
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

ICSE Class X Prelims 2026 : Mathematics (The Shri Ram School (TSRS), Aravali, DLF Phase IV, Gurgaon)

9 pages, 73 questions, 0 questions with responses, 0 total responses,

	Aadiraj Sharma	+Fave Message
	Profile Timeline Uploads

Home > aadi2400 > F Also featured on: School Page

Formatting page ...

The Shri Ram School - Aravali Pre Board Examination (2025-26) Class: X Subject: Mathematics Max. marks:80 Time: 3 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 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 the brackets [ ]. 22 Take = 7 , unless stated otherwise SECTION A (Attempt all questions from this section.) Question 1 Choose the correct answers to the questions from the options given. (Do not copy the question, Write the correct answer only.) [15] (i) The equation of the line passing through the origin and parallel to the line 7 3 + 4 = 0 is, a. 7 b. 3 c. 3 d. 7 + 3 7 2 3 + 4 + 4 = 0 = 0 3 (ii) If matrix A = [ 4 2 a. [ ] 4 = 0 = 0 26 5 ] and AB =[ ] then matrix B is 0 2 4 b. [ ] c. [4 2] 2 d. [2 4] TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 1 (iii) If the ratio of the diameters of two right circular cones of equal height be 3 4, then the ratio of their volumes be a. 9 16 b. 3 4 c. 16 9 d. 27 64 (iv) The GST on an article is reduced from 12% to 5% and due to this, the price paid for the article is cut by 14. The original price of the article is a. 50 b. 98 c. 100 d. 200 (v) A company gives a dividend of 8% on shares of nominal value 100. For 5000 shares, the dividend is a. 40,000 b. 50,000 c. 4000 d. 8000 (vi) The scale factor of a picture and the actual height of Sonia is 20 : 1.6 . If her height in the picture is 18 cm, then her actual height is a. 14.4 b. 2.25 c. 1.8 d. 1.44 (vii) Sumita intended to open a Recurring Deposit account of 2000 per month for 1 year in a Bank paying at 10% per annum rate of S.I. The Bank reduced the rate to 8% per annum. How much must Sumita deposit monthly for 1 year so that her interest remains the same? a. 2000 b. 2500 c. 22000 d. 1000 (viii) In the adjoining diagram PQ is a tangent at A to the circle with centre O. If OAC = 25 , then ABC is a. 20 b. 65 c. 70 d. 130 (ix) Assertion (A): If = 2 2 and = 2 2 + 1, then the value of y = 2. Reason (R): For any value of , 1 + 2 = 2 a. A is true, R is false. b. A is false, R is true. c. Both A and R are true, and R is the correct reason for A. d. Both A and R are true, and R is incorrect reason for A. TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 2 (x) The ratio of diameter to height of a borosil cylindrical glass is 3 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is a. 120 b. 30 c. 60 d. 18 (xi) Assertion (A): The difference in class marks of the modal class and the median class of the following frequency table is 0. Reason (R): Modal class & median class are always the same for a given distribution. Class Interval 20-30 30-40 40-50 50-60 60-70 Frequency 3 2 6 4 1 a. A is true, R is false. b. A is false, R is true. c. Both A and R are true, and R is the correct reason for A. d. Both A and R are true, and R is incorrect reason for A. (xii) If the polynomial 2 3 + 3 2 2 3 is completely divisible by (2 + ) and the quotient is equal to ( 2 1), then one of the values of is a. 3 b. 1 c. 0 d. 3 (xiii) The roots of the quadratic equation 3 2 = 6 is a. 0 b. 2 c. 0, 2 d. 0, 6 (xiv) Given + 2 5 + 3 and is a prime number. The solution set of is a. b. {0} c. {1, 2} d. {2} (xv) The reflection of the point P ( 2, 5) in the point M (3, 2) is a. (8, 1) b. ( 5, 3) c. (2, 3) d. (8, 1) TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 3 Question 2 i) If 2 3 3 2 3 + 2 = (2 1)( 2 + + ). a. Find the values of & . b. Hence, factorise 2 3 3 2 3 + 2 completely. [4] ii) Calculate the ratio in which the line joining A( 4,2) and B(3,6) is divided by point P( , 3). Also, find a. . b. length of AB. [4] iii) In the given figure, with centre O and diameter AD, BED = 70 and BC is parallel to AD. Find: a. BAD b. BOD c. DBC d. DCF [4] Question 3 i) 20, 15, 10, , 35, 40 form a progression. Answer the following questions: a. What is the common difference? b. How many terms does the progression have? c. Find the value of the middle term. ii) An ice cream cone has a diameter of 7 and its height is 9 . If it is filled [4] [4] with a scoop of spherical shaped ice cream of radius 3.5 , find a. on melting, is the ice cream sufficient to fill the cone completely without any wastage? b. the volume of ice cream, if any, in excess or less. Give the answer correct to the nearest whole number. TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 4 iii) Use a graph sheet for this question. Take 1 cm = 1 unit along both the and axis. Plot ABCDE, where A (4, 0), B (4, 2), C (2, 2), D (2, 4) and E (0, 4). a. Reflect the points A, B, C and D on the -axis and name them F, G, H and I respectively. b. Join the points A, B, C, D, E, I, H, G and F in order. Reflect the figure ABCDEIHGF on the -axis and name it as AMNPQRSTF. c. Give the geometrical name of the closed figure AEFQ and name a line of symmetry of the figure formed. [5] SECTION B (Attempt any four questions from this section.) Question 4 i) Mr. Sunil invested 8000 in 7% 100 shares at 80. After a year he sold these shares at 75 each and invested the proceeds (including his dividend) in 18% 25 shares at 41. Find a. his dividend for the first year. b. his annual income in the second year. [3] ii) Solve the inequation 3( 7) 15 7 > solution set on the number line. iii) Prove: 1 +1 3 , where x R and represent the [3] 2 = (1+ ) . +1 [4] Question 5 i) In the given figure, PQRS is a cyclic quadrilateral. PQ and SR produced meet at T. [3] a. Prove that TPS~ TRQ. b. Find SP if TP = 18 , RQ = 4 , TR = 6 . c. Find the area of quadrilateral PQRS if the area of PTS = 27 2 . TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 5 ii) Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets 1200 as interest at the time of maturity, find a. the monthly instalment. b. the amount of maturity. [3] iii) The following table shows the marks scored by 140 students in an examination of a certain paper. Calculate the mean by using deviation method. [4] Marks No. of students 0 10 20 10 20 24 20 30 40 30 40 36 40 50 20 Question 6 i) Find the equation of the line passing through the intersection of the lines 4 + 3 = 1 and 5 + 4 = 2 and perpendicular to the line + 2 5 = 0. [3] ii) In the given figure ABC = 70 and ACB = 50 . Given O is the centre of the circle, PT is the tangent to the circle, AP = 9 and AB = 16 . Calculate: a. length of PT. b. CBT c. BAT [3] [4] iii) The following bill shows GST rate and the marked price of articles. Sl. No. 1 2 3 Item Wallet Cotton Bedsheet Utensils MRP ( ) 1500 800 1200 Discount 200 5% 100 Rate of GST% 18 5 12 Find the total amount to be paid including GST. TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 6 Question 7 i) The horizontal distance between two towers is 120 m. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the top of the second tower is 30 and 24 , respectively. Draw the figure and find the height of the two towers. Give your answer correct to 3 significant figures. [5] ii) The ogive represents the monthly income of a group of 320 employees in a company. Given 2 = 1000 on one axis and 2 = 50 employees on the other axis. Find: a. the median wage. b. the number of employees whose income is below 8500. [5] c. the number of senior employees in the company, if the salary of a senior employee is above 11500. d. the upper quartile. TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 7 Question 8 i) A box contains 12 balls out of which are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double what it was before. Find . [3] ii) If 3 +3 2 3 +3 2 3 2 + 3 = 3 2 + 3 show that = [3] iii) An open cylindrical vessel of internal diameter 7 and height 8 stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of 1 whose base is 3 and height 8 . Find the volume of water required to fill the vessel. 2 3 If this cone is replaced by another cone, whose height is 1 and the radius of whose 4 base is 2 , find the drop in the water level. [4] Question 9 i) For the following frequency distribution table, draw a histogram. Hence calculate the mode. [3] Class 50 55 55 60 60 65 65 70 70 75 75 80 Frequency 5 20 10 10 12 6 ii) The fourth term of an A.P. is 11 and eighth term exceeds twice the fourth term by 5. Find a. A.P. b. the sum of first 50 terms. [3] . iii) Solve the quadratic equation decimal places. 1 1 2 = 3, 0, 2. Give your answer correct up to two [4] TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 8 Question 10 i) If the 6th term of a G.P. is 32 and the 9th term is 256, find the a. first term and common ratio. b. sum of its first 10 terms. [3] 1 1 ii) Given B = [ ]. Find matrix X, if X = B 2 4B. 8 3 [3] iii) Use a ruler and compass to answer this question. [4] a. Construct a circle of radius 4.5 and draw a chord AB of length 6.5 . b. At A, construct CAB = 75 , where C lies on the circumference of the circle. c. Construct the locus of all points equidistant from A and B. d. Construct the locus of all points equidistant from CA and BA & mark the point of intersection of the two loci as P. TSRS/AR/Math/Form10/Pre Board Exam/ 2025-26 This paper consists of 9 printed sides Page 9

Formatting page ...

aadi2400 chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: