ALGEBRA PAPER THREE WITH SOLUTION

Q1. Attempt any five sub – questions:   [5]

i. Find t_n of the given A.P. : 3, 8, 13, 18, ……… [Ans]

ii. Write the given quadratic equation in the standard form. n + ⁷ / _n = 4. [Ans]

iii. Find x + y   from the given simultaneous equations. 12x + 13y = 29 and 13x + 12y = 21. [Ans]

iv. A coin is tossed. Find sample space 'S' and n(S). [Ans]

v. Find the next two terms of the given sequence 2, 4, 8, 16, ……… [Ans]

vi. Write the class mark of the class 60 – 69. [Ans]

Q2. Attempt any four sub – questions: [8]

i. Write the values of a, b and c  from the given quadratic equation and hence find the value of the discriminant. 3x² + 2x – 1 = 0. [Ans]

ii. Find the first four terms of an A.P. , if   a  = 0 and d = - 3 . [Ans]

iii. A box contains 20 cards marked with numbers from 1 to 20. One card is taken out of the box at random. What is the probability that the number on the card is a prime number? [Ans]

iv. Form a quadratic equation whose roots are 5 and – 7. [Ans]

v. Examine whether the point ( 2 , 5 ) lies on the graph of the equation  3x – y = 1. [Ans]

vi. For a certain frequency distribution, the value of the Mean is 101 and that of the Median is 100. Find the value of the Mode. [Ans]

Q3. Solve any three sub – questions:     [9]

i. Solve the given quadratic equation by formula method. m² – 3m – 10 = 0. [Ans]

ii. The first and the last terms of an A.P. are 13 and 216 respectively. The common difference is 7. How many terms are there in that A.P.? Also, find the sum of all the terms in it. [Ans]

iii. In the given experiment, write sample space S and the events P and Q. Write also n(S), n(P) and n(Q). Three coins are tossed simultaneously. P is the event of getting at least two heads and Q is the event of getting no head. [Ans]

iv. Below is given the distribution of money in (Rs.) collected by students for a flood relief fund. [Ans]

Money (in Rs.)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
No. of students	5	7	5	2	6

Find the Mean of money collected by a student by using 'Direct Method'.

v. The number of hours spent by a school boy in different activities in a day is given below: [Ans]

Activity	Sleep	School	Play	Homework	Others	Total
No. of hours	8	7	2	4	3	24

Represent the above information using a pie diagram.

Q4. Attempt any two sub questions. [8 ]

i. Solve the given equation. 2(x² + 1/x²) – 9(x + 1/x)+14 = 0. [Ans]

  ii. The sum of two number is 60. The greater number is 8 more than thrice the smaller number. Find the numbers. [Ans]

iii. A die is thrown. Find the probability of the following events.  (a) getting a number less than 3. (b) getting a number divisible by 2.  (c) getting a prime number. [Ans.]

Q5. Attempt any two sub – questions. [10]

i. The sum of the first n terms of an A.P. is  3n + n². [Ans]

(a) Find the first term and the sum of the first two terms. (b) Find the second, third and the 15^th terms.

ii. A boat takes 10 hours to travel 30 km upstream and 44 km downstream and it takes 13 hours to travel 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water. [Ans]

iii. The sales of a salesman in a week are given below in a pie diagram. Study the diagram and answer the following questions. If the total sales due to salesman 'A' is Rs. 18,000, then .  [Ans]
(a) find the sales of each salesman.
 (b) find the salesman with the highest sales.  

(c) find the difference between the highest sale and the lowest sale. (d) find the total sales.