OMTEX - CLASSES“THE HOME OF SUCCESS” Algebra assignment for the year 2009 - 10 PAPER - I Q1. Attempt any six of the following sub – questions: 1. What is the equation of Y – axis? Hence find the point of intersection where the line 3x – y + 4 = 0 cuts y – axis. 2. Find the HCF of the following polynomials: 152, 18y3. 3. Simplify the following algebraic expression: 4xx-1-x+1x-1. 4. Solve the following quadratic equation by factorization method. 25q2 = 36. 5. Solve and answer the following. 11012 = 10. 6. Find tn for the following sequence, if it is an A.P. 24, 21, 18, 15, …… 7. A coin is tossed. Find the probability of getting head or tail. 8. Find the amount received by selling 150 shares of face value s. 10 at Rs. 65 market price. Brokerage 2%. Q2. Solve any four of the following sub – questions. 1. Solve the following equations by Cramer’s Rule. 3x-4y=7;5x+2y=3. 2. The HCF of two polynomials px=x-3x2+x-2and qx= x2-5x+6 is x-3.Find LCM of pxand qx. 3. Convert the decimal integer to its binary equivalent by using division – remainder technique. 10210. 4. Find the common difference, if a = 100 and t20 = 176. 5. Calculate the mode: Class 125 – 175 175 – 225 225 – 275 275 – 325 325 – 375 375 – 425 425 – 475 Frequency 8 10 25 35 12 10 4 6. A manufacturer buys raw material for Rs. 50,000. He sells the ready stock for Rs. 90,000. Find the VAT paid by the supplier of raw material and by the manufacturer. [Rate of VAT is 12.5%] Q3. Solve any four of the following sub – questions. 1. If (x-k)is the HCF of kx2-3x-k and x2+3x-10, find the value of k k>0. 2. The radius of a circle is greater than the radius of the other circle by 3m. The sum of their areas is 89πm2. Find the radius of each circle. 3. Solve the following by converting the binary numbers to decimal number system. 1112 + 1012 – 1002. 4. A ball is picked up at random from a box containing three red balls, three white balls and there green balls. A is he event that the ball picked up is red ball. B is the event that the ball picked up is not a green ball. 5. A DVD set (Digital Video Disc) is available for Rs. 5500 cash or for Rs. 2500 cash down payment and balance amount and interest on it. Rs. 3195 to be paid after six months in one instalment. Find the rate of interest. 6. A musician paid Rs. 18,720 for a music system. If the rate of central sales tax is 4%, find the list price of the music system when no discount was given. ANSWERSS Q4. Solve any four of the following sub – questions: 1. Let AB be the diameter of a circle. C is the point on the circumference such that in a ∆ABC, ∠B is less by 150 than twice the ∠A. Find the measures of all angles of ∆ABC. 2. Simplify the following. m2+3m-4m2+16m+64÷m2-9m+18m2-2m- 48÷m+8m+4 3. Solve the following quadratic equation by formula method. 2x2+1x2-9x+1x+14=0 4. On fifth June i.e. on world environment day, the mathematics teacher asked the students of Standard X to plant 190 trees in rows to form an isosceles triangle, the number of tress in the successive rows increasing by one from the apex to the base. How many trees have the students to plant in the row which forms the base of the triangle? 5. The expenditure on different items in a month by a householder whole monthly salary amounting to Rs. 7,200 is given below. Items Clothing Food House Rent Education Miscellaneous Amount spent (in 1200 4000 600 1000 400 Rs) Represent the information in the form of pie diagram. 6. The monthly salary of Sarojben is Rs. 20,000. She contributes Rs. 1000 per month towards provident fund. She buys NSC of Rs. 10,000 and pays annual premium of Rs. 5,000 to LIC. Calculate the income tax she will have to pay. Q5. Solve any three of the following sub – questions: 1. AB is a segment. The point P is on the perpendicular bisector of segment AB such that AP is double that of AB. If perimeter of ∆ABP is 35cm, find the sides of ∆ABP. 2. Simplify: m+n+n2m-n÷m2+n2+n4m2- n2 3. A committee of two is to be formed from 3 men and 3 women. Find the probability of the following events A and B and mention whether the events are complementary / mutually exclusive. i. A: Only women should be in the committee. ii. B : Only men should be in the committee. 4. Find the median: Class interval 0 – 5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 Frequency 2 7 18 10 8 5 5. An inverter is sold for Rs. 8000 cash or Rs. 2000 cash down payment together with six equal monthly instalments. If the rate of the interest is 8% p.a. find each instalment. 6. A person invested Rs. 22,950 and bought shares of a company whose market price is Rs. 125. The face value of a share is Rs. 10. Brokerage was paid at 2%. If the company paid 60% dividend at the end of the year. What was his income that year? ANSWERSS PAPER – II Q1. Attempt any six of the following sub – questions 1. Solve the following linear equation in one variable: 4(m + 3) = 16. 2. Find the LCM of the following polynomials: 14a2; 21a3b. 3. Which of the following are rational algebraic expressions? i. 3y2-2y-11 2 ii. x2+3x+43x-2 4. If x = 1 is the solution of kx – x – 1 = 0, then what is the value of k? 5. Subtract the following: 100012 – 10102. 6. For an A.P., if t1 = 100, tn = 1000 and n = 10, find Sn. 7. A die is thrown. Find the probability that an odd number comes up. 8. A share of face value Rs. 10 was purchased for Rs. 75. The company declares a dividend of 30%. What is the rate of return on investment? Q2. Solve any four of the following sub – questions: 1. Solve the following simultaneous equation using the method of elimination by substitution: 2x-y-3=0 ;4x-y-5=0. 2. Find the HCF of the following polynomials. 2a3-54;6a2- 36a+54. 3. Add the following numbers. Verify your answers in decimal number system. 11012 + 10012. 4. If 7 times the seventh term of an A.P. is equal to 11 times the eleventh term, show that the 18th term of the A.P. is zero. 5. Find the mean of the daily income from the following frequency distribution: Daily inform in (Rs) 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350 350 – 400 Number of workers 2 7 9 8 6 4 6. Kalyanrao Patil purchased twelve ‘plant protection nets’ for Rs. 9152 which includes 12% discount on marked price and 4% central sales tax on the remaining price. Find the marked price of the ‘plant protection nets’. Q3. Solve any four of the following sub – questions: 1. The HCF of two polynomials is 5(x+3)(x-1) and their LCM is 20x(x2 – 9) (x – 1). If one of the polynomials is 20(x2 – 9) (x – 1), find the other. 2. The length of one of the diagonals of a rhombus is greater than the other by 5 cm. If its area is 18 sq.cm. find the length of the diagonals of the rhombus. 3. Find the difference between the greatest 4-bit binary number and the smallest 4 – bit binary number. 4. In the following experiment write down the sample space A, number of sample points n(S), events A, B and n(A), n(B). Two coins are tossed. A is the event of getting at the most one head. B is the event of getting both heads. 5. A certain amount of money is borrowed with promises to pay it back in two years in two equal annual instalments, with compound interest calculated at the rate of 10% p.a. If a man pays Rs. 10890 as each instalment, find the sum borrowed and the interest paid. 6. For a person (man) monthly salary is Rs. 8650 (exclusive of C.A.) and his deductions are as follows. LIC – Rs. 135 p.m., GPF – Rs. 500 p.m., Professional Tax – Rs. 2500 p.a., Infrastructure bonds – Rs. 5000. Find his taxable amount, for the financial year 2006 – 07. Q4. Solve any three of the following sub – questions. 1. Solve the following simultaneous equations. 49x – 57y = 172; 57x – 49y = 252. 2. Simplify: x3-2x2-19x+20x3-3x2- 13x+15. 3. A teacher wants to divide 150 bananas equally among certain number of students. If there were 25 students more, each student would have received 1 banana less. Find the number of students. 4. Find the sum of all natural numbers from 50 to 250 which are exactly divisible by 4.. 5. Find mode: Class interval 0 – 10 10 – 20 20 – 30 30 – 40 Frequency (f) 2 4 9 7 6. Mr. Shekhar earns Rs. 15,000 p.m. He contributes Rs. 1,000 p.m. towards provident fund. He pays Rs. 2500 as quarterly premium to LIC. Calculate the income tax Mr. Shekhar will have to pay for the year 2006 – 07. Q5. Solve any three of the following sub – questions: 1. In a cricket match of Amravati and Nashik teams the sum of 13rd of the runs made by Amravati team and 17th of the runs made by Nashik team is 137. If Amravati team made runs just sufficient to win the match, then how many runs are made by Amravati team? 2. Simplify: 4x2-15x-43x2-x-4÷4x2-3x-13x2-7x+4. 3. There are 40 tickets numbered 1 to 40 in a box. A ticket is drawn at random. What is the probability that the ticket drawn (i) bears an odd number? (ii) bears a number which is a perfect square? 4. Calculate the mean and median from the distribution given below. Marks (x) 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 No. of students (f) 8 20 36 24 12 5. A man borrows a certain amount which is to be paid back in three equal annual instalments. Compound interest is calculated at the rate of 12.5% p.a. If each instalment is Rs. 36,450, find the sum borrowed. 6. Rajani Parekh invested equal amount in two companies, buying equity shares having market price Rs. 45 and Rs. 60 each. At the end of the year the two companies declared dividends of 20% and 30%. In which company was her investment profitable? ANSWERSS PAPER III Q1. Solve any six of the following. 1. If 3x + 2y = 8 and 2x + 3y = 7, find the value of x + y. 2. Find the HCF of the following polynomials: 24x2y3; 36x3y2. 3. Determine whether the given rational algebraic expression is meaningful or not for the value of the variables given against it. m-5m-4,m=5 4. Write the following equations in the form of ax2+bx+c=0and then write the values of a,b and c: 5 – 2x = x2. 5. Convert the decimal integer to its binary equivalent by using division – remainder technique: 2710. 6. Show that sequence {3n – 7} is an A.P. 7. Form two digit numbers using the digits 0, 3, 5, 7 without repeating the digits. Find S and n(S). 8. Anita Ahuja invested Rs. 3570 in shares of face value Rs. 10 each at Rs.70 market price and brokerage at 2% was paid. How many shares did she purchase? Q2. Solve any four of the following sub – questions: 1. Complete the tables for drawing the graph of the following given equation: y = x – 2 . X 1 2 3 Y … … … (x, y) … … … 2. Find the HCF and LCM of the following polynomials: 2a2 – 7a + 3; 3a2 – 7a – 6. 3. Convert the following decimal integer to their binary equivalent by using expansion method: 26710. 4. For an A.P. if t4 = 20 and t7 = 32, find a and d. 5. Calculate the mode Height (in cm) (x) 130-134 135-139 140 – 144 145 – 149 150 – 154 155 – 159 160 – 164 No. of students (f) 5 15 289 24 17 10 1 6. The list price of a radio is Rs. 2400. The shopkeeper declared 10% discount on the list price. If the CST is 4%, find (i) the sale price and (ii) the selling price. Q3. Solve any four of the following sub – questions: 1. If the GCD of the polynomials x-2x2+ax+12and x+3x2-bx+6is x+3x-2, find a and b. 2. Solve the following quadratic equation by the formula method. x2-x-1=0. 3. Solve the following. Verify your answers in decimal number system. 11112 – 10012 . 4. Two dice are thrown. Find the probability that, i. The sum of the numbers on the dice is at least 11. ii. The sum of the numbers on the dice is divisible by 9. iii. The sum of the numbers on their upper faces is a perfect square. 5. A bicycle is sold for Rs. 1645 cash or for Rs. 1000 cash down payment followed by two monthly instalments of Rs. 330 each. Compute the rate of interest charged under the instalment scheme. 6. Anna Dudhate donated an overhead project of Rs. 52,000 to a school. If the rate of central sales tax is 4%, find he list price and the total tax paid. Q4. Solve any three of the following sub – questions. 1. Solve the following simultaneous equation by using graphical method. 2x-y7=0;3x+y+1=0. 2. Simplify: (x2-y2)3+y2-z23+z2-x23x-y3+y-z3+z-x3. 3. Solve the following equation: 30x2+1x2-77x-1x-12=0. 4. If a student saves Re 1 on the first day, Rs. 2 on the second day, Rs 3 on the third day and so on, what will be his total savings in 200 days? 5. Find the median: Class interval 6-10 11-15 16-20 21-25 26-30 Frequency 20 30 50 40 10 6. Ajay and Vishwas together bought twenty wrist – watches to donate to the students in Mahatma Phule hostel. They paid Rs. 20,800 for it. If the rate of central sales tax is 4%, find the list price of one piece of wrist – watch. Q5. Solve any three of the following sub – questions: 1. 8 men and 12 boys can do a piece of work in 10 days while 6 men and 8 boys can do the same work in 14 days. Find the time taken by a single man or a single boy to do the same work. 2. Simplify: x8-y8x6-y6. 3. A coin is tossed thrice. Find the probability of the events that i. Head appears twice. ii. Head appears at the most twice. iii. At least one tail turns up. 4. A pie diagram represents the expenditure of a family on different items. Find the percentage expenditure on different items by reading the pie diagram. 5. A TV set can be purchased for Rs. 11,200 cash or for Rs. 3600 cash down payment followed by ten monthly equal instalments of Rs. 800 each. Calculate the rate of interest in this plan. 6. Suratwala invested Rs. 3672 in equity shares of face value Rs. 10 at Rs. 300 market price. Company declares a dividend of 90% on them. After getting the dividend, all these shares were sold at Rs. 275. In each of the transactions, he paid 2% brokerage. Did he gain or loss in the total transaction? By how much? ANSWERSS Q1. Attempt any six of the following sub – questions: 1. Find the value of the following determinant: 6523 2. Find the HCF of the following polynomials: 9x2-16y2;3x-4y2. 3. Simplify: y2y+5+10yy+5+25y+5. 4. Solve the following quadratic equation by factorization method:x2+7x+12=0. 5. Convert the following decimal integer to its binary equivalent by using division remainder technique:2410. 6. For an A.P., t1 =20, tn =200 and n = 10, find Sn. 7. A box contains balls marked with the numbers 1 to 15. One ball is drawn at random. A is the event that its number is divisible by 4. Write the event A and n (A). 8. A sum of Rs. 1836 was invested in equity shares of Rs. 10 each at Rs. 150 market price and brokerage of 2% was paid. How many shares were purchased? Q2. Solve any four of the following sub – questions: 1. 2. 3. Solve the following simultaneous equations. 13x + 15y = 19; 15x + 13y = 9. Find LCM of the following polynomials. x2 -4; x2 +2x – 8. Add the binary numbers: 10102 +11102. PAPER IV 4. Find the seventh term in A.P. 1, 5, 9, 13,… 5. Find the median: 6. Sukhadev purchased ten plywood doors. The sale price of one piece is Rs. 1125 and the rate of central sales tax is 4%. Find the net selling price of 10 pieces. Q3. Solve any four of the following sub – questions. 1. The HCF of the polynomials px= 2x3-2 and qx= x2-2x+1 is x-1. Find their LCM. 2. Solve:101012-10012. 3. Two coins are tossed. A is the eent that atleast one head turns up. Find the probability of event A. 4. An electric iron is sold for Rs. 600 cash or for Rs. 300 cash down payment together with Rs. 330 to be paid after 8 months in one instalment. Find the rate of interest charged in the instalment scheme. 5. The value of purchasing an article is Rs. 860 and the value of its selling is Rs. 920. Find M-VAT by invoice method at the rate of 12.5%. 6. Simplify: m2+9m+20m2-16÷m2-2m-35m2+3m-28 ANSWERSS Q4. Solve any three of the following sub – questions. 1. A bus covers 300 km distance with a uniform speed. If its speed is increased by 10km/h, it will take 1 hour less to cover the same distance. Find the speed of the bus. 2. Find the sum of all natural numbers between 50 and 250 which are divisible by 6. 3. Draw a pie diagram to represent the following information. Mode of transport Bicycle Bus Walk Train Car Total Number of students 140 100 70 40 10 360 4. Solve the following simultaneous equation by using graphical method: y=6-3x;y=4-x. 5. Smt. C. Archana has her gross annual income for the financial year 2006 – 2007 of Rs. 1,48,000 and her savings are as follows: i. LIC Rs. 4800 p.a. ii. PLI Rs. 2750 p.a. Find the net income tax to be paid by Smt. C. Archana, for the financial year 2006 – 2007. 6. Solve using formula, 2x2-4x+5=0. Q5. Solve any four of the following. 1. An obtuse angle of a rhombus is greater than thrice the acute angle by 200. Find the measure of each angle. (use two variable) 2. Simplify: x2-2x+4-x3x+2 3. A die is thrown. A is the event that the prime number comes up. B is the event that the number divisible by 3 comes up. C is the event that the perfect square number comes up. Write the sample space S, number of sample points n(S), events A, B, C, and n(A), n(B) and n(C). 4. Find the mode: Marks (x) 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Number of students (f) 4 16 15 20 7 5 5. Sum of Rs. 31500 is borrowed and paid back in two years in two equal instalments at 10% p.a. compound interest. Find the amount of each instalment. 6. A person buys 100 shares of face value Rs. 10 each from a company. He sells these shares at Rs. 15 each. While selling he pays 2% brokerage. Find his profit and profit percent. ANSWERSS Q1. Attempt any six of the following sub – questions: 1. If x = 2, y = a is the solution of the equation x + 2y =10, find a. 2. Factorise the following polynomials: 8x3 + 125y3. 3. Determine whether the rational algebraic expression given in the following is meaningful for the value of the variable given against it. 2x23y; x=1, y=2. 4. Find the value of b2 - 4ac from the following quadratic equation. x2- 3x+1=0. 5. Solve and answer the following: 9210 = 2. 6. Find the 5th term of the A.P. 3, -1, -5, …… 7. A coin is tossed twice. Write the sample space S and the number of sample points n(s). 8. Sachin invested Rs. 500 in shares of face value Rs. 10 each. Company declares a dividend of 10%. Find his dividend. Q2. Solve any four of the following. 1. Draw the graph of y = 3x – 2. 2. The HCF of two polynomials is (x+2) and their LCM is 2x3 – 3x2 – 8x +12. If one of the polynomials is 2x2 + x – 6, find the other. 3. Solve the following. Verify your answer in decimal number system: 1112 – 1012. PAPER V 4. How many terms are their in the A.P. 201, 208, 215, ……, 369? 5. The pie diagram shows cultivation of crop in a village. If the total crop production is 1800 tonne, find the production of each crop in tonne. 6. Yusufbhai purchased an instrument for Rs. 9776 which includes 6% discount on printed price and then 4% central sales tax on the remaining price. Find the printed price of that instrument. Q3. Solve any four of the following sub – questions. 1. Find the HCF and LCM of the following polynomials: 2x3+128; 4x2 - 16x + 80; 2x2 – 32. 2. Solve: 5x4 – 22x2 +8 = 0. 3. Convert the binary integers to their decimal equivalents: i. 110012. ii. 101012. iii. 110112. 4. Two coins are tossed. Find the probability of the events that_ i. The tail appears on both the coins ii. The tail does not appear. 5. A ceiling fan is available for Rs. 845 cash or for Rs. 500 cash down payment together with Rs. 175 to be paid in next two months in two equal instalments. Find the rate of interest under this plan. 6. ANSWERSS 7. Rajendra purchased an instrument for Rs. 9152 which includes 12% discount on the printed price and then central sales tax on the remaining sale price. Find the printed price. Q4. Solve any three of the following sub – questions. 1. 9 years ago, grandfather’s age was 9 times his grandson’s age at that time. After 15 years his age will be thrice as his grandson’s age. Find their present ages. 2. Simplify the following: 11+pq+r+11+qr+p+11+rp+q. 3. The length of a rectangle is twice as long as the side of a square. The side of a square is 4cm longer than the width of the same rectangle. If their areas are equal, find their dimensions. 4. A sum of Rs. 3900 is paid off in 12 instalments, such that each instalments is Rs. 10 more than the preceding one. Find the amounts of the first and the last instalments. 5. The following table gives the profit made by retail shops. Find the mode and mean. Profit in (x) ( in thousand 1- 1 0 10 – 20 20 – 30 30 – 40 40 – 50 rupees) No. of shops (f) 4 12 18 14 8 6. Mr. Ganesh Rathod is working in an advertising company. His gross annual income is Rs. 2,00,000. His age is about 67 years. He pays Rs. 3000 to Prime Minister Relief Fund and buys NSC of Rs. 10, 000. What will be the income tax in the year 2006 – 07 he has to pay? Q5. Solve any three of the following sub – questions. 1. If the sum of two numbers is divided by 12, quotient obtained is 3 and remainder 4. If the difference of the same number is divided by 4, then quotient is 1 and remainder 2. Find the numbers. 2. If x = 100, y = 98, then find the value of x31-x+1+x+x2÷1-y+y2-y31+y. 3. Three boys A, B and C are in a race. A is twice as likely to win as B and B is twice as likely to win as C and P(A) + P (B) + P(C) = 1. What are the respective probabilities of winning? 4. The pie diagram represents the number of valid votes by four students who contested for school captain. The total number of valid votes polled was 720. Answer the following questions. i. Who has won the election? ii. What is the minimum number of votes obtained by any candidate? iii. By how many votes did the winner defeat the nearest contestant? 5. An electronic instrument is available for Rs. 6000 cash or for Rs. 1035 cash down payment and three equal half yearly instalments at the rate of 20% per annum compound interest. Find the amount of each instalment. 6. Nalini was allotted 300 shares of face value Rs. 10 each. The company declared a dividend of 10%. She sold all the shares when their price rose to Rs. 20. She invested the proceeds in shares of face value Re. 1 at Rs. 5 per share. This company declared 30% dividend. Find the difference between the annual returns from the two companies. (Brokerage not be considered).