CBSE 10th Class Sample paper 2

General Instruction

1. All the questions are compulsory
2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks cach. Section D comprises of 6 questions carrying 4 marks each.
3. There is no overall choice
4. Use of calculator is not permitted.

Section A

1. Find the LCM of 96 and 360 by using Fundamental Theorem of Arithmetic.
2. A line segment is of length 5 cm. If the coordinates of its one end are (2,2) and that of the other end are (-1, x), then find the value of x.
3. In figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA is perpendicular to PB, then find the length of each tangents.

4. The first three terms of an A.P. respectively are 3y - 1, 3y +5 and 5y +1. Find the value of y.
5. A die is thrown once. What is the probability that it shows a number greater than 4?
6. A Solid sphere of radius r is melted and cast into the shape of a solid cone of height r. Find the radius of the base of cone.
7. The graph of y= p(x) is given in the figure. The number of zeros of p(x) are
a) one
b) three
c) zero
d) two

8. In the figure DE || BC then the value of EC is
(a) 1 cm
(c) 1.5 cm
(b) 2 cm
(d) 3 cm

9. From a point Q the length of tangent to a circle is 24 cm and distance of Q from the centre is 25 cm. The radius of the circle is
(a) 7 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm
10. The angle of elevation of the top of a 15 metres high tower from a point 15 metres away from its foot is
(a) 30
(b) 45
(c) 60
(d) 90
11. The difference between the circumference and the diameter of a circle is 30 cm, then the radius of the circle is
(a) 5 cm
(b) 7.7 cm
(c) 7cm
(d)6 cm
12. Probability of event E+ Probability of event not E =
13. A polynomial of degree two is called __________ polynomial
14. The line x- y=8 intersect y-axis at (0, -8) ( T/F)
15. Number of solutions in the given pair of equations infinitely many solutions.
x+2y-8 =0
2x + 4y =16
16. 3 cot² 60° + sec² 45°
17. Cards marked with numbers 3,4,5 ..... 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box, find the probability that the selected card bears a perfect square number.
18. In the figure ∆ABC, DE||AB. IF AD=2x, DC=X+3, BE=2x-1 and CE=x then find the value of x.

19. In the figure, l|| m, ∠OAC = 80°,∠ODB = 70°. Is ∆OCA ∼ ∆ODB?

20. Find the value of k, for which one root of the quadratic equation Kx²-14x + 8 = 0 is six times the other.

Section B

21. In a single throw of a pair of different dice, what is the probability of getting (1)a prime number on each dice (ii) a total of 9 or 11?
22. A Hemispherical tank of diameter 3 m is full of water. It is being emptied by a pipe at the rate of 25/7 litre per second. How much time will it take to make the tank half empty?
23. Cards marked with numbers 13,14,15,..... 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is:
(i) a number which is a perfect square.
(ii) divisible by 5
24. The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am and 6:40 am
25. Solve for x and y:

4/x +5y= 7
3/x +4y =5

26. Show that any positive odd integer can be written in the form 6m+1,6m+3, 6m+5 where m is a positive integer.

Section C

27. Show that the cube of any positive integer is of the form 9 m, 9 m+1 or 9 m +8.
28. Find all zeroes of the polynomial 2x⁴ - 10x³ +5x²+15x-12 when its two zeroes are √(3/2) and -√(3/2)
29. Solve for x:
(x+1)/(x-1) + (x-2)/(x+2) = 4- (2x+3)/(x-2) for x ≠ - 1, -2, 2.
30. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
31. If an isosceles triangle ∆ABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, find the area of the triangle.
32. In an A.P of 50 terms, the sum of first ten terms is 210 and the sum of last 15 terms is 2565. Find the A.P.
33. Find the value of: (3 tan 41° / cot 49°)² - (sin 35° sec 55°/ (tan 10° tan 20° tan 60° tan 70° tan 80°))²
34. In the given figure ABCD is a trapezium with AB || DC and BCD = 60^o. IF BFEC is a sector of a circle with centre C and AB=BC=7 cm and DE=4 cm, then find the area of the shaded region: ( π=22/7 , √3 = 1.732)

Section D

35. Draw the graph of the following equations and answer the following questions:
x+y=5,
x-y-5=0 .
(i) Find the solution of the equations from the graph.
(ii) Shade the triangular region formed by the lines and the y-axis.
36. If A and B are (-2,-2) and (2, -4) respectively, find the coordinates of P such that AP= (3/7)AB and P lies on the line segment AB.
37. Construct ABC with BC=7 cm, ∠B = 60° and AB=6 cm. Construct another triangle whose sides are 3/4 times the corresponding sides of ∆ABC.
38. As Observed from the top of 100 m high light house from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3= 1.732)
39. A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted to form a cone of base diameter 8 cm. Find the height and the slant height of cone.
40. Find the mean and median of the following distribution: