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CBSE CLASS X MATHEMATICS SUBJECT SAMPLE PAPER

General Instructions:
1.All questions are compulsory.
2.The question paper consists of 30 questions divided into four sections – A, B, C and D. Section A contains 10 questions of 1 mark each, Section B is of 5 questions of 2 marks each, Section C is of 10 questions of 3 marks each and section D is of 5 questions of 6 marks each.
3.In question on construction, the drawing should be neat and exactly as per the given measurements.
4. In question on construction, the drawing should be neat and exactly as per the given measurements.
5.Use of calculator is not permitted.
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SECTION – A

1. Is number 5 x 3 x 17 + 17 a prime number?
2. The sum and product of the zeroes of the quadratic polynomial are – ½ and – 3. What is the quadratic polynomial?
3. For what value of k for which the pair of linear equations 10x + 5y = ( k – 5 ) and
20x + 10y = k have infinitely many solutions.
4. If Tan A = ¾ and A+B = 90, then what is the value of Cot B?
5. In ABC, DE||BC, AD:DB = 1.5cm:3cm and AE=1 cm , find EC.
6. Find Emperical formula for finding the mode.
7. A sphere of radius 10.5 cm is melted and then recast into smaller cones of radius 3.5 cm and height 3 cm. find the number of cones.
8. From a point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre of circle is 13cm. Find the diameter of the circle.
9. A bag contains 4 white, 3 red and 2 black balls. A ball is drawn at random from the bag. Find the probability that it is not a white ball.
10. Find the value of m so that m+2, 4m–6 and 3m– 2 are three consecutive terms of an A.P.
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SECTION – B

11. Find the discriminant of the equation 3x¬2 – 2x + 1/3 = 0 and hence find the nature of its roots. Find them, if they are real.
12. In ABC,angle ACB = 90 and CD perpend. AB. Prove that CB2 : CA2 = BD : AD.
13. Find the ratio in which the line 2x + 3y – 30 = 0 divides the line segment joining the points ( 3, 4 ) and ( 7, 8). Find also the coordinates of the point of section.
14. A circle touches all the four sides of a quadrilateral ABCD.
Prove that AB + CD = BC + DA.
15. If the zeroes of the polynomial x3 – 3×2 + x + 1 are a – b, a and a + b, find the value of a and b.
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SECTION –C

16. Show that √3 is irrational.
17. Prove that : tan A + sec A – 1 = 1 + sin A
________________ _________
tan A – sec A + 1 cos A
18. A bag contains 50 balls bearing 1, 2, 3,………., 49, 50. A ball is drawn at random from the bag. Find the probability that the number on the ball is :
a. not divisible by 5 b. divisible by 7 or 11.
19. Solve the pair of equations: 44 + 30 = 0 and 55 + 40 = 13.
_______ _____ _____ ____
x + y x – y + y x – y
20. Find the area of the minor and major segment of a circle, given that the central angle is 600 and radius of the circle is 14 cm.
21. Which term of an A.P 3, 10, 17…………. will be 84 more than its 13th term?
22. Two circles of radii 2 cm and 3 cm with their centres 7 cm apart. Draw the tangents from the centre of each circle to the other circle.
23. Find the ratio in which the point P( m, 6 ) divides the join of A( – 4, 3 ) and B ( 2, 8 ). Also find the value of m.
24. A two digit number is such that product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.
25. In ABC, right angle at B. AD and CF are the two medians drawn from A and C, if AC = 5 cm and AD = ( 3√5) / 2 cm, find the length of CE.
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SECTION –D

26. In a flight of 600 km an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/h and the time of flight increased by 30 minutes. Find the duration of the flight.
27. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream, also find the silver paper required to cover each ice cream cone.
28. Prove that the ratio of the areas of two similar triangles is equal to the ratio of squares of their correspond sides.
Using the above, prove the following : the diagonal of a trapezium ABCD with AB||DC intersects each other at the point O. If AB = 2CD, find the ratio of the area of triangle AOB to the area of triangle COD
29. From a window h metres above the ground of a house in a street, the angle of elevation and depression of the top and the foot of another house on the opposite side of the street are A and B respectively. Show that the height of the opposite house is h(1 + tan A cot B ).
30. The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
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