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ICSE Class X Prelims 2024 : Mathematics (Smt. Sulochanadevi Singhania School, Thane)

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Srikant Uchil
Ryan International School ICSE (RIS), Malad, Mumbai

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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Exam Class Subject Date Prelims X Maths 16-01-04 MarksTime 80 2% hrs No. of sides General Instructions: 1. Attempt all questions from Section A. 2. Attempt any four questions from Section B. 3. All working, including rough work, must be clearly shown, and must be done on the same sheet as rest of the answer. 4.Omission of essential working willresult in loss of marks. SECTION A (Attempt all questions from this section) Question1 Choose the correct answer to the question from the given options and-write in the [15] separate answer sheet, 1) The centroid of triangle whose vertices are (5, -6), (-2, 3) and.(-6, 15) is B) (-1, -4) A)(1,-4) 2) 5sec A 5tan'A + 1 is equal to A)-4 D) 7 C) 4 B) 6 D) (1, 4) C) (-1, 4) 3) The reflection of the point A (5, 0)in the line y= 0 is A)(5, 0) 4) Ifn" term of an AP is 13 4n, then the 20" term is B)67 A) -67 D) (0, -5) C)(-5, 0) B)(0, 5) C)76 D) -76 5) Arjun invests Rs.8800 in buying shares of face value Rs.100 each at a premiumn ofT0%;the number of shares he bought is D) 800 B) 880 C) 80 A)88 6) Theyintercept of the line whose equation is 11x 5y 11 2 D) B) 11 + 2 = 0 is 7) If 6 is the mean proportional between two numbers 'x' and 'y' and 48 is the third proportional to 'x' and 'y', then the numbers are: B) x= 4, y =9 A) x=3, y = 12 D) x = 9, y = 24 C) * = 6, y = 6 8) The value of kfor which the quadratic equation 16x*+ 4kx +9 =0 has real and egualroots are A) 6, -3 B) 36, -36 4' 4 6 1 D) 6, -6 -2x + 2. is (9) Ifx ER.then the solution set for 5-3x > A)all real numbers less than or equal to 3 B) allreal numbers greater than or equal to 3 C) all real numbers less than or equal to (-3) D) all real numbersgreater than or equal to (-3) 10) Find the class mark of the modal class for the following distribution: Class Interval Frequency A)12.5 0-5 S- 10 10- 15 15- 20 10 15 12 20 D)22.5 C) 17.5 B) 20 20 - 25 (11) The slope of a line perpendicular to the line passing through the points (2, 5) and (-3, 6) is A) D); C) -5 B) 5 LM of (12) In the adjoining figure, sides MN, NL and and C ALMN touch a circle at the points A, B CM-6cm, respectively. If AN=5cm, CL=4cm and then the perimeter of ALMN is A)15cm B) 40cm C) 30cm D) 60cm (13)Inthe given figure, AB|| DE, B then the length of CDis 4.5cm E X 3cm D A) 10/3cm B) 3.5cm C) 2.5 cmn D) 2.7cm sun's long on the ground, then the 2/3m shadow casts high (14) If a pole bm elevation is A) 30 B) 60 C) 45 D) 90 (15) Assertion (A): The curved surface area of cylinder with radius 2cm and height 10cm is 40zcm . Reason (R):The volume of cone is one third the volumeof cylinder. (A)Both Assertion and Reason are true and R is the correct explanation of A. (B) Both Assertion and Reason are true and Ris not the correct explanation of A. (C) Assertion is true but Reason is false. (C) Assertion is false but Reason is true. Question 2 [4] A) Prove the following trigonometric identity: cot +cosec - 1 1+ cos cot-Cosec 9+1 sin 0 B) In the adjoining figure, O is the centre of 110 the circle and LAOC = 110 . Find : () ZADC (ii) ZABC B [4] (iii) L0AC V2a+1+v2a-1 C)Ifx = V2a+1-V2a-1 then using properties of proportion, prove that : (4) r-4ax + 1=0 Question3 bank for 3 years. If the rate A) Mr. Joseph opened a recurring deposit account in a interest at the time of of interest is 8% p.a. and the bank pays Rs.1776 as maturity. 4] maturity. Find ()The monthly deposit (ii) The amount at the time of into B)The surface area of asphere is 1386 cm. Ifthe sphere is melted and recast solid cylinders of radius 3.5cm and height bcm. Caleulate: (i) Radius of the sphere (i) Number of cylinders recast. (S] C)Use graph paper for this question. (5,0) i) Plot A, B, C where A (2,4), B (-2, ),C ( ) Reflect pointsA and B on the x-axis and name them as A' and B'. Write their co-ordinates. ( i) Give ageometrical nane to the figure forned by joining the points ABBA'C. Find its Area. (iv) Name two points from the figure which are invariant on reflection in x-axis. 3 SECTION B (Attempt any four questions from this section) Question 4 A) Solve the following inequation and represent the solution set on the number line. -2s;-s1xeN (3) B)The sum of three numbers in an A-P is (-12)and their product is 36 Find the numbers. [3] [4] C)Mr. Rohit went to a department store and buys the following articles. Quantity Discount Sr. No Bought Items Price per items 1 A packet of sweets Rs.450 3 2 Hair oil Rs.500 2 3 Chess board Rs.300 18% 10% 12% (1) Find the total amount of the GST Paid. (ii) The total bill amount including GSTpaid-by him. Question 5 A) Determine the ratio in joining the points which the line 22x +y = 4 divides the line segment [3] A(2,-2). a d B (3,7). B) Construct aAABC with BC = 6.5cm, AB = 5.5cm, AC = 5cm. Construct the incircle of the triangle. Measure and write down the radius of the circle. (3] L C) In ALMN, PQ|| MN such that 2cTn, PM = 6cm, MN = 20cm. LP Fnd bcn (i) the length of PQ (i)Area of Trapezium PQNM : Area of M Triangle LPQ 20cm N (4) Question 6 river. Between them in the A)A and B are two points on the opposite banks of a width of the river if angles river, is a boat with a mast of height 20m. Find the and 26 from the the point A of elevation of the tip of the mast are 38 from mast are on the same level. point B. The points A and B and the foot of the [5] Give your answer to the nearest metre. 4 B) Scores obtained by 120shooters in a shooting competition are given below. Scores No. of shooters 0-10 10 -20 5 10 20-3030 40 18 40- 50 50-60 26 19 23 for the given Use a graph paper to draw an ogive 60-70 70- 80 11 distribution taking 2cm 10 on the other axis. SCores on one axis and 2Cm = 20 shooters Use the ogive to estimate: (i) Median obtained more than (i) The number of students who [5] 60 scores. Question 7 and give your answer A) Solve the following equation x2-3x -9=0 figures. correct to three sign+tic nt 3] 3 71, where I is an identity matrixof + -54 4' find =|then A If B) [3] order 2 X 2. shares paying 12% per ahnum. He sold Rs.10 4500, bought Deepak C) shares and invested the proceeds in Rs.25 them when the price rose to Rs.23 paying 10% per annum, at Rs.18. Find the changein his [4] annual income. Question 8 AB3.5cm,AC = 6cm, and ZBAC= 105 . with ABC triangle a Construct A) equidistant from BA and BC Hence, (i)Construct the locus of points points quidistant from B and C (i ) Construct the locus of [3] the above two loci as P. (ii) Mark the point which satisfies 14, 16, 18and 20 are kept in a bag. B)Cards bearing numbers 2, 4, 6, 8, l0, 12, probability of getting a card A card is drawn' trandom from the bag. Find the which is: i) A prime n mber. (ii) A number divisible by 4. [3] (i) Anumber that is multiple of6. and B (5, -2). C)A'straight line passes through the points A(2, -4) Find: (i) Slope of the line AB (ii) The equation of the line AB point (iii) The value of k,ifAB passes through the P(k+3,k-4) [4) Question 9 plot A)On a map drawn to a scale of 1:20,000 a rectangular of land ABCD has AB = 32cm and BC=24cm, Calculate (i)The diagonal distance of the plot in km. (ii)The area of the plot in square km. 5 [3] B)Find the mean of the following distribution by step deviation method. Class - Intervals 20-30 30-40 40 - 50 50 --60 Frequency 10 6 8 12 [3] 70- 80 60-70 C)A plane travels adistance of 1600km at an average speed of xkm/hr. On the return jouney, due to bad weather as the speed was reduced by 40 km/hr, it [4] took 1 hour 20 minutes more than onward journey. Find x. Question 10 A)The $h term of aG.P is 48 and the 8" term is 384. Find its 11" term. 3) t leaves a B) What must be added to the polynomial 2x-3x-8x, so that (3] remainder 10 when divided by (2x + 1). school: C) The following distribution represents the height of the students of a Height 145 - 150 150 155 155 - 160 160 - 165 165- 170 25 6 13 (in cm) No. of students 34 42 paper and Draw a histogram for the above data using graph hence. find the mode. [4]

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