## Maths CBSE Model Paper

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Time allowed : 3 hours Maximum Marks : 100 | |||||||||||||||||||||||||||||||||||||||||||||||

General Instructions :(i) Question number 1 to 10 carry 3marks each. (Section A ) (ii) Question number 10 to 20carry 4 marks each. (Section B) (iii) Question number 21 to 25 carry 6 marks each. (Section C ) (iv) Write the serial number of the question before attempting it. (v) Use of logarithmic and trignometric tables is permitted. Use of calculator is not permitted | |||||||||||||||||||||||||||||||||||||||||||||||

(Section A ) | |||||||||||||||||||||||||||||||||||||||||||||||

1. | Determine K so that the equation x ^{2} + 4x – K = 0 has two equal roots. | ||||||||||||||||||||||||||||||||||||||||||||||

2. | A rectangular piece of paper is 44 cm long and 20 cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder. | ||||||||||||||||||||||||||||||||||||||||||||||

3.
| Calculate the mean and mode of 21, 16, 15, 14, 15, 18, 17, 22, 28, 15, 26, 15 .OR
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4 | From the diagram given below calculate (i) AB (ii) AP (iii) DAPC : DABC | ||||||||||||||||||||||||||||||||||||||||||||||

5 | If the areas of three adjacent faces of cuboid are p, q and r and volume is v, prove that V ^{2} = p q r | ||||||||||||||||||||||||||||||||||||||||||||||

6 | Prove that Sin(90-q) Cos (90-q) = (1-sin ^{2}q} tanq | ||||||||||||||||||||||||||||||||||||||||||||||

7 | If x^{3} + y^{3} / x^{3} - y^{3} = 91 / 37 . Show that x : y = 4 :3 | ||||||||||||||||||||||||||||||||||||||||||||||

8 | Aarti buys a saree costing Rs. 2500/- at Rs. 2700/- after paying sales tax. Find side of square whose diagonal is 12 cm. | ||||||||||||||||||||||||||||||||||||||||||||||

9 | 3x + 2y = 6 ;(k + 1 )x + 4y = (2k + 2) For what value of k, will the above system of equation have infinite solution. | ||||||||||||||||||||||||||||||||||||||||||||||

10 | The mean of 5 numbers is 15. If one number is excluded, the mean becomes 12.5, find the excluded number. | ||||||||||||||||||||||||||||||||||||||||||||||

Section | |||||||||||||||||||||||||||||||||||||||||||||||

11. | In figure ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC = 92 ^{o}, FAE = 20 ^{o}, find BCD. | ||||||||||||||||||||||||||||||||||||||||||||||

12. | In a trapezium PQRS, PQ || SR and SR = 2 PQ. XY drawn parallel to PQ cuts PS in X and QR in Y such that . Diagonal QS intersects XY in Z. Prove that . | ||||||||||||||||||||||||||||||||||||||||||||||

13.
| Find the GCD of the polynomials 4(X-3) If | ||||||||||||||||||||||||||||||||||||||||||||||

15. | In the given figure DE || BC and AD : DB = 5 : 4 Find ( DFE)/( CFB) | ||||||||||||||||||||||||||||||||||||||||||||||

16. | Draw a cyclic quadrilateral ABCD in which BD = 4cm,A = 90 ^{0}, CD = 2.5cm and AB = 3cm | ||||||||||||||||||||||||||||||||||||||||||||||

17. | Calculate cost of living index from the following data :-
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18. | An aeroplane takes 1 hour less for a journey of 1200 km. If its speed is increased by 100 km/hr, from its usual speed, find its usual speed. | ||||||||||||||||||||||||||||||||||||||||||||||

19. | The dimensions of a rectangular tank are 2 m, 7 m and 2 m. It is being filled with water using a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s. Calculate the time required to fill the tank. | ||||||||||||||||||||||||||||||||||||||||||||||

20. | 80% and 60% pure acid solutions are mixed to obtain 10 litres of 75% pure acid solution . Find the amount of each type of acid to be mixed to form the mixture. | ||||||||||||||||||||||||||||||||||||||||||||||

SectionC | |||||||||||||||||||||||||||||||||||||||||||||||

21a . b | Draw graphically the following equations: 2y = + 4x x + 2y = 4 | ||||||||||||||||||||||||||||||||||||||||||||||

A circle with centre O. AB and CD are two parallel chords on the same side of the centre. If the radius of the circle is 65 cm and the length of the chords are 112 cm and 126 cm respectively, find area of rectangle ABCD. | |||||||||||||||||||||||||||||||||||||||||||||||

22a . | Construct ABC such that AXB = 116 ^{o}, AB = 7.8 cm, CF = 5 cm, CF AB.X is the point of intersection of the altitudes AD and BE. Measure seg. AC | ||||||||||||||||||||||||||||||||||||||||||||||

23 | Page from a saving bank passbook for the year 2000 is given below. Calculate the interest at the end of the year at the rate of 5% p.a.
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24 | Ramkumar has a total income of Rs. 95,000 excluding HRA. He pays a premium of Rs. 2,000 half-yearly towards life insurance policy. Calculate the income tax he has to pay. Assume the following rates: Assume the following rates:
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25
| Solve for x : 4(x ^{2} + 1/x^{2}) + 8(x - 1/x) - 29 = 0 A tower in a city is 150 m high and a |