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CBSE Pre Board Class 10 2021 : Mathematics (New Horizon Public School (NHPS), Panvel)

10 pages, 62 questions, 4 questions with responses, 4 total responses,

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Government Engineering College (GEC), Thrissur

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NEW HORIZON PUBLIC SCHOOL CBSE Affiliation No. 1130164 Sector-13, Khanda Colony, New Panvel (W)- 410206 Preparatory Examination 1 Subject: Mathematics Name: Roll No: Grade: X Div: Max Marks : 80 Max Time : 3 Hrs Date:21/12/2020 General Instructions: 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part A: 1. It consists three sections- I and II. 2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part B: 1. Question No 21 to 26 are Very short answer Type questions of 2 mark each, 2 .Question No 27 to 33 are Short Answer Type questions of 3 marks each 3. Question No 34 to 36 are Long Answer Type questions of 5 marks each. 4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks. PART-A SECTION-I Section I has 16 questions of 1 mark each. Internal choice has been provided in 5 questions. Q1. Find the zeroes of the polynomial( ) = 2 2 9 + 9. Q2. In a triangle ABC, DE BC and AE = a, EC = b, Find the value of DE / BC. Q3. If 2k + 1, 6, 3k + 1 are in AP, then find the value of k. OR Q3. Find the A.P : 3/2, 1/2, -1/2, -3/2,.Write the first term a and the common difference d . Q4. Find the radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm. Q5. Circumference of a circle exceeds its diameter by 180 cm. Find its radius. Q6. The graph of y = p(x) , where p(x) is a polynomial in variable x , is as follows. Find the number of zeroes. Q7. Find the value of K, the pair of linear equations 3x+y=3 and 6x+ ky = 8 does not have a solution. Q8. Check whether the given pair of linear equation is consistent/inconsistent? X y=8 3x - 3y =16 Q9. Find the 10th term of the A.P. : 2,7,12,............. OR Q9. Find the A.P : 3/2, 1/2, -1/2, -3/2,. .................. Write the first term a and the common difference d . Q10. Find the value(s) of a in the quadratic equation 30 ax2 -6x +1 =0 has no real roots? Q11. How many tangents can a circle have? OR Q11. A line intersecting a circle in two points is called a ........................ Q12. In the given figure if B1,B2 and A1, A2, A3 have been marked at equal distances . In what ratio point C divides line segment AB? Q13. If 2 + + = 0 has real and distinct roots, find the value of c. Q14. In the given figure, PA and PB are tangents to the circle drawn from an external point P. CD is the third tangent touching the circle at Q. If PA = 15 cm. Find the perimeter of the triangle PCD. OR Q14. In a circle of radius 21 cm arc subtends an angle of 60 degree at the centre. Find the length of arc. Q15. For what value of k do the equations 3 + 8 = 0 & 6 = 16 represents coincident lines. Q16. Find the value of sin300 + cos600. OR Q16. Find the probability of getting a red jack when a card is drawn at random from a well- shuffled pack of 52 cards. Section-II Case study based questions (Q.17 TO Q.20) are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark Q 17. Case Study Based-1 CRICKET FIELDING POSITIONS AND PLAYERS In sport of cricket the captain sets the field according to a plan. He instructs the players to take a position at a particular place. There are two reasons to sets a cricket field - to take wickets and to stop runs being scored. The following graph shows the position of players during a cricket match. a. If the distance between the points showing the players at Gully A (1,0) and as a wicketkeeper B (4, p) is 5m, then p = 4m (II) 8 m (III) 6 m (IV) 9 m b. Suppose the length of a line segment joining the players of Mid- off and Mid - on be 10 units. If the (I) coordinates of its one end are (2, -3) and the abscissa of the other end is 10 units, then its ordinate is (I) 9 , 6 (II) 3, -9 (III) -3 , 9 (IV) 9 , -6 c. The coordinate of the point on x-axis which are equidistant from the points representing the players at Cover P(-3,4) and Mid- wicket Q(2,5) are (I) (20,0) (II) (-23,0) (III) (4/5,0) (IV) None of these d. The ratio in which (4,5) divides the line segment joining the points Extra Cover S (2,3) and Fine Leg(7,8) is (I) 4:3 (II) 5:2 (III) 3:2 (IV) 2:3 e. If the points (4,3) and (x,5) are on the circular field with centre (2,4), then the value of x is (I) 0 (II) 1 (III) 2 (IV) 3 Q18. CASE STUDY BASED- 2 Underground water sump is popular in India. It is usually used for large water sump storage and can be built cheaply using cement-like materials. Underground water sump are typically chosen by people who want to save space. The water in the underground sump is not affected by extreme weather conditions. The underground sump maintain cool temperature in both winter and summer. A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by ( ) = 3 + 2 4 4 a. He planned in such a way that its base dimensions are ( + 1) & ( + 2). How much he has to dig? I) ( + 1) II) ( + 2) III) ( 2) IV) ( 3) b. If is 4 meter, what is the volume of sump? I) 30 3 II) 15 3 III) 20 3 IV) 60 3 c. If = 4 and the builder wants to pant the entire inner portion on the sump, what is the total is to be painted? I) 102 2 II) 74 2 III) 96 2 IV) none of these d. If the cost of paint is Rs.25 per square meter, what is the cost of painting? I) Rs.1300 II) Rs.2600 III) Rs.1850 IV) Rs.5200 e. What is the storage capacity of this tank? I) 3000 L II) 6000 L III) 30000 L IV) 60000 L Q19. Case Study Based 3 Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below a. Name the shape in which the wire is bent (I) Spiral (II) ellipse (III) linear (IV) Parabola b. How many zeroes are there for the polynomial( shape of the wire) (I) 2 (II) 3 c. The zeroes of the polynomial are (I) -1,5 (II) -1,3 (III) 1 (IV) 0 (III) 3,5 (IV) -4,2 d. What will be expression of the polynomial? (I) x2 + 2x - 3 (II) x2 - 2x + 3 (III) x2 - 2x - 3 (IV) x2 + 2x + 3 e. What is the value of the polynomial if x= -1 (I) 6 (II) -18 (III)18 (IV) 0 Q20. CASE STUDY BASED- 4 Mr. RK Agrawal is owner of a famous amusement park in Delhi. Generally he does not go to park and it is managed by team of staff. The ticket charge for the park is Rs.150 for the children and Rs.400 for adults. One day Mr. Agrawal decided to random check the park and went there. When he checked the cash counter, he found that 480 tickets were sold and Rs.134500 was collected. a. Let the number of children visited be x and the number of adults visited be y. Which of the following is correct system of equation model the problem? I) + = 480 & 3 + 8 = 2690 II) + 2 = 480 & 3 + 4 = 2690 III) + = 480 & 3 + 4 = 2690 IV) + 2 = 480 & 3 + 8 = 2690 b. How many children attended? I) 250 II) 230 III) 500 IV) 260 III) 500 IV) 260 c. How many adults attended? I) 250 II) 230 d. How much amount collected if 300 children and 350 adults attended? I) 185000 II) 154000 III) 225400 IV) none of these e. One day total attended children and adults together is 750 and the total amount collected is Rs.212500. What are the number of children and adults attended? I) (700, 800) II) (350, 400) III) (800, 700) IV)(400, 350) Part B All questions are compulsory. In case of internal choices, attempt any one. Q. 21 to Q.26 Carry 2 marks each Q21. Consider the number 4n, where n is a natural number. Check whether there is any value of n, for which 4n ends with the digit zero. Q22. If P(a/3, 4) is the midpoint of the line segment joining the points Q( 6,5) and R( 2,3), then the find the value of a . OR Q22. If the distance P(x,y) from the points A(3,6) B(-3,4) are equal, prove that 3x+y= 5 Q23. Find a quadratic polynomial whose zeroes are (5 3 2) and (5+3 2) Q24. Draw a line segment AB of length 9cm. With A and B as centers, draw circles of radius 5cm and 3cm respectively. Construct tangents to each circle from the centre of the other circle. Q25. If tan(A+B)= 3and tan(A-B)=1/ 3 ; 0 < (A + B) 90 ; A > B, find A and B. OR Q25. Express the trigonometric ratio sin A, in terms of cot A . Q26. Two concentric circles are of radii 5cm and 3cm. length of the chord of the larger circle, (in cm), which touches the smaller circle is.? Q. 27 to Q 33 carry 3 marks each. Q27. Prove that 3 is an irrational number. Q28. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel makes in 10 minutes when the car is travelling at a speed of 66 km per hour? Q29. Show that in a right triangle, the square of the hypotenuse is equal to sum of squares of the other two sides. OR Q29. The following distribution shows the daily pocket allowance of children of a locality. Find Median pocket allowance of the following data. 11 13 Daily Pocket allowance (in Re) Number of children 3 13 15 15 17 17 19 19 21 21 23 23 25 6 9 13 8 5 4 Q30. Using quadratic formula, solve the following equation for : 2 + ( 2 ) = 0. OR Q30. In the given fig., DE || AC and DF || AE. Prove that BF /EF = BE/ EC Q31. A kite is attached to a string. Assuming that there is no slack in the string , find the height of the kite above the level of the ground if the length of the string is 54 m and it makes an angle of 30 with the ground. Q32. Find the Mode of distribution given below. Class internal Frequency 0 10 10 20 20 30 30 40 40 50 50 60 Total 5 4 20 15 3 5 20 Q33. In given figure ABC is a quadrant of circle of radius 14 cm and the semicircle is drawn with BC as diameter find the area of the shaded region, Q. 34 to Q.36 carry 5 marks each Q 34 .The angle of elevation of a jet plane from a point A on the ground is 60 after a flight of 15 seconds, the angle of elevation changes to 30 . If the jet plane is flying at a constant height 1500 3 meter find the speed of a jet plane. OR Q 34. A man standing on the deck of a ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 60 degree and the angle of depression of the base of the hill as 30 degree. Calculate the distance of the hill from the ship and the height of the hill. Q35. A hemispherical tank full of water is emptied by a pipe at the rate of 3 4 litres per second. How 7 much time will it take to half empty the tank, if the tank is 3 metres in diameter? (Take = 22/7) Q 36. Solve the following pair of equations by reducing them to a pair of linear equations.

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