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Class 10 CBSE 10th Board 2017 : Mathematics

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Geeta Nilesh Chandani
St. Mary Convent Sr. Sec School

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DELHI PUBLIC SCHOOL BOKARO STEEL CITY ASSIGNMENT FOR THE SESSION 2011-2012 Class: X Subject : Mathematics Assignment No. 3 QUADRATIC EQUATIONS 1. Solve by completing the square 2x2 + x 4 = 0. 2. Solve by quadratic formula 6 x2 4x - 2 6 = 0 3. Solve for x : p2x2 + ( p2- q2)x q2 = 0 1 1 1 1 4. Solve : = + + , x 0, x ( a + b) a+b+ x a b x Without solving, examine the nature of roots of the following equations 5. a) 2x2 + 2x + 3 = 0 b) 2x2 - 7x + 3 = 0 c) x2 - 5x - 2= 0 ) 4x2 - 4x + 1 = 0 6. Find the value of k for which the equation kx2 2(k 1 )x + 4 = 0 has real and equal roots. 7. The hotel bill for a number of people for overnight stay is Rs4800. If there were four people more, the bill each person had to pay would have reduced by Rs200. Find the number of people staying overnight. 8. Sheela can row a boat 8km downstream and return in 100 minutes. If the speed of the stream is 2km/hr, find the speed of the boat in still water. 3 9. Two water taps can together fill a tank in 9 . The tap of larger diameter takes 10 hours less than 8 the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. 10. If I had walked 1km/hr faster, I would have taken 20minutes less to walk 2km. Find the rate of my walking. ARITHMETIC PROGRESSION 1. For what value of k, (2k-1),7 and 3k will form an AP? 2. If tn = 3-4n, find S20. 3. How many terms of the AP -6, -11/2, -5, . are needed to give the sum -25. 4. The sum of first 9 terms of an AP is 171 and that of the first 24 terms is 996. Find the AP. 5. Find the 10th term from the end of the AP 4, 9, 14, ., 254. 6. Find the sum of all the three digit numbers which leave the remainder 3 when divided by 5. 7. The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum. 8. Find the AP whose sum of first n terms is 5n2 3n. Also find its 10th term. 9. The rate at which the monthly salary of a person increases annually is an AP. If he was drawing Rs.4500 per month in his 11th year of service and Rs.6900 per month in his 27th year of service, find his salary at the start and the annual increment. Also find the monthly salary after 30 years. 10. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs.2000 for the first day, Rs.2500 for the second day, Rs.3000 for the third day and so on, the penalty for each succeeding day being Rs.500 more than for the preceding day . How much money the contractor has to pay as penalty if he has delayed the work by 30 days? CIRCLES 1. In a ABC , AB = AC and its incircle, with centre O , touches the side BC of triangle ABC at point L. Prove that the point L bisects BC. 2. In a ABC, incircle touches AB, BC and AC at P,Q,R respectively. Show that AP + BQ + CR = (Perimeter of ABC). 3. Two circles with center O & O touch each other externally at A. BC is a direct common tangent of the given circles. Prove that tangent at point A bisects BC.

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