CBSE 10th Class Sample paper 3

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. The LCM of two numbers is 1200. Which of the following cannot be their HCF?
A) 4
(b) 3
(c) 5
(d) 6
2. The median of a given frequency distribution is found graphically with the help of
(a) histogram
(b) frequency curve
(c) frequency polygon
(d) ogive
3. If the arithmetic mean of x, x+3, x+6,x+9 and x+12 is 10, then x =
(a) 1
(b) 2
(c) 6
(d)4
4. Two different dice are tossed together. The probability that the product of two numbers on the top of dice is 6 is
a) 1/3
b) 1/6
c) 1/9
(d) 2/3
5. A Cylinder, a cone and a hemisphere are of same base and have same height. The ratio of their volumes is
(a) 3:1:2
(b) 1:2:3
(c) 3:2:1
(d) 1:3:2
6. Two isosceles triangles have equal angles and their areas are in the ratio 16: 25. The ratio of their corresponding heights is
(a)4:5
(b) 5:4
(c)3: 2
(d) 5:7
7. In figure DE || BC and AD= 1/2BD. If BC= 4.5 cm , find DE.

8. If Radii of two concentric circles are 4 cm ond 5 cm. find the length of each chord of one circle which is tangent to the other circle.
9. If the diameter of a circle is increased by 40% find by how much percentage its area increases?
10. Find the discriminant of the quadratic equation 3√3x² +10x+ √3 = 0
11. Write the nth term of the A.P. 1/m, (1+m)/ m, (1+2m)/m.....
12. If x+a is a factor of 2x² + 2ax + 5x + 10, find a.
13. What is the point of intersection of the Iine represented by 3x-2y=6 and the y-axis.
14. Find the coordinates of the point on y axis which is nearest to the point (-2, 5).
15. If the ratio of the height of a tower and the length of its shadow is √3:1. What is the angle of elevation of the sun?
16. In figure PQ is a tangent point C to a circle with centre O. If AB is diameter and ∠CAB =30^o find ∠PCA

17. If a quadratic polynomial F(x) is factorisable into linear distinct factors, then the total number of real and distinct zeros of f(x) is.....
18. The distance between the points A( sinA - CosA ,0) and B (0, sinA + cosA) is....
19. Sides of two similar triangles are in the ratio 4:9. The areas of these triangles are in the ratio......
20. If tan A= 5/12 , then the value of (cos A.Sin A) cosec A is

Section B

21. Prove 3-√5 is an irrational number
22. Solve for x and y:

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

23. A solid piece of iron is in the form of a cuboid of dimensions 4.4m✕ 2.6m✕ 10m is melted to form a hollow cylinder of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
24. Following data, find the values of p and q. Also find the median class and modal class.

25. If 7sin²θ + 3 cos²θ = 4, then find value of tanθ .
26. A Box contains cards numbered from 13,14,15,........60. A card is drawn at random from the box. Find the probability that the number on the drawn card is
(i) divisible by 2 or 3
(ii) a prime number

Section C

27. Find the HCF of 180, 252 and 324 by prime factorization method:
28. Find all zeros of the polynomial 2x⁴-9x³+ 5x² + 3x-1. if two of its zeros are (2+√3) and (2-√3).
29. Solve for x:
1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3 x≠ 1, 2, 3
30. The ninth term of an A.P. is equal to seven times the second term and twelfth term exceeds five times the third term by 2. Find the first term and the common difference.
31. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
32.Two tangents TP and TQ are drawn to a circle with centre O , from an external point T. Prove that ∠PTQ = 2∠QPQ.
33. Prove that (cotθ- cosecθ)² =(1-cosθ)/(1+ cosθ)
34. In ∆ABC, ∠B=90°, BC=5 cm and AC-AB=1 cm. Find the value of sin C and cosC.

Section D

35. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
36. Determine the ratio in which the line 3x + y- 9 = 0 divides the line-segment joining the points (1,3) and (2,7).
37. The angle of elevation of the top of a building from the foot of the tower is 30 and the angle of elevation of the top of the tower from the foot of the building is 60. If the tower is 60 m high, find the height of the building.
38. Due to sudden floods, some welfare "associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs rs 100 per sq. m, find the amount, the associations will have to pay.
39. The following distribution gives the daily income of 50 workers of a factory

Convert the distribution to a less than type cumulative frequency distribution and draw its ogive. Hence obtain the median daily income.
40. Draw a circle of radius 5 cm. From a point P , 8cm away from its centre, construct a pair of tangents to the circle. Measure the length of each one of the tangents.