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SIIRI BALAJI INTERNATIONAL SCHOOL PRELIMINARY EXAMINATION - JANUARY 2024 Form 10 Datc:08/01/2024 Marks: 80 Time: 2 hrs 30 mins. MATHEMATICS Al/empt all questions from Section A and any four questions from Seel/on B. 17,e intended mar/cs for questions or parts ofquestions are given in brackets [}. SECTION A (40 marks) Attempt all questions from tbis section Question 1 (15) Choose tbe correct answers to tbe questions from the given options: (i.) A die is rolled once. The probability of ge\fing a perfect square is: WI (ii.) ~o sin1A 1 +cos A (a.) I +sin A (b.) I +cos A (c.) I-sin A (d.) I-cos A (iii.) PA and PB are tangents to the circle from an cxtemal point P. CD is another tangent at Q. f IfPA= 12cm,QC= QD=3cm,t henPC+PD = _ __ (a.) 18 cm (b.) 12 cm (c.) 10 cm (iv.)The inclination 8 ofthe line whose slope is 2.9042 is: (c.) 70 (b.) 71 (a.) 600 (d.) 14 cm (d.) 69" (v.) The coordinates ofthe point (2, 3) after reflection in the line x = 3 is: (d.) (4, 3) (c.) (-2, -3) (b.) (3 , 4) (a.) (3 , 2) (vi.) The 12lh term from the end of the A.P. 10, 7, 4,............. - 62 is: (a.) 32 (b) -32 (c.)-29 (d.)- 30 Contd. pg..... 2 Shri Ilalnji ln1ernn1iorml School Forni: 10 (vii.) If A= Ma1hema1ics -2- r 0\ , 2 Lo -2J Date: 08/0112024 then A2 is: (a.) 21 (b.)41 (viii.) lf9 ~ 14 - 5x > 3x - S; xo (a.) (0, I, 2) (c) I (d.)A W; then the solu1ion set is: (b.)(0, I) (c.)(I, 2) (d.)(0, I, 2, 2.37) (ix.) Mr. Ravi gets Rs. 6390 at the end of I year at the rale of 12% per annum in a R.D. accoun Then the monthly installment t. will be: (a.) Rs. 500 (b.) Rs. 400 (c.) Rs. 550 (d.) Rs. 639 (x.)Two cylindrical vessels con tain same amount of waler. If the the ratio of the height is: ir diameters are in the ratio 2:3 , (a.) 4 : 9 (b.) 2: 3 (c.) 9: 2 (d.) 9 : 4 (xi.) lfx+4 is the mean pro portional between x+I and x+ I0, then the valucofx is: (a.)3 (b.)2 (c.) I (d.)-1 (xii.) lff (x) is a polynomial and 'a' is real number, then x + a is the factor of f (x) only wh en: (a.) f(a ) = 0 (b.) f(-a) = - (d.) f(a) = I (xiii.) In the figure, O is the cen tre o f ~ n d the value ofx: (a.)300 (b.) 600 (c.) 1200 (d.) 7!'f' ) M Akash took a life ins urance policy for himself and paid Rs.1800 as SGST. The to~ . I annual premium paid by him if the rate ofGST is 18'/o rs: (b .), 20,000 (a.) ' 18,000 (d.)'18,500. (c. ), 10,000 (xv.) If one of the factors ofx l + x - 20 is (x -4 ) then the oth er factor is: b.) (a.)(x + 2) ( (x + 5) (c.)(x - S) (d.) (x - 2) ( Contd. pg..... 3 , r /' '" ''' 2a Fonn: 10 Question Shri Oalaji International School Mathematics -3- i (i.)Using properties of proportion, solve for x: .fi + Date : 08/01/202 1 {i;:' = 3 (4) fi-~ (ii.)Finda2x2matrixXwhichsatisfiestheequation: fj 13 17 ro 2l+2x =r, -51 (4) 4-J 1:4 produced at Q. (iii.)ln the figure given below, AB is a diameter. The tangent at c meets AB A~ If LCAB is 34", find: (a.)LCBA (b.)LCQA (4) Question 3 (i.) A two-digit number is such that the product of the digits is 14. If 45 is then the digits interchange their places. Find the number. added to the number, (4) . Prove that t,. ABC (ii.) In the given figure, ABC is a triangle with LEDB = LACB A t,. EBO o/2C 2 If BE= 6 cm, EC= 4 cm, BD = 5 cm and area ofl!. BED~ 9 cm Calculate: (a.) length of AB ; (4) (b.) Arca oflJ. ABC (iii.) Construct a frequency distribution table for the following ages (in years) equal class intervals, one of them being 9 - 12, where 12 is not included. Draw a histogram for the same. 18, 12, 7, 6, f !, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12 17, IS, 6, 18, 23, 16. 9. 21, II, 16, 22 of30 students using (5) Contd. pg..... 4 Shri Balaji International School Fonn: 10 Mathematics -4- Date : 08/0 I/2024 SECTION B (40 mtrks) Attempt any four questions from this section Question 4 (3) (i.) The 4th tenn ofa G.P. is square of its second tenn and the first tenn is -3. Dctennine the G.P. (ii.) A child has a die whose six faces show the letters as given below: The die is thrown once. What is the probability ofgetting: (c.) not B? (b.) either A or B? (a.) A? (iii.) Dccpa has 4 years R.D. account in a bank and deposits Rs.1800 per month. If she gets Rs.1,08,450 (4) at the time of maturity, find the rate of interest. Question S (i.)Solve:-3+x S k +2 S H+2x; x&I; forx.Representthesolutionsetonthenumberline. (3) 3 3 (3) (ii.)Ifx-a sin A cos C, y = a sin A sin C, z = a cos A, show that a2 = x2 + y2 + z2 (iii.)The surface area ofa solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate: (a.) radius ofthe sphere (b.) the number of cones recast (take lt = 22/7) (4) Question 6 (i.) Draw a circle of radius 4 cm with centre 0. Construct two tangents inclined at an angle of75 to each other. (3) (ii.) Solve the quadratic equation 4x2 - Sx - 3 = 0, for x. Give the answer correct to two decimal places. (3) (iii.)Using a graph paper, plot the points A(6, 4) and B(O, 4). (a.) Reflect A and B in the origin to get images A' and B'. Also, write the co-ordinates. (b.) State the geometrical name for the figure AB A' B'. (4) (c.) Find its perimeter. Contd. pg..... 5 \ Shri Balaji International School Date: 08/01/2024 Mathematics .5. Question 7 (i.) A man invests Rs.4,500 in shares of a company which is paying 7.5% dividend. If Rs.100 shares are available at a discount of I0%, (3) (b.) his annual income. Find: (a.) number of shares he purchases (ii.) If the rate ofGST is 12%, Sonia has to pay Rs.600 for 10 kg of rice. What amount she has to pay (3) if the GST is decreased to 5%? (iii.) Find the value ofp, if the lines 5x. 3y + 2 =Oand 6x. py + 7 =0 are perpendicular to each other. (4) Hence, find the equation ofa line passing through (-2,-1) and parallel to 6x - PY+ 7 = 0. Question 8 (i.) The sum of three numbers in an A.P. is 12 and the ratio of the first number to the third number is I: 3. Find the numbers. (3) (ii.) A man 1.54 m tall can just sec the sun over a wall 3.64 m high which is 2.1 m away from him. Find the angle ofelevation of the sun. (3) (iii.) Given a line segment AB joining the points A (-4, 6) and B (8, -3) Find: (a.) the ratio in which AB is divided by the y-axis (b.) the coordinates ofthe point of intersection (4) (c.) the length of AB Question 9 3 2 (i.) Find the values ofp and q, if(x + 3) and (x 4) are the factors ofx - px qx + 24. (ii.) On a map drawn to a scale of I: 20000, a rectangular plot of land ABCD has AB= 24 cm, BC=32c m. Calculate: (a.) the diagonal distance of the plot in km (b.) the area of the plot in sq.km. (iii.) Find P and Q, if 2P + 3Q = Ti 17) and 3P + 4Q = :J f3 251 (3) (3) (4) ~3 -2J Contd. pg..... 6 Shri Balaji International School Fonn: 10 Date: 08/01/2024 Mathematics -6- Question 10 (i.) PQRS is a cyclic quadrilateral. GivenLQPS = 73 , LPQS = ss and LPSR = 82 . ~e_ Calculate: (a.)LQRS (b.)LRQS (4) (c.) LPRQ (ii.) Draw an ogive for the following frequency table: C.I. Frequency 8-12 10 12-16 16 16-20 22 20-24 18 24-28 12 28-32 4 From this ogive, Calculate: (a.) the median (b.) lower quartile and upper quartile (c.) interquartile range ................................... (6)
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