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THE BISHOP'S SCHOOL, PUNE FIRST PRELIMINARY EXAMINATION (2024-2025) MATHEMATICS MARKS - 80 CLASS: 10 TIME: 3 HRS DATE: 16.11.2024 Answers to this paper must be written on the paper provided separately. Youwill not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. the answers. The time given at the head of the paper is the time allotted for writingSection B. from questions four any and Attempt all questions from Section A must be done on the same sheet as Allworking, including rough work, must be clearly shown, and the rest of the answer. Omission of essential working will result in loss of marks. brackets [J. The intended marks for questions or parts of questions are given in SECTION A (Answer all questions in this section) Question 1. [15X 1] options. Choose the correct answers to the questions from the given becomes number to its double, the resulting i. The greatest integer which is such that if 7 is added greater than three times the integer is a. 4 b. 5 a b. d. 7 c. 6 is The slope of aline perpendicular to the line 3x= 4y + 11 ii d. -: is If sec A-tan A =k, then the value of sec A + tan A iii. a. iv. 1 b. 1-k d. c. 1+k 400 eggs is 0.035, then the Assertion (A): If the probability of getting a bad egg in a lot of number of bad eggs in a lot is 21. number of outcomes favourable to E Reason (R): Probability of an event E is defined as P(E) a. cotal number of possible outcomes A is true b. A is false, R is true A c. Both A and R are true, and R is the correct reason for forA. reason incorrect d. Both A andR are true, and R is V dividend. If his annual income is Manish has some shares of 20 of a company paying 12% 9600, then the number of shares he possesses is a. 4000 vi vii. viii. The discriminant of 2x2 5x + 1 =0 is: X c. 5200 c. 17 b. 33 a. 25 x + mx + 10, then the value of m is: of factor If (x 2) is a c. 4 b. -7 a. 7 The nh term of the A..P 15, 10, 5,....is: a. ix b. 5000 Sn - 20 b. 20 - 5n c. 20 + Sn d. 5600 d. 15 d. 5 d. 10 +Sn The reflection of thepoint P1, -2) in the line y=-1is; d.(1,0) c. (1, 4) b. (1, -4) a. (-3,-2) then: 3, x 2 order of matrix a is B and If A is a matrix of order3x2 a. A+B is possible b. B+Ais possible C. AB is possible d. neither AB nor BA is possible Xi. dividend, with total The number of ?25 shares, paying 24% a. 125 xii. b. 27 c. 225 G.P3.6, 12, ....3072 is: The fourth term from the end of the a. 300 b. 352 C. 384 dividend 1350 is: d. 200 d. 390 transformation, then k>Imeans: Ifk be the scale factor of asize d. none of these C. same size b. reduction a. Enlargement xiii. and B(7, 4) in the ratio: The point P(1,2) divides the join of A(-2, 1) d. 2:3 c.3:2 xiv. b. 2: 1 The roots of the quadraticequation 3x?- 5x +1=0are: c. Imaginary a. Real and distinct b. real and equal a. XV. 1:2 d. none of these |4+4+4] If he interest. simple p.a years at 7.5% a. Mr. Singh has a recurring deposit account in a bank for 3 gets 8325 as interest at the time of maturity find: The monthly deposit (ii) The maturity value. (i) consumer at a profit b. Amanufacturer sells a T.V to a dealer for 18000and the dealer sells it to a Question 2 of 1500. If the sales are intra state and rate of GST is 12%, find; the amount of GST paid by the dealer to state government. (i1) the amount of GST received by central government. (ii) (ii) the amount of GST received by state government. (iv) the amount that the consumer pays for the T.V C. Through the mid-point M of the side CD of parallelogram ABCD, the line BM is drawn intersecting AC at L and AD produced in E. Prove that EL = 2BL A D 14+4+5] Question 3; a. Prove the following trigonometric identity: (sin 8 + cos 0) (cosech - seco) = COsecoseco - 2 tan b. Find the mean of the following distribution by step deviation method: Class interval 20-30 30 - 40 40 - 50 50 - 60 60- 70 10 6 8 12 5 70- 80 Frequency C. The points P(3,4) is reflected to P' in the x-axis and 0' is the image of O(origin) when reflected in the line PP'. Using graph paper, give: (i) The coordinate of P' and 0. (ii) The length of the segments PP' and O0. The geometrical name of the figure POP'O. (ii) SECTION B (40 MARKS) (Attempt any four questions from this section) Question4: a. Solve the following inequation and represent solution set on a number line 5 1 (3+3+4| 2x -2;<5-S2,x EW b. Raj and Rajni are friends. They were both born in 1990. What is the probability that they have (i)same birthday? (ii) different birthdays? c. In the figure, Ois the centre of the circumcircle of ZXYZ. Tangent at Xand Yintersect at T. Given LXTY =0 and Z XOZ = 140 , calculate the value of ZZXY. 2 Question5: [3+3+4] a. Given= A 2B - and C=b find the matrix X such that A + X = 2B +C b. If the mean of the following observation is 54, find the value of p. Class Frequency 0-20 7 20 - 40 40 - 60 60- 80 P 10 9 C. Find the values of 'a' and b' so that the polynomial x + ax + bx 80- 100 13 45 has (x 1l) and (x+ 5) as its factor. For the values of 'a' and "b', as obtained above, factorise the given polynomial completely. (3+3+4] Question 6: Solve the following quadratic equation for x and give your answer correct to 2 decimal places. 3x7 +5x-9=0 A box contains acertain number of balls. Some of these balls are markedA, some are marked B and the remaining are marked C. When a ball is draw at random from the box P(A) = and P(B)=*.Ifthere are 40balls in the box which are marked C, find the number of balls in the box. c Using ruler and compass draw circle circumscribing a regular hexagon with side 5 cm. Measure the radius of the circle. [4 + 6] Question 7: a Using the properties of proportion find the value of x: V3x+4 +V3x-4 V3x+4 - V3x-4 b The marks obtained by certain number of students in a mathematics test are given below : 50 - 6060-70 70-80 80- 90 0- 10 10 - 20 20 -30 30- 40 40- 50 Marks No. of students 9 16 22 26 18 11 90- 100 4 6 Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for ogive. Use your ogive to estimate i. the median ii. the number of students who obtained more than 75% marks in a test. ii.the lower quartile. Question 8: Find a. Hamid buys 100 shares at 20 premium of acompany paying 15% dividend. i. the market value of 600 shares ii. his annual income ii. his percentage income 1,2). b. ABCD is a rhombus. The coordinates of Aand C are (3, 6) and (Find the equation of BD. age. Ten years hence her age will be C. Five years ago, a woman's age was the square of her son's twice that of her son's age. Find their present age. Q estion 9: for 2 years. If he gets a. Anup has a R.Daccount and deposits 600 per month of maturity, find the rate of interest earned by him. 15600 at the time polynomial b. Using remainder and factor theorem, factorise completely, the given 2x3 + x2-13x + 6 : point P meets AB produced in Q, c. AB isa diameter of a circle with centre O. The tangent at a ZPAQ=34 , find ZPBAand ZPOA. 3 3 P Question 10: a. The sum of first three terms of G.P is of G.P i) the common ratio b. IfA-; 39 10 and their product is 1. Find (ii) the first three terms of this G.P and and BB=, = ind Mso that AM =B C. The equation of aline is 7- 3x 4y=0. Find i. slope of the line. ii. the equation of the line perpendicular to the given line and passing through the intersection of the lines x-y+2=0and 3x +y- 10 =0. **
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