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ICSE Class X Prelims 2024 : Mathematics (Vasudev C. Wadhwa Arya Vidya Mandir (VCW AVM), Mumbai)

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VASUDEVc.WADHWA ARYA VIDYAMANDIR, BANDRA (EAST) PRE-PRELIMINARY REVIEW- DECEMBER 2023 Std. X Math MATHEMATICS Marks: 80 Time: 2 Ahrs Date: 4/12/2023 (Two and 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 tobe spent in reading the Question Pape. The time given at the head of this paper is the time allowed for writing the answers. Attempt allquestions from Section Aand any four from Section B. Allworking 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 the loss of marks. The intended marks for questions or parts of questions are given in brackets []. This paper consists of eight printed pages. Section A- (40 Marks) (Attempt all questions from this section) QUESTION 1 Choose the correct answers to questions from the given options : i If the discriminant of a quadratic polynomial, D >0, then the (a) two real and equal roots (c) imaginary roots [15] polynomial has (b) two real and unequal roots (d) no roots In an Arithmetic Progression, if a= 28, d = 4, n=7, then a, is: (a) 4 (c) 3 iii The midpoint of a line segment joiningtwo points A(2,4) and B(-2, -4) is (a) (-2, 4) (c) (0, 0) iv. (b) 5 (d) 7 (b) (2, -4) (d) (-2, -4) If the order of matrix A is m x p and order of matrix B is p xn. Then order of the matrix AB is (a) n xp (b) m x n (c) m xp (d) nx m .2. -2 Cont...Std Pre-Preliminary XMath Review- December,2023. the y-axis. (A): The point (0, 4)lies onpoint is zero. Assertion Reason (R): The X-COordinate o the onthe y-axis is the and reason (R) correct (a) Both assertion (A) and reason (R) are true explanation of assertion (A). not the (b) Both assertion (A) and reason (R) are true but reason (R) is correct explanation of assertion (A). ( ) Assertion (A)is true but (R)is talse. (a) Assertion (A)is false butreason reason (R) is true. V ideoint P(al3,4) segment joinina the points Q (-6, 5) and R(-2, } then the value of a is (a) -4 (b) -6 (c) 12 vi. (d) -12 The slope of aline ax + by tc=0 is (a) -a/b (b) a/b (c) c/b (d) -c/b Vl. Agame consists of tossing a one rupee coin 3 times and noting its outcome eacn time. Aryan wins if allthe tosses aive the same result i.e. three heads or three tails and loses otherwise.Then the probability that Aryan will lose the game. (a) 4 (b) (c) 1 0x. A teacher ask one of his students to find the average marks obtained by all the class students in Mathematics, the student will have to find the, (a) mode (c) median X. (b) mean (d) sum The radii of the top and bottom of a bucket of slant height 45cm are 28cm and 7 cm respectively. The curved surface area of the bucket is: (a) 4950 cm? (b) 4951cm? (c) 4952 cm? (d) 4953 cm ..3.. -3 Review Pre-Preliminary Cont...Std .X Math xi. AB is a chord of the circle zACB = 50 that diameter such equalto and AOCis its then BAT is A, If AT is the tangent to the circle at the point (a)65 (b)60 same and base same the are having ofthe cone. cone volume Assertion: Acylinder and right circular timesthe volume will cylinder is three (c)50 xii. December,2023. (d)40 height. The volume of the the halved height is and doubled cylinderis Reason: if the radius of the be doubled. correct explanation of A the is R and true explanation of A (a) BothAand R are R is not correct but true are R and A (b) Both false (c) A is true but R is (d)A is false but R is true integers is 360. To find the positive consecutive two xii. The product of the form of quadratic equation as in represented be (b)x + X- 360 = 0 0 = 360 + X (a) x' + (d) x - 2x360 = 0 integers, this can (c) 2x' +X-360 5,10,20,..is 1275 thennis ? GP the in numbers ofn xiV. The sum (a) 6 (c) 8 XV. (b) 7 (d) 9 the Ifsin A + sin'A = 1, then the value of (a) 1 (c)2 expression (cosA + cosA) is (b)1/2 (d) 3 QUESTION 2 a. a dividend of 8%. 41 Aman buys 200 ten-rupee shares at 12.50each and receives cash. Find the amount invested by him and the dividend received by him in ..4. 4 Cont...Std.X Math b. Pre-Preliminary Review - Find the value of xin the following the number line: 5 1 December, 2023. the inequation and also graph solution on [41 2 6 - S 2 , zeW. C. in the figure, given below, Ois the centre of the circle. If zAOB =140 and [4] LOAC = 50:: B 1400 50 find the following : () ZACB, (ii) 2OBC, (iii) <OAB, QUESTION 3 Mr.Shah has a Recurring Deposit Account in a bank and deposits Rs 80 per month 14] for 18 months. Find the rate of interest paid by the bank, if the maturity value of the account is Rs 1,554. b An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 4 29th ternm of the A.P. C. Construct a triangle ABC, in which AB =4.2 cm, BC = 6.3 cm and AC=5 cm. [5] Draw a perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C. ..5. Cont...Std .X December,2023. -5 Math Pre-Preliminary Review - Section -B(40 Marks)this section. (Attempt any four questions from (3] QUESTION4 a. and Find X such that A + X= 2B+C b In a T.T. match between Geeta and Ritu, the [31 Rituis 0.73. of winning probability off the Find the probability of: (i)winning of Geeta (i)not winning of Ritu C. integers is 208. If the square of the larger The sum of the squares of two positive number is 18 times the smaller number, find the numbers. (4] QUESTION 5 a. [3] Prove that, (cosec - sin 0) (sec - cos )(tan 0 +cot 0) =1 b. C Solve for x the quadratic equation x - 4x - 8 = 0 Give your answer correct to three significant figures. (3] Using the properties of proportion , solve for x [4] (x + 1) =17 2x? 8 ..6.. -6 ReviewCont.Std .X Math Pre-Preliminary December , 2023. Question 6 the chord and PT is the 31 In the following figure O is the centre of the circle, PQ is a tangent to the circle at P. If 2POQ =70 , find TPQ. b. C. AB is a diameter of a circle with centre C = (-2, 5). If A= (3,-7). Find the length of radius AC [3] a histogram for the frequency Construct distribution and graphs. (4] Class interval frequency 1-10 11 estimate the mode from 11-20 21-30 31-40 41-50 23 30 20 16 Question 7 Prove that (x-3) is a factor of the polynomial f(x)= x-x-9x +9. Hence factorize it completely. b. If a,b,c and d are incontinued ad(c + d ) = c (b+ d) C. proportion ,then prove that A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the (3) (3] [4] Cone. ..7.. -7 Review- December., Cont..Std X Math Pre-Preliminary 2023. Question 8 a. Plot A(3, 2) andB (5, 4) on graph both the axes. paper. Take 2cm = 1 unit on points also onthe [5] Reflect A and Bin the x-axis to A' and B' respectively. Plot these same graph paper. Write down: () the geometrical name of the figure ABBA; (ii) the measure of angle ABB'; (i ) the image of A" of A, when A is reflected in the origin. (iv) the single transformation that maps A' to A". b. m high.From either side of a river, one of them is 50 Of the two trees which are on depression of the top and the foot of the other tree the top of this tree the angles of the height of the other 5] of the river and are 30 and 60 respectively. Find the width tree. Question 9 a. b. and 2x-x-(p +3)x -6 leave When divided by x - 3the polynomials x- px + x +6 (3] Find The four vertices of aparallelogram are A(-2, 3), B(3, -1), C(p, q) and D(-1, 9). [3] At ashooting competition the score of a competitor were as given below: [4] the same remainder. Find the value of 'p'. the value of pand q. C. 2 Score No.of 3 6 4 4 5 7 5 shots 1. What was his modal score? 2. What was his median score? 3. What was his total score? 4. What was his mean score? ..8.. -8 Cont...Std .X Math Pre-Preliminary Review - December, Z0Z3. Question 10 (3] Findr and y. b The equation of the line ) (i) Write down the slope of the Calculate the the x-axis. C (3] POQ is 3y -3x +7=0 line PQ. angle that the line PQ makes with the positive direction of MS.Roy went to a store and the following items. The and the quantity ofdepartmental each items and marketbought price of each are given below: GST rates 4) S.no Items Pricer item Quantity in Rs 1. GST rate Walnut 650 1 5% 2 Chips 50 2 0% 3 Coffee 80 2 18% Find the: i.The total amount of SGST paid i.The total amount of the bill --The End

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