## CLASS: X

### General Instruction:

(i) All the questions are compulsory.
(ii)The question paper costs of 40 questions divided into 4 sections ABC, and D
(iii) Section A comprises of 20 questions of 1 marks each. Section B comprises of 6 questions of 2 marks Section B comprises of 8 questions of 3 marks each. Section D comprises of 6  questions of 4 marks each.

#### SECTION -A

Questions 1 to 20 carry 1 mark each.

1. LCM of two co-prime numbers is always

(a) product of number
(b) sum of numbers
(c) difference of numbers.
(d)none

2 .For some integer q. every odd integer is of the form
(a)q
(b)q+1
(c)2q
(d)2q+1

3.$\sqrt{3}$ is

(a) a natural number
(b) a rational number
(c) not o a real number
(d) an irrational number

4. The product and sum of zeroes of the quadratic polynomial x2 + bx + c respectively are:

(a) b  ,   c
a      a

(a) c  ,   b
a      a

(a) c  ,   1
b

(a) c ,   -b
a      a

5. The ratio in which x-axis divides the line segment joining the points (5, 4) and (2-3) is
(a) 5:2
(b) 3:4
(C) 2:5
(d) 4: 3

6. Point on y-axis has coordinates

(a)(a,b)
(b)(a,0)
(c) (0,6)
(d) (-2, -b)

7 .From a point P,10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn Find the radius of the circle

(a)4 cm
(b) 5 cm
(c) 7 cm
(d)6 cm

8.

9. A box contains 3 blue, 2 white, and 5 red marbles. If a marble is drawn at random from the box then what is the probability that the marble will be blue ?

(a)  3,
10

(b) 1
2

(c) 1

(a)  0

11. The end points of diameter of circle are (2,4) and (-3,1). The radius of circle is _____

12. Value of tan 30 - cos 45 is ______

13. The value of san60° cos 30° - cos 60°sin30° is_____

14. 1f ∆ABC and ∆DEF are two triangles such that AB. = BC  = CA  =2 , Then ar(∆ABC) =
DE.     EF.     FD.   5            ar(∆DEF)

15. If (6, k) sa solution of the equation 3x + y-22=0, then the value of k is

16. Find the area of a sector of a circle with radii 6 cm if angle of the sectors is 90°.

17. IF P(E) = 0 47, what is the probability of 'not E'?

18. Find the 9th term from the end (towards the first term) of the AP 5,9.,13,..... ,185.

19. 1f  cot2© =tan1© , where 2θ nd 4θ are acute angles, find the value of sin 3θ.

20.ABC and BDE are two equilateral triangles such that D is the  midpoint of BC .Find the ratio of the areas of triangles ABC and BDE

### SECTION B Questions 21 to 26 carry 2 marks each

21. Three cards of spades are lost from a pack of 52 playing cards The remaining cards were well stuffed and then a card was drawn al random from them .Find the probability that the drawn cards of black colour

OR

Find the probability that a leap year should have exactly 52 Tuesday.

22. Two different dice are tossed together. Find the probability (i) that the Number on each dice is  Even (ii) that the sum of numbers appear on two dice is 5.

23. A wie s loped in the form of a circle of radan 28 cm .It reverted into a square form.Determine the side of the square.

24. Show that tan48° tan 23° tan 42°tan 67° =1

25. Find a quadratic polynomial whose zeroes are -5 and 7.

26. A quadrilateral ABCD is drawn to circumscribe circle Prove that AB + CD = AD + BC.

### SECTION -C Questions 27 to 34 carry marks each.

27.Find the HCF and LCM of 180 and 288 by prime factorisation method.

28 To conduct Sports Day activities, in your rectangular aided 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 1m from each other along AD, as shown in the  figure Aditi name 1/5th the distance AD on the 2nd lne and posts a green fag Priyanka runs 1/4th the distance AD on the eighth line and posts a red flag
(i) What is the distance between both the flags?

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

29. Find the zeroes of the quadratic polynomial 9t - 6t + 1, and verify the relationship between the zeroes and the coefficients.

30. Solve the following system of equations graphically for x and y 3x + 2y= 12, 5x-2y=4

31. Prove that The lengths of the two tangents from an external point to a circle are equal.

32. Draw a line segment of length 9 cm and divide in the rate 3:4. Measure the two parts.

33. Prove that. A conec Ayrcos A CAY - 7+ A+ cor A

OR

Prove that

setan

14 sin A 1-m 4

34. In the below for sure OABC is inscribed quadrant OPBQ. If OA =20 cm, find the area of the shaded region.(Use Π= 3.14)

### SECTION -D Questions 35 to 40 carry marks rach

35. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

36. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

37. Find the sum of first 24 terms of the list of numbers whose nth term is given by An= 3 + 2n

38.Prove that If Image is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio

OR

State and prove converse of Pythagoras theorem

39. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

40.