### Sample Paper 1 | Based on full NCERT | MATHS | Class 10

SUBJECT: MATHEMATICS
SAMPLE PAPER 1
CLASS : X
MAX. MARKS: 80
DURATION : 3 HRS

General Instruction:

(i) All the questions are compulsory.

(ii) The question paper consists of 40 questions divided into 4 sections A, B, C, and D.

(iii) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of 4 marks each.

(iv) Use of calculators is not permitted.

SECTION - A

1.The decimal expansion of pie
(a) is terminating
(b) is non terminating and recurring
(c) is non-terminating and non-recurring
(d) does not exist.

2.The product of L.C.M and H.C.F. of two numbers is equal to
(a) Sum of numbers
(b) Difference of numbers
(c) Product of numbers
(d) Quotients of numbers

3. What is the H.C.F. of two consecutive even numbers
(a) 1
(b)2
(c) 4
(d) 8

4. A quadratic polynomial can have at most... zeros
(a) 0
(b) 1
(c)2
(d) 3

5. Which are the zeroes of p(x) = (x - 1)(x-2):

(a) 1,-2
(b) - 1,2
(c) 1,2
(d)-1,-2

6. X-axis divides the join of A(2.-3) and B(5,6) in the ratio
(a) 3:5
(b) 2:3
(c) 2:1
(d) 1:2

7. If the distance between the points (8. p) and (4.3) is 5 then value of p is
(a) 6
(b) 0
(c) both (a) and (b)
(d) none of these

8. TP and TQ are the two tangents to a circle with center O so that angle POQ = 130°. Find angle PTQ.

(a) 50°
(b) 70
(c) 80"
(d) none of these

9. Cards are marked with numbers 1 to 25 are placed in the box and mixed thoroughly. What is the probability of getting a number 5?

(a) 1
(b) 0
(c) 1
25

(d) 1
5

10. The value of y for which the points A(1.4), B(3. y) and C-3, 16) collinear is

11. If  ∆ABC is right-angled at B, then the value of cos(A + C) is

12. If tanA =  , then the value of cosA is
3
13. In ABC, DE || BC and AD = 4 cm, AB =9 cm. AC = 13.5 cm then the value of EC is

14. The value of k for which the quadratic equation 4x 3kx +1=0 has real and equal roots

15. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the sector formed by the arc

16. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out a lemon flavoured candy?

17. In ∆ ABC, right-angled at B, AB = 5 cm and ㄥACB = 30° then find the length of the side BC

18. If sin 30 = cos(0-6) here, 30 and (0-6°) are acute angles, find the value of 0.

19. For what value of p, are 2p+1, 13,5p - 3 three consecutive terms of an AP?

20. The areas of two similar triangles ABC and ADEF are 144 cm and 81 cm, respectively. If the longest side of larger ABC be 36 cm, then find the longest side of the similar triangle ADEF.

SECTION B

21.15 cards, numbered 1,,. 3,. . ,15 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card is drawn bears (i) an even number (ii) a number divisible by 3.

22. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card is drawn is neither an ace nor a king.

23. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in three minutes. [Use pie = 22/7]

24.If tan A = cot B, prove that A+B= 90°

25. If the product of the zeroes of the polynomial    is 4, then find the value of a. Also, find the sum of zeroes of the polynomial.

26. The two tangents from an external point P to a circle with centre O are PA and PB. If APB = 70°, what is the value of AOB?

SECTION C

27. Prove that     is an irrational number.

28. Find the zeroes of the quadratic polynomial      and verify the relationship between the zeroes and the coefficients of the polynomial.

29. Given   linear equation 3x - 5y = 1 form another linear equation in these variables such that the geometric representation of pair so formed is: (i) intersecting lines (ii) coincident lines (iii) parallel lines.

30. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the below figure. Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag.

(i) What is the distance between both the flags?

(ii) If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

31. Prove that:

32. Construct a triangle ABC with BC = 7 cm. ㄥB = 60° and AB = 6 cm. Construct another triangle whose sides are times the corresponding sides of AABC.

OR

Draw a line segment of length 10 cm and divide it in the ratio 3:5. Measure the two parts.

33. In the below figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

34. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

SECTION D

35. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see the below figure). Find the distance travelled by the balloon during the interval.

36. In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

37. Show that a1 ......... form an AP where an is defined as the first 15 terms in each case.
=9-5n. Also find the sum of

38. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
OR
State and prove Basic proportionality theorem,

39. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. (Take pie =3.14)