Page 1 : Sample/Pre-Board Paper 8, Class X Term 1 Exam Nov -Dec 2021, Mathematics (Standard) 041, , Time Allowed: 90 minutes Maximum Marks: 40, General Instructions:, 1. The question paper contains three parts A, B and C., 2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions., 5. There is no negative marking., , SECTION A, Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 1., , 2., , The LCM of smallest two digit composite number and, smallest composite number is, , 5., , Which of the following cannot be the probability of, an event?, , (a) 12, , (b) 4, , (a), , (c) 20, , (d) 44, , (c) 3%, , For which value(s ) of p , will the lines represented by, the following pair of linear equations be parallel, , 6., , 3x − y − 5 = 0, 6x − 2y − p = 0, , 1, 3, , (b) 0.1, (d), , 17, 16, , Sides of two similar triangles are in the ratio 4 : 9., Areas of these triangles are in the ratio., (a) 2 : 3, , (b) 4 : 9, , (c) 81 : 16, , (d) 16 : 81, , (a) all real values except 10, (c) 5/2, , If cos A = 4 , then the value of tan A is, 5, (b) 34, (a) 35, , (d) 1/2, , (c), , (b) 10, , 3., , 4., , 7., , It is given that, TABC + TEDF such that, AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm, then the sum of the remaining sides of the triangles is, (a) 23.05 cm, , (b) 16.8 cm, , (c) 6.25 cm, , (d) 24 cm, , In the given figure, TABC ~TPQR. The value of, y + z will be, , 8., , 9., , 4, 3, , (d), , 5, 3, , The decimal expansion of the rational number 14587, 1250, will terminate after, (a) one decimal place, , (b) two decimal places, , (c) three decimal places, , (d) four decimal places, , If x = a and y = b is the solution of the equations, x − y = 2 and x + y = 4 , then the values of a and b, are, respectively, (a) 3 and 5, , (b) 5 and 3, , (c) 3 and 1, , (d) − 1 and − 3, , 10. The distance of the point (− 12, 5) from the origin is, , (a) 2 2 + 3, , (b) 3 3 + 4, , (c) 3 2 + 1, , (d) 2 3 + 2, , (a) 12, , (b) 5, , (c) 13, , (d) 169, , 11. If one zero of the quadratic polynomial x2 + 3x + k is, 2, then the value of k is, (a) 10, , (b) − 10, , (c) − 7, , (d) − 2

Page 2 : 12. If a = 23 # 3 , b = 2 # 3 # 5 , c = 3n # 5, LCM (a, b, c) = 23 # 32 # 5, then n is, (a) 1, , (b) 2, , (c) 3, , (d) 4, , and, , (b) –2, , (c) 1, , (d) –1, , (d) 3368 m2, , 16. TABC and TBDE are two equilateral triangle such, that D is the mid-point of BC . Ratio of the areas of, triangles ABC and BDE is ................. ., , 13. sin2 60c − 2 tan 45c − cos2 30c = ?, (a) 2, , (c) 1694 m2, , 14. In the given figure, AOB is a diameter of a circle with, centre O, The value of tan A tan B. will be, , (a) 1 : 1, , (b) 3 : 1, , (c) 2 : 1, , (d) 4 : 1, , 17. Two similar triangles ABC and PQR have their areas, 25 cm2 and 49 cm2 respectively. If QR = 9.8 cm, what, is the length of side BC ?, (a) 2 cm, , (b) 5 cm, , (c) 7 cm, , (d) 4 cm, , 18. If x = 3 sin θ + 4 cos θ and y = 3 cos θ − 4 sin θ then, x2 + y2 is, , (a) 1, (c), , (d) 3, , 15. If a circular grass lawn of 35 m in radius has a path, 7 m wide running around it on the outside, then the, area of the path is, (a) 1450 m2, , (b) 45, , (c) 7, , (d) 49, , 19. Given the linear equation 3x + 4y = 9 . Select another, linear equation in these two variables such that the, geometrical representation of the pair so formed is, intersecting lines., , (b) 2, 3, , (a) 25, , (b) 1576 m2, , (a) 3x − 5y = 10, , (b) 6x + 8y = 18, , (c) 8x + 12y = 18, , (d) above all, , 20. The probability of getting a number greater then 3 in, throwing a die is, (a), , 1, 3, , (b), , 1, 4, , (c), , 3, 4, , (d), , 2, 3, , SECTION B, Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 21. If p1 and p2 are two odd prime numbers such that, p1 > p2 , then p 12 − p 22 is, (a) an even number, (b) an odd number, , (a), , 2, 3, , (b), , 7, 2, , (c), , 5, 3, , (d), , 5, 2, , 24. A fraction becomes 4 when 1 is added to both the, numerator and denominator and it becomes 7, when 1 is subtracted from both the numerator and, denominator. The numerator of the given fraction is, , (c) an odd prime number, (d) a prime number, 22. If A ^ m3 , 5h is the mid-point of the line segment joining, the points Q (− 6, 7) and R (− 2, 3), then the value of, m is, (a) − 12, , (b) − 4, , (c) 12, , (d) − 6, , 23. If sin θ − cos θ = 1 , the value of sin θ + cos θ will be, 2, , (a) 2, , (b) 3, , (c) 5, , (d) 15, , 25. If zeroes of the polynomial x2 + 4x + 2a are a and 2 ,, a, then the value of a is, (a) 1, , (b) 2, , (c) 3, , (d) 4

Page 3 : 26. A number is chosen at random from the numbers − 5 ,, − 4 , − 3 , − 2 , − 1, 0, 1, 2, 3, 4, 5. Then the probability, that square of this number is less than or equal to 1, is .......... ., (a), , 9, 11, , (b), , 3, 11, , (c), , 8, 11, , (d), , 7, 11, , 27. A number x is selected at random from the numbers, 1, 2, 3 and 4. Another number y is selected at, random from the numbers 1, 4, 9 and 16. What is the, probability that product of x and y is less than 16?, (a), , 1, 2, , (b), , 5, 16, , (c), , 9, 16, , (d), , 7, 16, , 28. If cos θ + cos θ = 4; θ # 90º the value of θ will, 1 − sin θ 1 + sin θ, be, (a) 30°, , (b) 45°, , (c) 60°, , (d) 90°, , 29. If the point P ^2, 1h lies on the line segment joining, points A ^4, 2h and B ^8, 4h , then, (a) AP = 13 AB, , (b) AP = PB, , (c) PB = 13 AB, , (d) AP = 12 AB, , 30. Triangle TABC is right angled at C. If p is the length, of the perpendicular from C to AB and a, b, c are, the lengths of the sides opposite +A, +B and +C, respectively, then 12 is equal to, p, (b) aa ++ bb, (a) aa −+ bb, 2, , (c), , 1, a2, , 2, , 2, , + b1, , 2, , (d), , 2, , lengths of sides of each triangle., , The length of side AB is, (a) 9, , (b) 12, , (c) 15, , (d) 24, , 35. In what ratio does the point ^ 24, 11 , y h divides the line, segment joining the points P ^2, − 2h and Q ^3, 7h ?, Also find the value of y., (a) 2 : 9, , (b) 2 : 7, , (c) 7 : 5, , (d) 6 : 5, , 36. If the difference between the circumference and the, radius of a circle is 37 cm, then using π = 227 , what is, the circumference of the circle?, (a) 44π cm, , (b) 44 cm, , (c) 22 cm, , (d) 22π cm, , 37. In given figure APB and AQP are semi-circle, and, AO = OB . If the perimeter of the figure is 47 cm,, what is the area of the shaded region? Use π = 227 ., , 2ab, a2 + b2, , 31. What is the ratio in which the straight line, x − y − 2 = 0 divides the line segment joining ^3, − 1h, and ^8, 9h ?, (a) 5 : 6, , (b) 4 : 5, , (c) 3 : 4, , (d) 2 : 3, , 32. If, , sin φ, 1 + cos φ, = 4 then φ is equal to, +, 1 + cos φ, sin φ, , (a) 9º, , (b) 90º, , (c) 45º, , (d) 30º, , 33. Select the smallest number which is divisible by both, 306 and 657., , (a) 231 cm2, , (b) 155.5 cm2, , (c) 55.5 cm2, , (d) 111 cm2, , 38. If the zeroes of the quadratic, x2 + ^a + 1h x + b are 2 and − 3 , then, (a) a = − 7, b = − 1, , (a) 16498, , (b) 22398, , (b) a = 5, b = − 1, , (c) 22338, , (d) 16414, , (c) a = 2, b = − 6, , 34. In Figure, if TABC + TDEF and their sides of, lengths (in cm) are marked along them, then find the, , (d) a = 0, b = − 6, , polynomial

Page 4 : 39. In given figure, ABCD is a square with side 2 2, cm and inscribed in a circle. What is the area of the, shaded region? (Use π = 3.14 )., , (a) 9.2 cm2, , (b) 4.6 cm2, , (c) 12.4 cm2, , (d) 8.4 cm2, , 40. In the figure, ABCDE is a pentagon with BE z CD, and BC z DE . BC is perpendicular to CD. AB = 5 cm,, AE = 5 cm, BE = 7 cm, BC = x − y and CD = x + y., If the perimeter of ABCDE is 27 cm. The value of x, and y , will be, , (a) 3 and 2, , (b) 2 and 3, , (c) 1 and 6, , (d) 6 and 1, , SECTION C, Case study based questions:, Section C consists of 10 questions of 1 mark each. Any 8 questions are to be attempted., Case Based Questions: (41-45), Pyramid, in architecture, a monumental structure, constructed of or faced with stone or brick and having, a rectangular base and four sloping triangular sides, meeting at an apex. Pyramids have been built at, various times in Egypt, Sudan, Ethiopia, western Asia,, Greece, Cyprus, Italy, India, Thailand, Mexico, South, America, and on some islands of the Pacific Ocean., Those of Egypt and of Central and South America are, the best known., , length of a side of the square base ?, (a) 9 (y + 3), , (b) 9 (y + 3) 2, , (c) 3 (y + 3), , (d) 3 (y + 3) 2, , 42. If area of base is 576 metre, what is the side of base?, (a) 24 metre, , (b) 16 metre, , (c) 13 metre, , (d) 12 metre, , 43. What is the height of pyramid at above area of base ?, (a) 4 metre, , (b) 6 metre, , (c) 5 metre, , (d) 12 metre, , 44. What is the ratio of length of side to the height ?, (a), , 1, 5, , (b), , 2, 5, , (c), , 5, 24, , (d), , 24, 5, , 45. What is surface area of pyramid ?, , The volume and surface area of a pyramid with a, square base of area a2 and height h is given by, ha2, 2, V = 3 and S = a2 + 2a ^ a2 h + h2, A pyramid has a square base and a volume of, 3y 3 + 18y2 + 27y cubic units., 41. If its height is y , then what polynomial represents the, , (a) 800 m2, , (b) 2400 m2, , (c) 1200 m2, , (d) 1600 m2, , Case Based Questions: (46-50), Satellite Images : Satellite images are images of, Earth collected by imaging satellites operated by, governments and businesses around the world., Satellite imaging companies sell images by licensing, them to governments and businesses such as Apple, Maps and Google Maps. It should not be confused for, astronomy images collected by space telescope.

Page 5 : 46. What is the distance between grocery store and food, court?, (a), , 137 cm, , (c) 8 15 cm, , (b), , 129 cm, , (d) 16 3 cm, , 47. What is the distance of the school from the house?, , Barun lives in Jaipur in Vaishali. Satellite image of his, colony is shown in given figure. In this view, his house, is pointed out by a flag, which is situated at the point, of intersection of x and y - axes. If he goes 2 cm east, and 3 cm north from the house, then he reaches to a, grocery store, If he goes 4 cm west and 6 cm south, from the house, then he reaches to his office. If he goes, 6 cm east and 8 cm south from the house, then he, reaches to a food court. If he goes 6 cm west and 8 cm, north from the house, he reaches to a his kid’s school., Based on the above information, answer the following, questions., , (a) 10 cm, , (b) 15 cm, , (c) 20 cm, , (d) 25 cm, , 48. If the grocery store and office lie on a line, what is the, ratio of distance of house from grocery store to that, from office ?, (a) 2 :1, , (b) 3 : 1, , (c) 4 : 1, , (d) 5 : 1, , 49. What is the ratio of distances of house from school to, food court., (a) 1 :1, , (b) 2 : 1, , (c) 3 : 1, , (d) 4 : 1, , 50. What shape is formed by the coordinates of positions, of school, grocery store, food court and office?, (a) square, , (b) rectangle, , (c) rhombus, , (d) quadrilateral