Tenth Std/ SSLC/ 10th Standard : Maths Sample Question Paper Samacheerkalvi
Name of the Organization : Samacheerkalvi Tamil Nadu
Name Of The Exam : 10th Maths
Document type : Model Question Paper
Website : samacheerkalvi.in
Download Sample/Model Question Papers :https://www.pdfquestion.in/uploads/5135-Maths.pdf
Samacheerkalvi Maths Sample Question Paper
Time Allowed : 21/2 Hours
Maximum Marks : 100
Related : Samacheerkalvi Tamil Nadu Class X Social Science Model Question Paper : www.pdfquestion.in/5155.html
INSTRUCTION : Check the question paper for fairness of printing.
Section II :
Note :
(i) Answer 10 questions.
(ii) Question No. 30 is Compulsory. Select any 9 questions from the first 14 questions.
(iii) Each question carries Two marks
1. If A = {4, 6, 7, 8, 9}, B = {2, 4, 6} and C = {1, 2, 3, 4, 5, 6}, then find A ∪ (B ∩ C).
2. 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.
3. 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.
4. 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.
5. A ladder leaning against a vertical wall, makes an angle of 60° with the ground. The foot of the ladder 3.5m away from the wall. Find the length of the ladder.
6. A right circular cylinder has radius of 14cm and height of 8cm. Find its curved surface area.
7. The circumference of the base of a 12m high wooden solid come is 44m. Find the volume.
8. Calculate the standard deviation of the first 13 natural numbers.
9. Two coins are tossed together. What is the probability of getting at most one head.
Section − III :
Note :
(i) Answer 9 questions.
(ii) Question No. 45 is Compulsory. Select any 8 questions from the first 14 questions.
(iii) Each question carries Five marks
1. Use Venn diagrams to verify De Morgan’s law for set difference A \ (B ∩ C) = (A \ B) ∪ (A \ C).
2. 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.
3. Find the area of the quadrilateral formed by the points (− 4, − 2), (− 3, − 5), (3, − 2) and (2, 3).
4. The vertices of ABC 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.
5. A boy is designing a diamond shaped kite, as shown in the figure where AE = 16 cm, EC = 81 cm. He wants to use a straight cross bar BD. How long should it be?
6. A vertical tree is broken by the wind. The top of the tree touches the ground and makes an angle 30° with it. If the top of the free touches the ground 30m away from its foot, then find the actual height of the tree
7. Using clay, a student made a right circular cone of height 48cm and base radius 12cm. Another student reshapes it in the form of a sphere. Find the radius of the sphere.
8. 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.
9.(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 2.8 cm. Find the diameter of each leadshots.
Section − IV :
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
1. (a) Draw the two tangents from a point which is 10cm away from the centre of a circle of radius 6cm. Also, measure the lengths of the tangents.
(OR)
(b) Construct ABC in which the base BC = 5cm, ∠BAC = 40° and the median from A to BC is 6cm. Also measure the length of the altitude from A.
2. (a) Draw the graph of y = x2 − x − 8 and hence find the roots of x2 − 2x − 15 = 0.
(OR)
(b) A cyclist travels from a place A to a place B along the same route at a uniform speed on different days. The following table gives the speed of his travel and the corresponding time he took to cover the distance.
Draw the speed-time graph and use it to find.
(i) The number of hours he will take if he travels at a speed of 5 km/hr.
(ii) The speed with which he should travel if he has to cover the distance in 40 hrs.