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ICSE Class X Sample / Model Paper 2026 : Chemistry : All chapters

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SET B PRELIMN 1 MATHEMATICS PAPER Maximum Marks: 80 Time allowed: Two hours 1. Answers to this Paper must be written on the paper provided separately. 2. You will not be allowed to write during first 15 minutes. 3. This time is to be spent in reading the question paper. 4. The time given at the head of this Paper is the time allowed for writing the answers. 5. Attempt all questions from Section A and any four questions from Section B. 6. All working, including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer. 7. Omission of essential working will result in loss of marks. 8. The intended marks for questions or parts of questions are given in brackets [ ]. 9. Mathematical tables are provided. SECTION A (40 Marks) (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options. (Do not copy the question, write the correct answers only.) (i) If one of the factor of 2 + 20 is (x 4), then factor is (a) x + 5 (b) x 5 (c) x + 4 (d) x 2 [15M] (ii) In the given figure, O is the centre of the circle, find x. (a) 70 (b) 85 (c) 80 (d) None of these (iii) Aashvi deposited 1000 per month for n months in a bank. If the bank pays a rate of interest 2.5% half yearly and the maturity value is 70675, then the value of n is (a) 48 (b) 54 (c) 60 (d) 72 (iv) (cos sin )2 + (cos + sin )2 = (a) 0 (b) 1 (c) 2 (d) None of these (v) Assertion: If in a cyclic quadrilateral, one angle is 40 , then the opposite angle is 140 Reason: Sum of opposite angles in a cyclic quadrilateral is equal to 360 Page 1 of 7 (a) Assertion is true and Reason is true and Reason is the correct explanation of Assertion (b) Assertion is true and Reason is true and Reason is not the correct explanation of Assertion (c) Assertion is true and Reason is false (d) Assertion is false and Reason is true (vi) A metallic solid cone is melted in the form of a solid cylinder of equal radius, If the height of the cylinder is 6 cm then height of the cone in centimeters was? (a) 10 (b) 12 (c) 18 (d) 24 (vii) Consider the following data: Class Interval 0 10 10 20 20 30 30 40 40 50 Frequency 5 8 12 6 3 The difference of the upper limit of the median class and the lower limit of the modal class is: (a) 0 (b) 15 (c) 10 (d) 8 (viii) From a well shuffled deck of 52 playing cards, one card is drawn at random. Find the probability that the card drawn is either a king or a red carpet 1 7 (a) 2 (b) 13 1 (c) 13 2 1 3 ] and = [ 2 3 1 7 3 (a)[ ] (b) 2 2 3 7 (ix) If = [ 2 + 2 + 2 2 (x) If = 2 2 (a) 2 +1 + 2 2 2 2 (b) 2 1 6 (d) 13 2 ], then what will be the order of the matrix X if AB = X? 1 5 1 (c) [ ] (d) 2 1 1 4 then the value of 2 : 2 will be 2 1 (c) 2+1 (d) 2 +1 2 (xi) The highest GST rate applicable now is: (a) 12% (b) 18% (c) 28% (d) 50% (xii) A man wants to buy 62 shares available at 132 (par value of 100). If dividend is 7.5%, what will be his annual income? (a) 645 (b) 564 (c) 465 (d) None of these (xiii) If > 7, {1, 2, 3, 4, , 10}, then the solution set is: (a) {1, 2, 3, 4, 5, 6,7} (b) {2, 3, 4, 5, 6, 7} (c) {1, 2, 3, 4, 5, 6} (xiv) Which of the following quadratic equation has 2 and 3 as its roots? Page 2 of 7 (d) None of these (a) 2 5 + 6 = 0 (c) 2 5 6 = 0 (b) 2 + 5 + 6 = 0 (d) 2 + 5 6 = 0 (xv) The image of (0, 0) in the line x = 2 is: (a) (2, 0) (b) (0, 2) (c) (4, 0) (d) (0, 4) Question 2 (i) If (x 2) is a factor of the expression 2 3 + 2 + 14 and when the expression is divided by (x 3) leaves the remainder 52, find the values of a and b. [4M] (ii) From the given figure, write (a) The co ordinates of A, B and C. (b) The equation of AC (c) The x intercept of AB (d) The y intercept of BC. [4M] (iii) (a) Prove that: ~ . (b) If PA = 4 cm, PC = 16 cm, AD = 2 cm, PD = 3 cm, find: (1) AB and BC (2) Area of : Area of (3) Area of : Area of ABCD Page 3 of 7 [4M] Question 3 (i) A manufacturer of TV set produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find: (a) the production in first year (b) the production in 10th year (c) total production in 7 years (d) total production in 15 years [4M] (ii) A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate: (a) The total surface area of the internal surface, excluding the base (b) The internal volume of the container in m3 [4M] (iii) Construct a triangle ABC, having given AB = 4.8 cm, AC = 4 cm and = 75 . Find a point P. (a) inside the triangle ABC. (b) Outside the triangle ABC Equidistant from B and C; and at a distance of 1.2 m from BC. [5M] SECTION A (40 Marks) (Attempt any four questions from this Section.) Question 4 (i) A man invests 22,500 in 50 shares available at 10% discount. If the dividend paid by the company is 12%. Calculate: (a) The number of shares purchased (b) The annual dividend received (c) The rate of return he gets on his investment. Give your answer correct to the nearest whole number. [3M] Page 4 of 7 (ii) Given A = { : 1 < 2 5 < 11, }, = { : 11 < 3 2 10, } (a) Represent A and B on number lines. (b) Also represent on the number line 1 (iii) Prove that: (a) +1 = [3M] 1 sin cos 2 (b) (sin + ) + (cos + sec )2 = 7 + tan2 + cot 2 [4M] Question 5 (i) PQRRS is a cyclic quadrilateral. Given = 73 , = 55 and = 82 . Calculate: (a) (b) (c) [3M] (ii) A manufacturer sells a camera for 10,000 to a dealer. The dealer sells it to a customer at a profit of 12%. If all the transactions are within the state and the rate of GST is 28%, calculate: (a) The GST paid by the dealer to the State Government. (b) The total tax received by the Central Government. (c) The price paid by the customer. [3M] (iii) Calculate the mean of the following distribution by step deviation method. Marks 0 10 10 20 20 30 30 40 40 50 50 60 Number of students 10 9 25 30 16 10 [4M] Question 6 (i) The three vertices of parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find (a) The co ordinates of the fourth vertex D. (b) Length of the diagonal BD. (c) Equation of side AB of the parallelogram ABCD. [3M] (ii) In the given figure, PQRS is a cyclic quadrilateral. PQ and SR are produced to meet at T. Page 5 of 7 (a) Prove that ~ (b) Find SP, if TP = 18 cm, RQ = 4 cm and TR = 6 cm. (c) Find area of the quadrilateral PQRS, if area pf = 27 2 . [3M] (iii) Tarun bought an article for 8000 and spent 1000 for transportation. He marked the article at 11,700 and sold it to a customer. If the customer had to pay 18% of the GST, find: (a) The price paid by the customer (b) SGST and CGST paid by the customer [4M] Question 7 (i) A man standing on the bank of river observes that the angle of elevation of a tree on the opposite bank is 60 . When he moves 50 m away from the bank, he find the angle of elevation to be 30 . Calculate: (a) The width of the river and (b) The height of the tree [4M] (ii) Marks obtained by 200 students in an examination are given below: Marks 0 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 100 Number of 5 11 10 20 28 37 40 29 14 6 students Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine (a) The median marks (b) The number of students who failed if minimum marks required to pass is 40? (c) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination. [6M] Question 8 (i) If 8 cards with the letter A, B, C, D, E, A, E, O written on them. When a card is randomly picked up from the set, what is the probability that it is a (a) vowel (b) consonant (c) letter E Page 6 of 7 (ii) Using componendo and dividend, find the value of x: 3 +4 + 3 5 3 +4 3 5 =9 [3M] (iii) A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm. Find: (a) its radius and (b) its slant height. [4M] Question 9 (i) x 5 10 15 20 25 30 f 6 4 6 12 8 4 (a) In the above distribution, calculate the mean. (b) If the frequency in each is doubled, what will be the new mean? (c) If each x is increase by 3, what would be the new mean? [3M] (ii) In an AP the fourth and the sixth terms are 8 and 14 respectively. Find the (a) the first term, (b) common difference, (c) the sum of the first 20 terms [3M] (iii) In an auditorium seats were arranged in rows and columns. The number of seats in each row is equal to the number of rows. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find: (a) The number of rows in the original arrangement. (b) The number of seats in the auditorium after the new arrangement [4M] Question 10 (i) Solve: ( + )2 2 ( + ) 6 = 0, + 0 [3M] 2 6 3 2 4 0 (ii) Given, = [ ], = [ ] and = [ ]. Find the matrix X such that + 2 = 2 0 4 0 0 2 2 + . [3M] (iii) Using a graph paper, plot the points A(6, 4) and B(0,4). (a) Reflect A and B in the origin to get the images A and B (b) Write the co ordinates of A and B . (c) State the geometrical name for the figure ABA B (d) Find its perimeter [4M] Page 7 of 7

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