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LA MARTINIERE FOR GIRLS REHEARSAL EXAMINATION-2023-24 MATHEMATICS CLASS X Time : 2', Hours + 15 mins. reading time Full Marks-80 This paper consists of seven printed pages & one blank page. Answer to this Paper must be written on the paper provided separately. You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section - A and any four questions from Section - B. All working, 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 loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECTION-A (40 Marks) (Attempt all questions from this section) 1. Choose the correct answers to the questions from the given options. (15] (Do not copy the question, write the correct answers only.) (i) If m, 2,10 andn are in continued proportion, then the value of m andn are (a) 0.2 and 100 (b) 10 and 2 (c) 0.4 and 50 (d) 4 and 5 [Turn Over ] X MATH-1 (LMG) x-3 81 5 4] then the value of x is (a) x = 8, (b) x= 13, (c) x = 7, (d) x = 5, (ii) The 4th term of the A.P 10, 7, 4, .... is (a) 1 (b) -2 (c) -5 (d) -8 (iv) The reflection of the point (-3, 2) in the x-axis, is the point (a) (3,2) (b) (3,-2) (c) (-3, -2) (d) (-2, 3) (v) Consider the following equations: |:x-x -9=0 I|: 4x 5x + 8 = 0 V:3x + x(1 -3x) + 4 = 0 II|:x(x + 1) + X- 14 = 0 IV: x(* -1) - x +3 = 0 Which of the above are not quadratic equations? (a) IV and V (b) Ill and V (c) Il and V (d) Iand IV (vi) The angle of elevation of the top of a tower from a point P on the ground is . After walking a distance d towards the foot of the tower, angle of elevation is found to be B. Then (a) a < B (b) a > B (c) a = (d) None of these X MATH-2 (LMG) (vii) Anita is a dealer in Kolkata (WB) supplies goods worth Rs.10,000 to Vimla in Lucknow (UP).If the rate of GSTis 28%,the tax levied under Integrated GST (IGST) (a) Rs. 0 (b) Rs. 2800 (c) Rs. 280 (d) Rs. 1400 (vii) The end points of a diameter of a circle are A (-4, 0) andB (0, 4), then the cOordinates of its center are (a) (-2, 2) (b) (2, -2) (c) (-4, 4) (d) (0, 0) (ix) The locus of points at a distance 4 cm from a fixed line (a) Apair of straight lines parallel to the given fixed line and at a distance 4cm from it (b) A straight line parallel to the given fixed line and at a distance 2 cm from it (c) Circumference of a circle with given fixed point as centre and (d) (x) Perpendicular bisector of the given line Maximum number of tangents that can be drawn outside the circle is radius 4 cm to a circle from a point lying (a) One (b) Two (c) four (d) Infinite (xi) tan?0 sec0 is equal to (a) 1 (b) -1 (c) 0 (d) 2 [Turn Over ] X MATH-3 (LMG) (XI1) The solid obtained on revolving a right- angled triangle about one of its sides (other than hypotenuse) is (a) Combination solid of a cone and cylinder (b) cuboid (c) hollow cylinder (d) cone (xii) In a single throw of a dice, the probability of getting a number less than 7 (a) 0.7 (b) 1 (c) 0 (d) 1 (xiv) lf x e N, then the solution set of the inequation 4x + 10 s 2x + 18 is (a) {... 2, -1, 0, 1, 2, 3, 4) (b) {0, 1, 2, 3, 4) (c) {1, 2, 3, 4) () {1, 2, 3, 4....) (v) The quadratic equation qx? +px +r= 0.pz0 has two real and unequal roots if and-onlyt {a) p - 4qr > 0 (b) p - 4qr < 0 (c) p - 4gr > 0 (d) p -Agr = 0 w2. (i) Solve the following equations for x and give your answer to 2 decimal places: 1 [4] 2x-y-70 ,(iiy Anya invests Rs. 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If she earns Rs.1200 at the end of the year as dividend, find the: (a) market value of each share to (b) number of shares she bought rb (c) the dividend percent per share ) X MATH-4 (LMG) (4) (iii) The aptitude test of 50 students was recorded as follows: Marks 50-60 60-70 70-80 80-90 90-100 7 10 18 12 3 No. of students Drawa histogram for the above data using a graph paper and estimate the mode. [4 and 6A -A= ml, find m where 1is a 2 x 2 unit matrix. [4) (ii) Arushi has a recuring deposit account in a bank, she deposits Rs. 2500 per month for 2years. If she gets Rs. 66250 at the time of maturity, find : ore (a) the interest paid by the bank (b) the rate of interest. [4] (ii) Use ruler and a compass only all constructions lines and arcs must be clearly shown. Construct a AABC in which BC = 6.5 cm, ZABC = 60 and AB = 5 cm (a) Construct the locus of points at a distance of 3.5 cm from A (b) Construct the locus of points equidistant from AC and BC (c) Mark 2points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. (d) Measure and record XY 5 [5] (40 Marks) SECTION-B (Attempt any four) 4. (i) The marks obtained by students in an examination are given below. Find the mean of the following data using shortcut method. Class Interval frequency (ii) If Sm +6n &m + 5n 20-30 30-40 40-50 50-60 60-70 70-80 9 5 7 12 6 11 use properties of proportion to find m:n (0) Use graph paper for this question. The point P(3, 4) is reflected to P' in the x-axis; and O is the image of O (the origin) when reflected in the line PP. Write: (a) the co-ordinates of P' and O. X MATH-5 (LMG) [Turn Over ] . segments PP and O0. (b) the length of the quadrilateral POP' (c) the perimeter of the [4] POPO!. figure the for name (d) state the geometrical minutes to house 150m high, takes 2 light a from away rowing ) A man in aboat lighthouse from 60 to 45 . the of top the of elevation change the angle of [4) Find the speed of the boat. parallel to Y-axis. AB and AC is BC and triangle a is ABC ( ) In the adjoining figure, [6] respectively. intersect the Y-axis at P and Q Bl-2,3) (a) Write coordinates of A. (b) Find the slope of AB. (c) Find the ratio in which Q divides AC. (d) Find the equation of the line AC. 6. J(1-cos A) (i) Prove that :1+cos A) X'+ D (-2,-4) [3] =COsec A- cot A and recast into solid right circular cones (ii) A solid sphere of radius 15 cm is melted [3] number of cones recast. of radius 2.5 cm and height 8 cm.Calculate the (x+y) (4) (ii) If x, y, z are in continued proportion, prove that (y+z) amount of bill. / ) For the following intra-state supply of good/services, find the 1 1 MRP (in Rs.) of each item 6000 7500 GST 12% 15% No. of items [3] (ii) A two-digit positive number is such that the product of its digits is 6. When 9 is added to this number, the digits interchange their places. Find the number. 23 (ii) In the given figure, PA and PB are tangents to a circle with center 0, diameter 10 cm, OP = mand ZOPB = 25 . Find the following and give reasons. (a) The measure of ZPAO (0 B (b) Length of PB. (c) The measure of ZAOB 100 (d) The measure of ZAPB Y X MATH-6 (LMG) [4) 0 Show that (x -2) is a factor of 3x?-5x -2. Hence, completely factorise the above expression (3] (3] (3] i) Draw a circle circumscribing a regular hexagon with side 5 cm. (ii) Marks obtained by 40 students in the examination are given below. Marks 10-20 20-30 30-40 40-50 50-60 60-70 8 14 9 4 2 No. of Students Using graph draw an ogive and estimate the median marks. [4] 9. () Find the first three terms of a G.P. whose 5th term is 48 and 8th term is 384. [31 (i) In a single throw of two dice, find probability of : (a) a doublet (b) A total of 5 (iii) Given A = (3] f4sin30 COs 0 COs 0 4 sin 30 andB/4) , if AX =B, l5 (a) Write the order of matrix X. (b) Find the matrix X. [4] 10 (0) Solve the following inequation and graph the solution on the number line: 4x - 19 < 2 s+x, xe R (3) (i) In the figure given below, 0 is the centre of the circle. If ZBAD = 75 , find (a) BOD (b) ZBCD (Give reasons) [3) 75 B o (ii) In an A.P., the fourth and sixth terms are 8 and 14 respectively. Find the first term and the common difference and hence find the sum of the first six terms. [4) [Turn Over ] X MATH-7 (LMG)
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