136 140 144 148 152 156 (in cm) 128 132 136 140 144 148 152 156 160 No. of 5 9 17 24 16 12 6 4 3 Children Use 2cm = 4cm on one axis and 2cm = 10children on another axis. [6] Draw a less than cumulative frequency curve for the above data. Calculate the median Lower Quartile Upper Quartile Calculate the number of children whose height is above 150cm. In the figure given, O is the centre of the circle and PT is a tangent at T. If PC = 3cm, PT = 6cm and = 64 . Find. [4] a. Radius of the circle b. MTHS_CLS_X_PREBOARD1_PG8/8

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