COURSE -7 2019
CBSE Class-X Mathematics Sample Paper 01 Time allowed: 3 Hours Max. Marks: 80 General Instructions: i. All questions are compulsory ii. The question paper consists of 30 questions divided into four sections A, B, C and D. iii. Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each. iv. There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. v. Use of calculators is not permitted. Section-A 1. Can two numbers have 18 as their HCF and 380 as their LCM? Give reason. 2. Find the root of the equation 16x2 3. Determine whet 4. The length of the shadow of a man is equal to the height of man. The angle of elevation is 10 her 50cm, 80cm, 100cm can be the sides of a right triangle or not. 5. If the perimeter & area of a circle are numerically equal, then find the radius of the circle 6. If3 coins are tossed simultaneously, then find the probability of getting at least 2 heads. Section-B 7. Is 7x 6x 5 x 4x 3x 2x 1+5 a composite number? Justify your answer. 8. The 11th term of an A.P. exceeds its 4th term by 14. Find the common difference. 9. Find the relation between and 'y', if the points (x, y), (1,2) and (7,0) are collinear. 10. Two tangents making an angle of 120 with each other are drawn to a circle of radius 6 cm, find the length of each tangent. 11. Prove that sec29+ cosec20 - sec20. cosec0 1/14 Material downloaded from myCBSEguide.com.
y CBSE^nide.com 12. A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere. Section-<C 13. Use Euclid's division lemma to show that cube of any positive integer is either of the form 9q, 9q*1 or 9q + 8 for some integer 'q'. 14. Obtain all other zeroes of x4 - 5x3- 2x2- 40x -48 if two of its zeroes are 2vV2and-22 15. Solve for 'x': 16. How many terms of the series 54, 51, 48... .e taken so that their sum is 513? Explain the double answer. In an AP pth, qth and r'h terms are respectively a, b and c. Prove that p(b c)+q(c-a) r(a -b)-0 17. The point A(3, y) is equ distant from the points P(6,5) and Q(0,-3). Find the value ofy. Or If A (4, 6), B (3,-2) and C (5, 2) are the vertices of A ABC, then verify the fact that a median of a triangle ABC divides it into two triangles of equal areas 18. If cos0 - sine- V2sin0, prove that cos0+sin0 - V2sin0 19. An observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45 . What is the height of the chimney? From the top of a 7m high building, the angle of elevation of the top of a cable tower is 600 and the angle of depression of the foot of the tower is 30 . Find the height of the tower 20. A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed in Km per hour in which the boy is cycling 21. The following table shows the gain in weight by 50 children in a year. Calculate modal gain in weight. 2/14 Material downloaded from myCBSEguide.com.
Gain in weight (in kg) 1-3 3-5 5-7 7-9 9-11 11-13 No. ofchildren 10 Compute the Median for the given data Class-interval Frequency 100-110 110-120 120-130 130-140 140-150 150-160 6 35 4S 100 32. What is the probability that a leap year. selected at random will contain 53 Thursdays? Section-D 23 Solve graphically the following equations 2x 3y 9x-2y -1. Shade the region bounded by the two lines and the x axis. Or Check graphically whether the pair of equations x -y- s and x-2y 2 is consistent. If sio solve them graphically. Also find the coordinates of the points where the two lines meet they-ais. 24. Athief away from a Police Station with a uniform speed 100m minutes. After one minute a Policeman runs behind the thief to catch him. He goes at a speed of 100m/minute in first minute an minutes the Policeman catches the thief. Now answer these questions: Which mathematical concept is being used to solve the above problem? ii Which trait of personality of the policeman is showed? d increases the speed 10m minute on each succeeding minute. After how many 25. In the adjoining figure, PQR, is a right triangle, right angled at Q. X and Y are the points on PQ and QR such that PX : XQ = 1 :2 and QY:R-2:1, Prove that 9(PF-XR-)-13 PR- Material downloaded from mrCBSEguide.com. 3/14
myCBSEguide.omn A quadrilateral ABCD is drawn to circumscribe a circle (fig-2). Prove that, AB CD AD+ . 26. Prove that the lengths of two tangents drawn from an external point to a circle are equal. 27. Construct an isosceles triangle whose base is 7cm and altitude 5 cm and then constru<ct another triangle whose sides are 3 times the corresponding sides of the isosceles triangle. Suppose a person is standing on a tower of height 15(V3+1)m and observing a car coming towards the tower. He observed that angle of depression changes from 30 to 45 in 3 seconds. Find the speed of the car. 29. A container ope ns at the top and made up of metal sheet is in the form of a frustum of cone of respectively. Find the cost of metal sheet used to make the container, if it 100cm2. (Use T-3.14) height 16cm with diameters of its lower and upper ends as 16cm and 40cm costs Rs.10 per 30. The mean of the following frequency distribution is 47. Find the value of p'. Classes 0-20 20-40 40-60 60 -80 80 -100 Frequency 15 20 Compute the mode for the following frequency distribution. Size of items:0448 8-12 12-1616-20 20-40 24-28 28-32 32-36 36-40 Frequency:5 7 917 1210 Material downloaded from myCBSEguide.com. 4/14
Section A Can ro numbors ha 18as hairHCF 3 go thair LCM7 Give eason? 380 aluas a acho HCF but8 is not a uation l6o jo 32 5 16 6
side 3 Determine whether Socm 8o cm, loocmesthe ot a sigkt tangeer not 50 CM 80 cm 10,000 50 0 +6400 0,000 8go0 Hence the idde, Hene ven side do not make a Because it dees not- at rian to man The en 's . 0
equal , then Bind the dlhe arcle 4oabji ot getting at as2 haads No Passible tcomus8 e LCHHH) , (HHT) , (HTH), (HTT), (TH ), (THT),(TTH CTTT] No avo rabla out cemes ( Head) than probability
Dr Pratibha Gupta
My name is Dr.pratibha Gupta .I am a teacher . My experience has been in teaching for math and science subject for several years in Delhi.