Tenth Std / SSLC / 10th Standard : Maths Sample Question Paper Samacheerkalvi

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Document Described : Maths Paper, Tamil Nadu Question Paper

Sample Question Paper - Class - X
MATHEMATICS
Time: 2.30 Hrs.] [Maximum Marks: 100
General Instructions:
(i) This question paper consists of four sections. Read the note carefully under each Section before answering them.
(ii) The roughwork should be shown at the bottom of the pages of the Answer book.
(iii) Use of Calculator and electronic devices not permitted.

SECTIon – A
Note: (i) Answer all the 15 questions
(ii) Choose the correct answer in each question. Each of these questions contains four options with just one correct option
(iii) Each question carries One mark 15 × 1 = 15
1. Let A = { 1, 3, 4, 7, 11 }, B = {–1, 1, 2, 5, 7, 9 } and : f A B " be given by f = { (1, –1), (3, 2), (4, 1), (7, 5), (11, 9) }. Then f is
(A) one-one (B) onto (C) bijective (D) not a function
3 (B) 0 (C) a 12 1 (D) a 14 1
4. The LCM of , , x y x yz x y z 6 9 12 2 2 2 2 is
(A) x y z 36 2 2 (B) xy z 48 2 2 (C) x y z 96 2 2 2 (D) xy z 72 2
5. If b = a + c , then the equation 0 ax bx c 2
+ + = has
(A) real roots (B) no roots (C) equal roots (D) no real roots
8. The perimeter of a triangle formed by the points (0, 0), (1, 0), (0, 1) is
(A) 2 (B) 2 (C) 2+ 2 (D) 2– 2
10. Chords AB and CD cut at P inside the circle; If AB = 7, AP = 4, CP = 2, then CD =
(A) 4 (B) 8 (C) 6 (D) 10
11. A man is 28.5 m away from a tower. His eye level above the ground is 1.5 m. The angle of elevation of the tower from his eyes is 45c. Then the height of the tower is
(A) 30 m (B) 27.5 m (C) 28.5 m (D) 27 m
(A) sin cos i i + (B) sin cos i i (C) sin cos i i - (D) cose c cot i i +
13. If the total surface area of a solid hemisphere is 12r cm2 then its curved surface area is equal to
(A) 6r cm2 (B) 24r cm2 (C) 36r cm2 (D) 8r cm2
14. Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of variation is
(A) 42 (B) 25 (C) 28 (D) 48

SECTIon – B
Note: (i) Answer 10 questions
(ii) Answer any 9 questions from the first 14 questions. Question No. 30 is Compulsory.
(iii) Each question carries Two marks 10 × 2 = 20
16. If {4, 6, 7, 8, 9}, { 2, 4, 6} {1, 2 , 3, 4, 5, 6} A B C and = = = , then find A B C , + ^ h.
17. Let X = { 1, 2, 3, 4 }. Examine whether the relation g = { (3, 1), (4, 2), (2, 1) } is a function from X to X or not. Explain.
18. Three numbers are in the ratio 2 : 5 : 7. If 7 is subtracted from the second, the resulting numbers form an arithmetic sequence. Determine the numbers.
19. If a and b are the roots of the equation 2 3 1 0 x x 2
- - = , find the value of a b - if > a b
22. The centre of a circle is at (-6, 4). If one end of a diameter of the circle is at the origin, then find the other end.
26. A right circular cylinder has radius of 14 cm and height of 8 cm. Find its curved surface area.
27. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.
28. Calculate the standard deviation of the first 13 natural numbers.
29. Two coins are tossed together. What is the probability of getting at most one head.

SECTIon – C
Note: (i) Answer 9 questions
(ii) Answer any 8 questions from the first 14 questions. Question No. 45 is Compulsory.
(iii) Each question carries Five marks 9 × 5 = 45
31. Use Venn diagrams to verify De Morgan’s law for set difference \ \ \ A B C A B A C + , = ^ ^ ^ h h h.
33. Find the sum of the first 2n terms of the series 1 2 3 4 2 2 2 2 g - + - +
34. Factorize the polynomial 5 2 24 x x x 3 2
- - +
35. If 28 12 9 m nx x x x 2 3 4
- + + + is a perfect square, then find the values of m and n.
36. The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.
38. Find the area of the quadrilateral formed by the points (-4, -2), (-3, -5), (3, -2) and (2 , 3).
39. The vertices of ABC 3 are A(2, 1), B(6, –1) and C(4, 11). Find the equation of the straight line along the altitude from the vertex A.
44. The probability that a new car will get an award for its design is 0.25, the probability that it will get an award for efficient use of fuel is 0.35 and the probability that it will get both the awards is 0.15. Find the probability that
(i) it will get atleast one of the two awards (ii) it will get only one of the awards.
45. (a) The sum of three consecutive term in an A.P. is – 6 and their product is 90. Find the three numbers.
[oR]
(b) A Cylindrical jar of diameter 14cm and depth 20cm is half-full of water . 300 leadshots of same size are dropped into the jar and the level of water raises by 2.8cm. Find the diameter of each leadshots.

SECTIon – D
Note: (i) This section contains Two questions, each with two alternatives.
(ii) Answer both the questions choosing either of the alternatives.
(iii) Each question carries Ten marks 2 ×10 = 20
46. (a) Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 6 cm.
Also, measure the lengths of the tangents.
[oR]
(b) Construct a D ABC in which the base BC = 5 cm, +BAC = 40° and the median from A to BC is 6 cm. Also measure the length of the altitude from

[Guest]

In triangle ABC, angle BAC=90 degree and segment AD is perpendicular to BC.
Prove that
1. triangle DBA is similar to triangle DAC
2. AD*AD=BD*DC

[Guest]

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