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INTERNATIONAL GOPAL SHARMA MUMBAI 400 076. POWAI VIHAR, POWAI, SCHOOL EXAMINATION 2023 - 2024 FIRST PRELIMINARY SUB : MATHEMATICS STD:X DATE: 04/12/2023 contains 6 (This question paper printed pages) MARKS : 80 TIME : 22 h Encl: 2 Graph paper separately on the paper provided written be must Paper this Answer to during thefirst 15 minutes. Youwill not be allowed to write the Question Paper. answers. This time is to be spent in reading tine allowed for writing the the is Paper this of head The time given at the questions from Section B. four any and A Section from brackets | |. Attempt all questions or parts of questions are given in questions for marks intended The Section - A [40 Marks] (Attempt all questions) Question 1 questions from the given options. the to answers correct the Choose [15] total amount is if the GST is 28% and the transaction, intra-state In an CGST? 8000, how much amount is paid as (b) 4000 (a) e) (d) 71120 7 1600 2000 deposited in a bank's recurring deposit is months 36 for month If200 per the bank. annum, find the interest paid by per 11% of rate the account at 1220 (b) 71200 (a) 72021 (d) 7 1221 7. 350, 20 shares at a premium of Calculate the money required to buy 79450 (b) 7000 (a) (d) 9540 Z7400 (c) -5 (a) (c) -4 -3 -2 -1 0 1 2 3 4 {x < 2, x E W } {-2 < x < 2, x ER} 5 the solution set is: (b) (d) {x> -2, x E I} {-2 sx < 2, x R} x'- 2x - 15 = 0 are: The roots of the equation (a) (-3, 5) (b) (5, 3) (c) (-5, 3) (d) (0, 3) The fourth proportional to 1.5, 4.5 and 3.5 is: 12.5 (a) (b) 10.5 (c) (d) 7.5 (y) The remainder obtained on dividing f(x) = x2 - 5x +8 by x (a) -2 (c) (b) (d) 2 3 (ii) In the AP 18, 16, 14, 12, .... The common difference is: 4 (a) 2 (b) (c) -2 -4 (d) (ixy Reflection of A(1, 2) in the X-axis is: (a) (c) (1,-2) (1, 2) (b) (d) (-2, 1) (-1,-2) Assertion: The mnidpoint of the line segment joining (5,-3) and (-1,7) is (2, 2) Reason: Mid point of A(x1y) and B(X2, y2) is (a) (b) (c) (d) 2 Assertion is True but Reason is False. Both Assertion and Reason are True. Reason is True but Assertion is False. Both Reason and Assertion are False. If the slope of a line is 1, the inclination is: (a) 30 (b) 60 45 () (d) (xijY Volume of a cylinder can be calculated as: (a) (c) TUp3 3 (b) Tr h (d) 3 (xiH) sec'A - tan?A = (a) 1 (c) (b) (d) -1 (b) (d) 7 2 (xiv) Median of 7, 8, 4, 3, 10 is: (a) (c) 4 6 3 (xyY In a single throw of a dice, the probability of getting a number less than or equal to 2 is 1 (a) 2 1 (c) 4 1 (b) 3 (d) 6 Question 2 If b A B = . ind A - 2AB + B (4] Solve and give the answer to two decimal places. x? 7x +3 = 0 (4] Solve the following inequation, and represent the solution set on the number line. [4] 3x 5 + 2 < X + 4 < 2 + 5 XER Question 3 (a' Using the properties of proportion, find x:y given: x2 + 22x y'+ 3y 2x + 4 3y + 9 [4] The surface area of a 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. (Take n=*7 ) Calculate: (ii) the radius of the sphere. the number of cones recast [4] centre O In the given figure TP and TQ are tWo tangents to the circle with touching at A and Crespectively. If Find: BCQ = 55 , BAP = 60 [5] (Giving reasons) 2OBA i) 2 OBC 2AOC LATC P T Section - B40 Marks] (Attempt any four questions) Question 4 (a) (b) 11 the 6h term of an AP is cqual to four times its first term arnd the Sum ol first six terms is 75, find the first tern and the common difference. Sne invests a sum of moncy in 50 sharcs, paying 15% dividend quoted at 20% premium. If his annual dividernd is 600, Calculate: (i) (ii) (iii) (c) [3] the number of shares he bought the total investment the rate of return on his investment Find the value of pif the lines 5x -3y + 2 = 0 and 6x- py are perpendicular to each other. Hence, find the equation of a line+7=0 passing through (-2, 1) and parallel to 6x-py +7 = 0 [3] [4] Question 5 (u) Swaraj opened arecurring deposit account for a period of 2 years. If the bank pays intercst at the rate of 6% per annum and the monthly installment is 21000, find: (i) (ii) (b) [3] maturity value Given IT 4' (c) interest carncd in 2years [3] 31, where I is the identity matrix of order 2, find x and y. Usinp uler and compn8s, construet triangle ABC where AB - 3 em, BC - 4cm and zABC = 00", Hence, construct a circle circumscribing the rianglc ABC, Meusure and write down the radius of the circle. [4] Quostlon 6 "he q, G n the lunt toru of a leometre ogreaion are l0, 0 ando-l0 renpectively. IWthe comon ratloiN poaitive, ind the tirst term and thc (3) (3] bottom of a From thetop of a cliff, the angle of depression of the top and tower to be 45 and 60 respectively. If the height of the tower are observed is 20 m, find: height of the cliff to the nearest metre 44 places of decimal 21-5 distance between the cliff and tower to 2 (4] ( uestion (a 7 competition the distance throWn (in 40students enter for a game of shot-put [5] metres) is recorded below: Distance 12 - 13 13 - 14 14 -15 (m) 16 - 17 17- 18 18 - 19 2 1 12 3 No. of 15 - 16 Students ogive for the above distribution. Use a graph paper to draw an and 2 cmn =5 students on y-axis. scale of 2cm = 1metre on x-axis Use a Hence using graph, find: the median upper quartile which is above 16 m. number of students who cover a distance (b) stones which are numbered from l to A bag contains 100 identical marble find the probability that 100. If one stone is drawn at random from the bag, [5] it bears: aperfect square number (ii) (ii) (iv) (v) a number divisible by 4 a number divisible by 5 a number divisible by 4 or 5 a number divisible by 4 and 5 Question 8 Palak visitsthe market and buys the following articles: Books costing ? 950 GST @ 5% A pairof shoes costing 3000 GST @18% A sling bag costing 1000with a discount of 30%, GST @ 18%. Calculate the total bill amount including GST paid by Palak. [3] A(5, x) , B(-4, 3) and C(y,-2) are the vertices of the triangle ABC whose [3] centroid is the origin. Calculate the values of x and y. e) U_e graph paper for this question. (i [4] Plot A(-4, 0), B(-3, 2), C(0, 4), D(4, 1), E(7, 3) Reflect B, C, D, E on the x-axis and name them B', C, D', E respectively. (ii Join A, B, C, D, E, E, D, C, B' and A in order. (i) Name the closed figure formed. Question 9 (a In what ratio is the line joining P(5, 3) and Q(-5, 3) divided by the y-axis? Also, find the coordinates of the point of intersection. 3] The difference of two natural numbers is 7 and their product is 450. Find the numbers. [3] (c/ In the figure, AB =9 cm, PA =7.5 cm and PC - 5 cm. Chords AD and BC intersect at P. (4] B Prove that APAB ~ APCD Find the length of CD beu i Find area of APAB:Area of APCD 4:4 7-5 cm uestion 10 Prove: tan A + cot A = sec A X cosec A [3] The mean of the following data is 16. Calculate the value of f. 5 Marks Number of students 10 15 7 f 20 25 6 Construct aregular hexagon of side 5 cm. Construct an incircle to it. **** *** **************** [3] *** ** (4]
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