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Std: X Max.Marks: 80 HIRANANDANI FOUNDATION SCHOOL, POWA i FIRST PRELIMINARY EXAMINATION 2024- 2025 Mathematics Date: 9 - 12 - 2024 Time: 3 Hours Answer to this paper must be written on the pape r provided separately You will not be allowed to write during the first 15 minutes This time is to be spent reading the question paper The time given at the head of the paper is the time allowed for writing the answers Attempt all questions from Section A and any four 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 the loss of marks. The intended marks for questions or parts of questions are given in brackets[ ].Mathematical table are provided. This paper consists of 9 printed pages. SECTION A (40 Marks] (Attempt all questions from this section) Question 1. Choose the correct answer to the questions from the given options: (15] (i)3-6+12-24+........ -384. Third term from end of the given G.P. is (a) (b) (c) (d) 48 -96 12 -48 (ii)Construction of a cumulative frequency table is useful in determining the (a)mean (b) median (c) mode (d)all the above three measures Turn Over..... HFS, Powai ......... 2 ....... . Std XI Mathemati cs ( iii)Two identical solid hemispheres are kept in contact to fonn a sphere. The ratio of the total surface areas of the two hemispheres to the surface area of the sphere formed lS (a)1 : 1 (b)3: 2 (c)2: 3 (d)2: 1 (iv) The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is: (a)3 cm (b) 5 cm (c) 7cm (d) 10 cm (v) A ladder makes an angle of 60 with the ground, when placed along a wall. If the foot of ladder is 8m away from the wall, the length of ladder is (a )4m (b)8m (c) 8'13 m (d) 16 m (vi)The coordinates of a point P, where PQ is the diameter of a circle whos e centre is (2, - 3) and Q is (1, 4) is: (a) (3, -10) (b)(2, -10) (c) (-3, 10) (d)(-2, 10) (vii) 30th term of the A.P: 10, 7, 4, ... , is (a) 97 (b) 77 (c) -77 (d)-87 HFS, Powai ..... ....4....... . Std X I Mathematics (xiii) If MBC - 6.QRP then the corresponding proportional sides are (a) AB/ QR=BC/RP (b) AC /QR=BC/RP (c) AB /QR=BC/ QP (d) AB/PQ=BC/RP (xiv) The solution set for the linear inequation -8 S x - 7<- 4, xE/ is (a) {x:xe -1Sx<3} (b) {O, l , 2, 3} (c) {-1, 0, l, 2, 3} (d) { -1, 0, 1, 2} (xv) Ankit had the option of investing in company where 7% , 100 shares are available at 120 or in a company B, where 8% , 1000 shares are available at 1620 Assertion (A) :Investment in company A is better than company B. Reason (R) : The rate of income in company A is better than in company B. (a) Both A and Rare true, and Ris the correct explanation. (b) Both A and R are true, and Ris not the correct explanation. (c) A is false, but Ris true. ( d) Both A and R are false. Question 2. (a) A person invested 20%, 30% and 25% of his savings in buying shares of three different companies :X, Y and Z which declared dividends of 10%, 12% and 15% respectively. If the total income on account of dividends be Rs 2,337.50, find his savings and the amount which he invested in buying shares of each company. [4] (b.) In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below: [4] 9 8 7 6 5 3 4 2 Marks l 3 4 5 10 6 3 3 2 No. of l students .. Calculate the following for the given distribution: (i) Median (11) Mean ( c.) Prove that cotA-1 2- sec 2 A cot A l+tanA 10 3 [4] HFS, Powai ......... 5...... . Std x / Mathematics Question 3: (a) The height of a cone is 40 cm. A small cone is cut offat the top by a plane parallel to the base. If the volume of the small cone be 1/64 of the volume of the given cone, at what height above the base is the section made? [4] (b) In the figure PA is a tangent, to the circle with centre 0. Calculate x and y [4] ?7 0 (c) Use a graph sheet for this question. Take 1 cm = I unit along both X and Y axis. (i) Plot the following points: A(0,5), B(3,0), C(l,O) and D(l ,-5) (ii) Reflect the points B, C and D in the Y axis and name them as B', C' and D' respectively. (iii) Write down the coordinates of B', C' and D'. (iv) Join the points A, B, C, D, D', C', B', A in order and give a name to the closed figure ABCDD'C'B'. (v) Find area of the closed figure. [5] Section - B [40 Marks) (Attempt any four questions) Question 4: (a) Give matrix A = 1. 11. !] and B = [x x 2] such that AB is a null matrix. Find: Order of the null matrix Possible values of x and y [3] Turn Over.....
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