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ICSE Class X Sample / Model Paper 2025 : Mathematics

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Maths Name: ____________________ Topics: Full paper Grade: 10 Time : 2hr 30 mins Section A Question 1: Choose the correct answers to the questions from the given options: (Do not copy the question, write the correct answers only) [15] (i) The coordinates of the point which divides the line segment joining the points (4, -3) and (9, 7) internally in the ra o 3 : 2 is (a) (7, 3) (b) (3, 7) (c) (35, 15) (d) (27, 21) (ii) If the lateral surface area of a cylinder is 94.2 cm2 and its height is 5cm, then the radius of its base is (a) 5cm (b) 3cm (c) 7cm (d)6cm (iii) g(x) = x + 1 and f(x) = x3 + 3x2 + 3x + 1, g(x) is factor of f(x) (a) True (b)False (c) Cannot Say (d) Par ally true/false (iv) A point S is re ected in the origin and the coordinates of its image are (2, -5). Find the coordinates of the image of S under the re ec on in the Y-axis is (a)(-2, -5) (b) (2, -5) (c) (2, 5) (d)(-5, - 2) (v) If 7 mes the 7th term of an AP is equal to 11 mes its 11th term, then its 18th term will be (a) 7 (b) 11 (c) 18 (d) 0 (vi) The solu on set for the given in-equa on is 3 - 2x x - 12, x e N is (a) {1,2,3,4} (b) {1,2,3,4,5} (c) {3,4,5,6} (d) {1,2,3,4,5,6} (vii) (a) x = 1, y = 1 (b) x = 0, y = 1 (c) x = 0, y = 0 (d) x = -1, y = -1 (viii) A sum of money is divided in the ra o 3: 5. If the largest part is Rs. 3125, the smallest part is (a) Rs. 1700 (b) Rs. 1875 (c) Rs. 1433 (d) Rs. 900 (ix) (d) Cannot say ti (c) isosceles triangle ti ti ti (b) right angled triangle ti fl fl ti ti (a) equilateral triangle ti All (x) In the given gure, if angle ACB = 50 , then angle ATO is (a) 30 (b) 50 (c) 40 (d)Cannot be determined (xi) Which term of the AP 5, 15, 25,. ... will be 130 more than its 31st term? (a) 42 (b) 44 (c) 46 (d)48 (xii) Which constant must be added and subtracted to solve the quadra c equa on (xiii) A man invests Rs. 5600 on Rs. 100 shares at Rs. 70. If the company pays him 18% dividend, the number of shares he bought are (a) 80 (b) 145 (c) 90 (d) 120 (xiv) Which of the following cannot be the probability of an event? (a) 1.5 (b) 3/5 (c) 25% (d) 0.3 (xv) Asser on (A): P(x) = 4x3 - x2 + 5x4 + 3x - 2 is a polynomial of degree 3. Reason (R) The highest power of x in the polynomial P(x) is the degree of the polynomial . (a) A is false, R is true (b) A is true, R is false (c) Both are true (d) Both are false Question 2: (i) Find the values of ,x ,y u and v, when [4] (ii) Mr. Amit opens a Recurring Deposit Account of Rs.300 per month at 8% simple interest per annum. On maturity, he gets Rs.9930. Find the period for which he continued with the account. [4] (iii) If a, b and c are in continued proportion, prove that [4] Question 3: (i) In the given figure, a cylinder with hemisphere on one side and a cone on the other side. Find the volume of the solid. [4] (ii) A point P divides the line joining A(-4,1) and B(17,10) in the ratio 1: .2 (a) Calculate the distance OP, where O is the origin. (b) In what ratio, does the Y-axis divide the line AB? [4] ti ti fi ti (iii) Manufacturer Tarun sells a microwave to a dealer Sonu for Rs.18000. The dealer Sonu sells it to a consumer at a profit of Rs.1800. If the sales are intra state and the rate of GST is 12%, find (a) the amount of tax (under GST) paid by the dealer Sonu to the central government. (b) the amount of tax (under GST) received by the state government. (c) what amount pays the consumer for the microwave. [5] Section B Attempt any four questions from this section Question 4: (i) Use graph paper to answer the following questions. (a) Point A(5,0) on reflection is mapped as A'(-5,0). State the equation of the mediator. (b) Show that the image of point B(4, - 3) on reflection is B'(4, 3). Also, state the equation of the mirror line. (c) Show that point C (-3, 5) is reflected in y=2and its image is C'. Also, find the coordinates of C . [3] (ii) If f(x) = x3 + lx + m leaves the same remainder 7, when divided by (x - 1) or (x + 1), find l and m. [3] (iii) Find mean by step-deviation method. [4] Question 5: (i) If the sum of the first m terms of an AP is the same as the sum of its first n terms (m n), show that the sum of its first (m + n) terms is zero. [3] (ii) Solve the following in-equation and represent the solution set on the number line. 2x - 5 5x + 4 < 11, where x e I (iii) In triangle ABC, points P and Q on sides AB and AC, are such that T such that PT = BC and PB = TC, then find the value of x. [3] If PQ is extended to [4] Question 6: (i) If the bisectors of angle A and angle B of a quadrilateral ABCD intersect each other at the point P, prove that P is equidistant from AD and BC. [3] (ii) [3] (iii) Rs. 480 can be divided equally among x children. If the number of children is increased by 20, then each child would receive Rs.12 less than the initial amount. Find the value of x. [4] Question 7: (i) A piggy bank contains hundred 50 paise coins, fifty Rs.1 coins, twenty Rs.2 coins and ten Rs.5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, then what is the probability that the coin (a) will be a 50 paise coin? (b) will not be a Rs. 5 coin ? [5] [5] (ii) In the adjoining figure, AB = 14 cm and BC = 18cm (a) Prove that triangle ACD ~ triangle DCB. (b) Find the length of DC. Question 8: (i) Draw a circle of radius 3.5 cm . Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent. [3] (ii) A tower is 64 m tall. A man standing erect at a distance of 36 m from the tower observes the angle of elevation of the top of the tower to be 60 . Find the height of the man. (root 3 =1.732). [3] (iii) [4] Question 9: (i) Find the equation of the line through (1, 3) making an intercept of 5 on the Y-axis. [3] (ii) The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1%. [3] (iii) Using ruler and compass only : (a) Construct a triangle ABC with BC = 6 cm, angle ABC = 120 and AB = 3.5 cm (b) In above figure, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. (c) Measure angle BCP. [4] Question 10: (i) A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (a) red? (b) white? (c) not green? [5] (ii) In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T and CD =7.8 cm, PD = 5 cm, PB = 4 cm. [5] Find (a) the length of AB. (b) the length of tangent PT.

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