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MOCK TEST MATHEM SUBJECT CLASS X SUBJECT- MATHEMATICS SESSION: - 2024-2025 SESSION: - 2022-2023 F.M. 80 TIMESECTION- A [ATTEMPT ALL] Question:1 Choose the correct answer of the question from the given option: [1 (i) When a x + 6 x +4 x + 5 is divided by (x + 3), the remainder is 7. The value of constant a is (a) 2 (ii) (b) 2 (c) 3 (d) -3 Kuntal gets 6260 at the end of one year at the rate of 8% per annum in a recurring deposit account. The monthly installment paid by him is (a) 200 (b) 250 (c) 500 (d) 560 (iii) In the figure given below, O is the center of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, then the radius of the circle. (a) 11cm (b) 11.25 cm (c) 11.5 cm (d) 11.75 cm (iv) In the below figure, if AOB = 125 , then COD is equal to (v) (a) 62.5 (b) 45 (c) 35 (d) 55 When the shadow of a pole h metres high is 3h metres long, the angle of elevation of the Sun is (vi) (vii) (a) 30 (b) 60 (c) 45 (d) 15 Assertion: If we join two hemispheres of same radius along their bases, then we get a sphere. Reason: A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is 3.3 m a) Both Assertion and Reason are correct and reason is correct explanation for the. b) Both Assertion and Reason are false but reason is not correct explanation for assertion. c) Assertion is correct but reason is false. d) Both Assertion and reason are false. If the mean of frequency distribution is 7.5 and fi xi = 120 + 3k, fi = 30, then k is equal to: (a) 40 (b) 35 (c) 50 (d) 45 (viii) A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then what is the probability of getting red balls only? (a) 3 (b) 8 (c) 3/8 (d) 8/3 (ix) If A = [aij] is a square matrix of order 2 such that aij = 1, when i j and aij = 0, when i = j, then A2 is (a) [ (x) ] (b [ ] (c) [ (d ) ] [ ] Input GST paid by the shopkeeper to the dealer is 5000 and output GST collected by the shopkeeper from a consumer is 5,500. GST paid by the shopkeeper to the government is (xi) (xii) (a) 5,000 (b) 5,500 ( c) 500 ( d ) 1,000 What sum should a person invest in Rs. 25 shares, selling at Rs. 36, and obtain an income of Rs. 720, if the dividend declared is 12%? ( a) 5,000 (b) 6,000 (c) 7,000 (d) 8,000 The roots of the equation x 5 x + 6 = 0 are (a) 6, 1 (b) 2, 3 (c) 1, 6 (d) 2, 3 (xiii) The equation of the line AB parallel to the x-axis as shown in the figure is (a) x = 2 (b) y = 2 (c) x = 2 (d) y = 2 (xiv) If the replacement set is the set of whole numbers (W), the solution set of the inequation 5x + 4 24 (a) {1, 2, 3, 4} (c) {4, 5, 6} (xv) (b) { , 2, 1, 0, 1, 2, 3, 4} (d) {0, 1, 2, 3, 4} The (n 1)th term of an A.P. is given by 7,12,17, 22, is (a) 5n + 2 (b) 5n + 3 (c) 5n 5 (d) 5n 3 QUESTION 2 (i) Using the factor theorem, Utsab show that (x 2) is a factor of x3 + x2 4x 4. (a) Is Utsab correct? Give reason. Hence factorize the polynomial completely. (ii) (iii) The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find: (a) The gradient of EF (b) The equation of EF (c) The coordinates of the point where the line EF intersects the x-axis. If I is the incentre of triangle ABC and AI when produced meets the circumcircle of triangle ABC in point D. If BAC = 66o and ABC = 80o. Calculate: (i) DBC, (ii) IBC, (iii) BIC (iv) [4+4+4=12] QUESTION 3 (i) In a GP., the third term is 24 and 6th term is 192. Find the 10th term. Also find the sum of first 5 terms. (ii) A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is 4(2/3) m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel. (iii) Use a graph sheet for this question.Take 1 cm = 1 unit along both x and y axis. (a) Plot the following points: A(0,5), B(3,0), C(1,0) and D(1, 5) (b) Reflect the points B, C and D on the y axis and name them as B , C and D respectively. (c) Write down the coordinates of B , C and D . (d) Join the points A, B, C, D, D , C , B , A in order and give a name to the closed figure ABCDD C B . [4+4+5=10] SECTION B ( Attempt any four questions from this Section ) QUESTION 4 (i) (ii) Ashok invests Rs. 26400 on 12% Rs. 25 shares of a company. If he receives a dividend of Rs. 2475, find: (a) The number of shares he bought. (b) The market value of each share. Solving the following inequation, write the solution set and represent it on the number line (x 7) 15 7x > (i) ,x R 2 (cot A 1)/ (2 sec A) = cot A/ (1 + tan A) [3+3+4=10] QUESTION 5 (i) n the adjoining figure, CBA is a secant and CD is tangent to the circle. If AB=7 cm and BC=9 cm, then, (a) Prove that ACD~ DCB. (b) Find CD (c) Find ACD: DCB. (ii) Ashish deposits a certain sum of money every month is a Recurring Deposit Account for a period of 12 months. If the bank pays interest at the rate of 11% p.a. and Ashish gets Rs 12,715 as the maturity value of this account, what sum of money did he pay every month? Calculate the mean of the following distribution by Step Deviation Method (iii) Class interval 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 8 5 12 35 24 16 [3+3+4=10] QUESTION 6 (i) (ii) Find the value of a for which the following points A (a, 3), B (2,1) and C (5, a) are collinear. Hence find the equation of the line. In the adjoining figure, medians AD and BE of ABC meet at the point G, and DF is drawn parallel to BE. Prove that (i) EF = FC (ii) AG : GD = 2 : 1 (iii) Find the amount of bill for the following inter-state transaction of goods/services. The GST rate is 18%. [3+3+4=10] Quantity (no. of items) 35 47 20 MRP of each item (in Rs.) 420 600 350 Discount % 10 10 20 QUESTION 7 (i) With reference to the given figure, a man stands on the ground at point A, which is on the same horizontal plane as B, the foot of the vertical pole BC. The height of the pole is 10 m. The man s eye s 2 m above the ground. He observes the angle of elevation of C, the top of the pole, as xo, where tan xo = 2/5. Calculate: (a) the distance AB in metres; (b) angle of elevation of the top of the pole when he is standing 15 metres from the pole. Give your answer to the nearest degree. (ii) The weight of 50 workers is given below: Weight in kg 50-60 60-70 70-80 80-90 90-100 100-110 110-120 No. of workers 4 7 11 14 6 5 3 Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis , and 2 cm = 5 workers along the other axis. Use a graph to estimate the following: (a) the upper and lower quartiles. (b) the median (c) if weighing 95 kg and above is considered overweight find the number of workers who are overweight. [5+5=10] QUESTION 8 (i) (ii) Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is: (a) 8 (b) 13 (c) less than or equal to 12 If (a + b + c + d) (a b c + d) = (a + b c d) (a b + c d), prove that a: b = c: d. (iii) Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that the width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m. (iv) Find the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc. [3+3+4=10] QUESTION 9 (i) Draw a histogram and estimate the mode for the following frequency distribution : Classes 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 2 8 10 5 4 3 (ii) The 15th term of an A.P. is 3 more than twice its 7th term. If the 10th term of the (iii) A.P. is 41, find its nth term. ( The roots of equation ( :2q=p+r, that is, p,q & r are in A.P. ( are equal . Prove that [3+3+4=10] QUESTION 10 (iv) The speed of an ordinary train is x km per hr and that of an express train is (x +25) km per hr. (a) Find the time taken by each train to cover 300 km. (b) If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train. (v) . (vi) Find + AC 5B. Using ruler and compass construct a triangle ABC where AB = 3 cm, BC = 4 cm and ABC = 90o. Hence construct a circle circumscribing the triangle ABC. Measure and write down the radius of the circle. [3+3+4=10]
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