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CBSE Class 10 Board Exam 2025 :

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Anirudh Ramesh
Regent Education & Research Foundation Group of Institutions, Kolkata

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lOMoARcPSD|61290839 B COIMBATORE SAHODAYA SCHOOLS COMPLEX PRE BOARD EXAMINATION (DEC 2022) GRADE : X MARKS: 80 DATE : MATHEMATICS(041) TIME : 3 HRS General Instructions: 1. This Question Paper has 5 Sections A-E. 2. Section A has 20 MCQs carrying 1 mark each 3. Section B has 5 questions carrying 02 marks each. 4. Section C has 6 questions carrying 03 marks each. 5. Section D has 4 questions carrying 05 marks each. 6. Section E has 3 case based integrated units of assessment (04 marks each) with subparts of. the values of 1, 1 and 2 marks each respectively. 7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks questions of Section E 8. Draw neat figures wherever required. Take =22/7 wherever required if not stated. SECTION A Section A consists of 20 questions of 1 mark each. 1. A quadratic polynomial whose sum of zeros is 5 & their product is 6 is (a) x 2 + 5x (b) x 2 5x +6 2. If n is a natural number then (a) 5 (b) 13 (c) x 2 5x +6 (c) both 5 & 13 (b) 6 (c) 3 4. If the equation a x 2 + 2x (a) a = 1 (d) x 2 + 5x +6 92n 42n is always divisible by (d) none of these 3. The value of k for which the system of equations x has no solution (a) 10 6 + 2y 3 = 0 & 5x + k y + 7 = 0 (d) 1 + a = 0 has two distinct roots if (b) a = 0 (c) a = 0,1 (d) a = 1, 0 5. If k, 2k 1 & 2k + 1 are three consecutive terms of an AP the value of k is (a) 2 (b) 3 (c) 3 (d) 6 6. The fourth vertex D of a Parallelogram ABCD whose three vertices are A( 2, 3), B(6, 7) and C(8, 3) is (a) (0, 1) (b) (0, 1) (c) ( 1, 0) (d) (1, 0) Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) lOMoARcPSD|61290839 7. If ABC and DEF are similar such that 2AB = DE and BC = 8cm then EF = _______ (a) 16cm (b) 12cm (c) 8cm (d) 4cm 8. If ABC, D & E are points on side AB & AC respectively such that DE || BC and AD : DB = 3 : 1. If EA = 3.3cm then AC = (a) 1.1cm (b) 4cm (c) 4.4cm (d) 5.5cm 9. If two tangents inclined at an angle of 60 are drawn to a circle of radius 3 cm, then the length of each tangent is equal to (a) 3 3 cm 2 (b) 6cm 10. If Cosec = 2 & cot (a) 1 = (a) 1/ 2 12. If cos ( 3 cm 3a then the value of a is (b) 2 11. If for some angle , cot 2 (d) 3 (c) 3cm 3 (c) 1 = 3 (b) 2 3 (d) 2/ then the value of sin 3 , where 3 (c) 0 90 is 3 /2 (d) + ) = 0 then the value of sin ( + ) is (a) sin (b) sin 2 (c) cos (d) cos 2 13. If the areas of 2 circles are in the ratio 4 : 9 then the ratio of the perimeters of their semicircles is (a) 2 : 3 (b) 3 : 2 (c) 1 : 2 (d) 1 : 3 14. If the angle of elevation of the top of a tower from a point on the ground 100m away from the foot of the tower is 30 then the height of the tower is (a) 100m (b) 100 3m (c) 100/ 3m 15. The sum of the length, breadth and height of a cuboid is 6 diagonal is 2 (a) 48cm2 3 cm. The total surface area of the cuboid is (b) 72cm2 (c) 96cm2 (d) 75 3 cm & the length of its (d) 108cm2 16. If the arithmetic mean of x, x + 3, x + 6, x + 9 and x + 12 is 10 then x = (a) 1 (b) 2 (c) 6 3m (d) 4 Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) lOMoARcPSD|61290839 17. Which of the following is not a measure of central tendency ? (a) mean (b) median (c) mode (d) standard deviation 18. A number was chosen at random from first 300 three digit natural numbers. The probability that the selected number has zero at units place is (a) 1/15 (b) 1/25 (c) 1/10 (d) 1/20 DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option 19. Statement A (Assertion) : Two congruent triangles are always similar. Statement R( Reason) : If areas of two similar triangles are equal, then they are congruent. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 20. Statement A (Assertion) : The sum of 20 terms of the A.P 1, 3, 5, 7 is 400 Statement R( Reason) : The sum of first n odd natural numbers is n2. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. SECTION B Section B consists of 5 questions of 2 marks each. 21. In what ratio does the point P( 4,6) divide the line segment joining the points A( 6,10) and B(3, 8) Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) lOMoARcPSD|61290839 22. In an equilateral triangle of side 24 cm, find the length of the altitude (OR) In ABC, D and E are the points on CA and CB respectively such that DE II AB. AD = 2x, DC = x + 3, BE = 2x 1 and CE = x. Find the value of x 23. Prove that the length of the tangents drawn from an external point to a circle are equal. 24. From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same height and same base radius is removed. Find the volume of the remaining solid. (OR) A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5cm and the total height of the solid is 9.5 cm. Find the volume of the solid. 25. A horse is tethered to one corner of a rectangular field of dimensions 70m x 52 m by a rope of length 21m. Find the area of the field that the horse can graze. SECTION C Section C consists of 6 questions of 3 marks each. 26. Solve for x & y : a x + by = a+b ; 3x + 5y = 4 2 27. In the given figure the tangents at P and Q of a circle intersect at point T. If PQ is a chord of length 8cm of the circle of radius 5 cm and centre O, find the length of TP. Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) lOMoARcPSD|61290839 ( OR) If a, b and c are the sides of a right triangle where c is the hypotenuse. A circle of radius r, touches the sides of the triangle. Prove that r = a+b c 2 28. Divide 56 into four parts in A.P such that the ratio of the product of their extremes (1st and 4th) to the product of the means( 2nd and 3rd) is 5 : 6. 29. If two adjacent vertices of a parallelogram are (3,2) and ( 1,0) and the diagonals intersect at ( 2, 5) then find the co-ordinates of the other two vertices. 30. If x sin3 + y cos3 = sin cos and x sin = y cos , prove that x2 + y2 = 1 (OR) Prove that : cosA sin A = cosA sin A 1 + tan A 1 + cot A 31. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a i) face card ii) black king or a red queen iii) spade SECTION D Section D consists of 4 questions of 5 marks each. 32. Prove that 5 is an irrational number and hence show that 2 irrational number. 5 is also an 33. A boy observes that the angle of elevation of a bird flying at a distance of 100m is 30 . At the same distance from the boy a girl finds the angle of elevation of the same bird from a building 20 m high is 45 . Find the distance of the bird from the girl. (OR) An aeroplane is flying at a height of 300 m above the ground. Flying at this height the angle of depression from the aeroplane of two points on both banks of the river in opposite direction are 45 and 60 . Find the width of the river. 34. One -fourth of a herd of camels was seen in a forest. Twice the square root of the herd had gone to the mountain and remaining 15 camels were seen on the bank of a river. Find the total number of camels. Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) lOMoARcPSD|61290839 35. The following distribution gives the weight of 60 students of a class. Find the mean and modal weights of the students. Weight in kgs Number of students 40 44 44 48 4 6 48 52 52 56 56 60 60 64 64 68 10 14 10 8 68 72 6 (OR) Literacy rates of 40 cities are given below in the table. It is given that mean literacy rate is 63.5. Find the missing frequencies x and y. Literacy rate( in %). Number of cities 35 40 1 40 45 2 45 50 3 50 55 x 55 60 y 60 65 6 65 70 8 70 75 4 75 80 2 80 85 3 85 90 2 SECTION E Case study based questions are compulsory. 36. An barrels manufacturer can produce up to 300 barrels per day. The profit made from the sale of these barrels can be modelled by the function P(x) = 10x2 + 3500x 66000 where P (x) is the profit in rupees and x is the number of barrels made and sold. Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) 2 lOMoARcPSD|61290839 Based on this model answer the following questions: (i) When no barrels are produce what is a profit loss? (ii) What is the profit/loss if 175 barrels are produced OR (iii) What is the profit/loss if 400 barrels are produced (iv) What is the break even point ? (Zero profit point is called break even) 37. Rohan is very intelligent in maths. He always try to relate the concept of maths in daily life. One day he is walking away from the base of a lamp post at a speed of 1 m/s. Lamp is 4.5 m above the ground. (i) If after 2 second, length of shadow is 1 meter, what is the height of Rohan ? (ii) What is the minimum time after which his shadow will become larger than his original height? (iii) What is the distance of Rohan from pole at this point ? Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com) lOMoARcPSD|61290839 OR (iv) What will be the length of his shadow after 4 seconds? 38. Underground water tank is popular in India. It is usually used for large water tank storage and can be built cheaply using cement-like materials. Underground water tanks are typically chosen by people who want to save space. The water in the underground tank is not affected by extreme weather conditions. The underground tanks maintain cool temperatures in both winter and summer. Electric pump is used to move water from the underground tank to overhead tank. Ramesh has build recently his house and installed a underground tank and overhead tank. Dimensions of tanks are as follows : Underground Tank : Base 2 m x 2 m and Height 1.1 m. Overhead tank : Radius 50 cm and Height 175 cm (i) What is the capacity of the underground tank ? (ii) What is the ratio of the capacity of the underground tank to the capacity of the overhead tank? (iii) If curved part of overhead tank need to be painted to save it from corrosion, how much area need to be painted? OR (iv) If water is filled in the overhead tank at the rate of 11 litre per minute, the tank will be completely filled in how much time? Downloaded by Anirudh Ramesh (anirudhramesh289@gmail.com)

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