Maths Topper`s Answer Sheet - 2019, Class 10 | Extra Documents, Videos & Tests for Class 10 PDF Download

General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 30 questions divided into four sections — A, B, C and D.
(iii) Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each.
(iv) There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
(v) Use of calculators is not permitted.

Section - A

1. If tan ∝ = 5/12, find the value of sec ∝.
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2. Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.
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3. Write the discriminant of the quadratic equation (x + 5)² = 2 (5x – 3).
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4. Express 429 as a product of its prime factors.
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5. Find the sum of the first 10 multiples of 6.
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6. The distance between point A (5, – 3) and B (13, m) in 10 units. Calculate the value of m.
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Section - B

Question numbers 7 to 12 carry 2 marks each.
7. A die is thrown once. Find the probability of getting (i) a composite number, (ii) a prime number. 
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8. Cards numbered 7 to 40 were put in a box. Poonam selects a card at random. What is the probability that Poonam selects a card which is a multiple of 7?
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9. In parallelogram ABCD, A(3, 1), B(5, 1) C(a, b) and D(4, 3) are the vertices. Find vertex C(a, b).
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10. Solve below simultaneous equations for x and y,. 3x – 5y = 4 and 9x – 2y = 7.
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11. If HCF of 65 and 117 is expressible in the form 65n – 117, then find the value of n.
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12. For what value of k, the given quadratic equation kx² – 6x – 1 = 0 has no real roots?
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Section-C

Question numbers 13 to 22 carry 3 marks each.
13. If tan (A + B) = 1 and tan (A – B) = 1/√3, 0° < A + B < 90°, A > B, then find the values of A and B.
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14. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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15. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

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16. A wiper blade has length 21 cm, sweeps 120°. Calculate the area swept by two blades. 
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17. In similar triangle, ΔABC and ΔPQR, AD and PM are the medians respectively Prove that AD/PM = AB/PQ.
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18. Verify g(x) = x³ – 3x + 1 in a factor of P(x) = x⁵ – 4x³ + x² + 3x + 1 or not.
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19. Prove that √3 is an irrational number.
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20. In ΔABC, A is (1, – 4). E(0, – 1) and D (2, – 1) are the midpoints of AB and AC. Calculate the area of ΔABC.
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21. Two numbers are in the ratio of 5 : 6. If 7 is subtracted from each there ratio becomes 4 : 5. Find the numbers.
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22. A Cylindrical task of radius 40 cm in filled upto height 3.15 m by an other cylindrical pipe with the rate of 2.52 km/h in 1/2 hour. Calculate the diameter of cylindrical pipe? 
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Section - D

Question numbers 23 to 30 carry 4 marks each.
23. In Figure, a decorative block is shown which is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 6 cm and the hemisphere fixed on the top has a diameter of 4·2 cm. Find (a) the total surface area of the block. (b) the volume of the block formed.  ( Take π = 22/7)

OR

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308·8 cm³. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use p = 3·14)

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24. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 
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25. Change the following distribution to a ‘more than type’ distribution. Hence draw the ‘more than type’ ogive for this distribution.

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26. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. Find the height of the tower. (Given √3 = 1·732)
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27. If m times the m^th term of an Arithmetic Progression is equal to n times its n^th term and m ≠ n, show that the  (m + n)^th term of the A.P. is zero.
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28. A shopkeeper buy certain number of books in ₹80. If he buy 4 more books then new cost price of each book is reduced by ₹1. Find the number of books initially he buy.  
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29. Construct a pair of tangents to a circle of radius 4 cm from an external point at a distance 6 cm from the centre of the circle.
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30. Prove that : 

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