# Maths Class 10

**Topics:**Taxation in the United States, Value added tax, Circle

**Pages:**5 (1233 words)

**Published:**June 27, 2011

You are on Set no 1 Qno. 1 to 20

Time allowed : 3 hours

Maximum Marks : 100

General Instructions :

(i) Question number 1 to 15 carry 2 marks each.

(ii) Question number 16 to 25 carry 4 marks each.

(iii) Question number 26 to 30 carry 6 marks each.

(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

Q1) Find the value of k for which the system of equations has no solution : 3x - 4y + 7 = 0

kx + 3y - 5 = 0 (Marks 2) =1.25

Answer

Q2) Find the g.c.d. of the following polynomials :

2x2 - x - 1 and 4x2 + 8x + 3 (Marks 2) =

Answer

Q3) If A = (x + 1)/(x - 1), find A - 1/A in the simplified form. (Marks 2) Answer

Q4) Form the quadratic equation in x whose roots are 2 + 5 and 2 - 5. (Marks 2) Answer

Q5) The base radii of two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes. (Marks 2) Answer

Q6) A colour T.V. is available for Rs. 13,440 inclusive of sales tax. If the original cost of T.V. is Rs. 12,000 find the rate of sales tax. (Marks 2) Answer

Q7) Evaluate : cot 54o/tan 36o + tan 20o/cot 70o - 2 (Marks 2) Answer

Q8) Simplify : (1 + tan2 )(1 - sin )(1 + sin ) (Marks 2)

Answer

Q9) Prove that : sin /(1 - cos ) = cosec + cot . (Marks 2) Answer

Q10) In Fig. 1, ABC and DEF are similar. The area of ABC is 9 sq.cm and area of DEF is 16 sq.cm. If BC = 2.1 cm, find the length of EF. (Marks 2)

Answer

Q11) In Fig. 2, O is the centre of the circle and AB is a chord of the circle. Line QBS is a tangent to the circle at B. If AOB = 110o, find APB and ABQ. (Marks 2)

Answer

Q12) In Fig. 3, chords AB and CD intersect at P. If AB = 5 cm, PB = 3 cm and PD = 4 cm, find the length of CD. (Marks 2)

Answer

Q13) Calculate the median of the following data :

83, 37, 70, 29, 45, 63, 41, 70, 30, 54 (Marks 2)

Q14) Find the Crude Death Rate (CDR) for the following data: (Marks 2) Age group

(in years)PopulationNumber

of Deaths

0 - 105000250

10 - 252000120

25 - 458000150

45 - 70700080

Above 703000250

Answer

Q15) Flow Chart. Omitted being out of Syllabus. (Marks 2)

Section - B

Answer

Q16) Solve for the following system of equations graphically : 2x + y - 3 = 0

2x - 3y - 7 = 0 (Marks 4)

Answer

Q17) Factorise. Omitted, being out of Syllabus. (Marks 4)

Answer

Q18) A man has only 20 paise coins and 25 paise coins in his purse. If he has 50 coins in all totaling Rs. 11.25, how many coins of each does he have? (Marks 4) Answer

Q19) Divide 29 into two parts so that the sum of the squares of the parts is 425. (Marks 4) Answer

Q20) The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of 28 cm diameter. Find the length of the wire. (Marks 4) Answer

Q21) “In a triangle, a line drawn parallel to one side, to intersect the other side in distinct points, divides the two sides in the same ratio". Prove. (Marks 4) Answer

Q22) The perpendicular AD on the base BC of a ABC intersects BC at D so that DB = 3CD. Prove that 2AB2 = 2AC2 + BC2 (Marks 4)

Answer

Q23) Find the mean of the following data : (Marks 4)

Class IntervalFrequency

0 - 108

10 - 2010

20 - 309

30 - 4012

40 - 5011

Answer

Q24) Algorithm. Omitted, being out of Syllabus. (Marks 4)

Answer

Q25) Flow Chart. Omitted, being out of Syllabus. (Marks 4)

Section - C

Answer

Q26) Solve for x :

4(x2 + 1/x2) + 8(x - 1/x) - 29 = 0 (Marks 6)

Answer

Q27) A tower in a city is 150 m high and a multistoried hotel at the city centre is 20 m high. The angle of elevation of the top of the tower at the top of the hotel is 5o. A building, h metres high, is situated on the straight road connecting the tower with the city centre at a distance of 1.2 km from the tower. Find the value of h if the top of the hotel, the top of the building and the top of the tower are in a...

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