| CBSE Home page | 2006 CBSE MATH SET - 1 |
| 1) Q1) Solve the system of equations for x : 
OR
A man sold a table and a chair together for Rs. 850 at a loss of 10% on the table and
a gain of 10% on the chair. By selling them together for Rs. 950, he would have made
a gain of 10% on the table and loss of 10% on the chair. Find the cost price of each.
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| 2) Q2) 
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| 3) If (x - 2) (x + 4) is the HCF of the polynomials p(x) = (x2 + 3x - 10) (2x2 + 5x + m) and q(x) = (x2 - x - 20) (3x2 - 8x + n), find the values of in and n. | ||||||||||||||||
| 4) Solve for x : (a+b)2x2 + 8(a2 - b2)x + 16(a - b)2=0 OR Two numbers differ by 3 and their product is 504. Find the numbers. | ||||||||||||||||
| 5) How many terms are there in an AP whose first term and 6th term are -12 and 8 respectively and sum of all its term is 120 ? | ||||||||||||||||
| 6) Find the sum of all natural number less than 100 which are divisible by 4. | ||||||||||||||||
| 7) A household article is available for us. 1,500 cash payment or Rs. 360 cash down payment followed by three equal monthly instalments. If the rate of interest charged under the instalment scheme is 16% per aimum, find the amount of each instalment. | ||||||||||||||||
| 8) A man borrows Rs. 75,660 from a bank and has to repay it in three equal half yearly instalments. Find the amount of each instalment if the rate of interest is 10% per annum compounded semi-annually. | ||||||||||||||||
| 9) Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal. | ||||||||||||||||
| 10) BC is an arc of a circle with centre O If A is a point on the remaining part of the circle as shown in Fig. 1, prove that ∠BAC + ∠OBC = 90° . 
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| 11) Draw the graphs of the equations 4x - 3y - 6 = 0 and x + 3y - 9 = 0 Determine the coordinates of the vertices of the triangle formed by the lines and the y-axis. | ||||||||||||||||
| 12) A solid is in the form of a right circular cylinder with hemispherical ends. The total height of the solid is 108 cm and the diameter of the cylinder is 42 cm. Find the volume and surface area of the solid. [ Use π = 22/7 ] | ||||||||||||||||
| 13) A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speeds of the two trains. | ||||||||||||||||
| 14) Prove that
OR Evaluate without using Trigonometric tables
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| 15) Draw a quadrilateral ABCD in which AS = 3 cm, BC = 5 cm, CD = 6 cm, AID = 4 cm and BD = 5 cm. Construct a quadrilateral A'BC'D similar to ABCD so that diagonal BD = 65 cm. | ||||||||||||||||
| 16) Show that the points A (3, -1), B (5, -1) and C (3, -3) are the vertices of a right angled isosceles triangle. OR Find the coordinates of a point which is equidistant from points (3, 1), (1, -3) and (6, -8). | ||||||||||||||||
| 17) If the points (10, 5), (8, 4) and (6, 6) are the mid-points of the sides of a tringle, find its vertices. | ||||||||||||||||
| 18) The Arithmetic Mean of the following frequency distribution is 56. Determine the vlue of p.
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| 19) The following table shows the monthly expenditure of a firm. Draw a pie-chart for the data.
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| 20) Cards marked with numbers 1, 2, 3 25 are placed in a box and mixed thoroughly and one card is drawn at random from the box. What is the probability that the number on the card is (i) a prime number ? (ii) a multiple of 3 Or 5 ? (iii) an odd number ? (iv) neither divisible by 5 nor by 10 ? | ||||||||||||||||
| 21) If a line is drawn parallel to one side of a triangle, prove that the other two sides are divided in the same ratio. Using the above result, find x from Fig. 2. 
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| 22) Prove that if a line touches a circle and from the point of contact a chord is drawn, the angles which this chord makes with the given line are equal respectively to the angles formed in the corresponding alternate segments. Using the above, do the following In Fig. 3, AB is a diameter of the circle and QC is a tangent to the circle at C. If ∠CAB = 30°, find (i) ∠CQA, (ii) ∠CBA. 
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| 23) A circus tent is cylindrical to a height of 4 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the cost of the canvas needed to make the tent if the canvas costs Rs. 100 per square metre. OR Water flows at the rate of 10 m per minute through a pipe having its diameter as 5 mm. How much time will it take to fill a conical vessel whose diameter of base is 40 cm and depth 24 cm ? | ||||||||||||||||
| 24) The angle of elevation of the top of a vertical tower from a point on the ground is 600. At a point 40 m vertically above the first point of observation, the angle of elevation is 30°. Find the height of the tower and the distance between the tower and the first point of observation. OR The angle of elevation 0 of the top of a light-house as seen by a person on the ground is such that tanθ = 5/12 . When the person moves a distance of 240 m towards the light-house, the angle of elevation becomes such that tanφ = 3/4. Find the height of the light-house ? | ||||||||||||||||
| 25) The monthly salary of Arjun is Rs. 31,500 (exclusive of HRA). He donates Rs. 15,000 to Prime Minister’s Relief Fund (100% exemption) and Rs. 10,000 to a charitable society (50% exemption). He contributes Rs. 6,000 per month towards his provident fund and pays an annual premium of Rs. 12,000 towards Life Insurance Policy. He also purchases NSC for Rs. 6,000. Calculate the income tax deducted from his salary in the last month of the year, if tax deduction is made from his salary for 11 months at the rate of Rs. 2,500 per month. Use the following for calculating income tax
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ANSWERS
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