ALGEBRA 3 MARKS IMPORTANT QUESTION FOR MARCH 2016 BOARD PAPER

SET ONE

i.            Is the sequence is an A.P?  2/3, 4/5, 6/7 

ii.         Find the smallest positive integer n such that tn of the arithmetic sequence 20, 19 1/4, 18 1/2, .... is negative?

iii.         Form the quadratic equation whose roots are  7 + √3 and 7 - √3.

iv.        In the following experiment write the sample space S, number of sample points n(S), events P, Q, R using set and n(P), n(Q) and n(R). There are 3 men and 2 women. A 'Gramswachaatta Abhiyan' committee of two is to be formed. P is the event that the committee should contain at least one woman. Q is the event that the committee should contain one man and one woman. R is the event that there is not woman in the committee.

SET TWO

i. In the following experiment write the sample space S, number of sample points n(S), events P, Q, R using set and n(P) , n(Q) and n(R). A die is thrown: P is the event of getting an odd number. Q is the event of getting an even number. R is the event of getting a prime number.

ii.  If α and β are the roots of the equation 2x² - 3x - 1 = 0, find the values of α - β.

iii. Without actually solving the simultaneous equation given below, decide whether it has unique solution, no solution or infinitely many solutions: x/2 + y/3 = 4; x/4 + y/6 = 2    [Ans.]

iv.         Solve by 'Step Deviation Method. Below is the frequency distribution of marks (out of 100) obtained by the students. Find mean.

SET THREE

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.

SET FOUR

i. Solve the given quadratic equation by factorization method,  3x² – x – 10 = 0.   (Ans.)

ii. If two coins are tossed simultaneously, then find the probability of the following events:(Ans.)

(a) at least one tail turns up.  

(b) no head turns up.  

(c) at the most one tail turns up.

iii. Find S₁₀ if a = 6 and d = 3.  (Ans. )

iv. Complete the following table of cumulative frequency.
(Ans.)

Class	20 – 25	25 – 30	30 – 35	35 – 40
Frequency	2	6	14	29
C.F. less than upper limit	2	?	?	?

v. The following table shows the frequency distribution of the waiting time at an ATM centre. Draw a histogram to represent the data. (Ans.)

Waiting time in seconds	0 – 30	30 – 60	60 – 90	90 – 120	120 – 150	150 – 180
No. of Customers	20	28	68	54	10	3

SET FIVE

i.             How many three digit natural number are divisible by 4? (Click  for answer)

ii.           Determine the nature of the roots of the equation 2y² + 5y – 3 = 0 from its discriminanats. (click for answer)

iii.         Solve the following simultaneous equations using graphical method.  x + 2 y = 5; y = -2 x – 2. (Click for answer)

iv.         Forty persons were examined for their Haemoglobin % in blood (in mg per 100 ml) and the results were grouped as below: Find Mode. (Click for answer)

Haemoglobin % (mg/100ml)	13.1 – 14	14.1 – 15	15.1 – 16	16.1 – 17	17.1 – 18
No. Of persons	8	12	10	6	4

SET SIX

(i) Find the first three terms of the sequence, whose nth terms is  t_n = 4n – 3. [Ans. 1, 5, 9]

(ii) Solve the following quadratic equation by factorization method: x² – 5x – 36 = 0. [Ans. x = 9 or – 4 ]

(iii) Two – digit numbers are formed from the digits 0, 1, 2, 3, 4 where digits are not repeated. Find the probability of the events that:

(a) the number formed is an even number. [Ans. 5/8]

(b) the number formed is a prime number. [Ans. 5/16]

(iv) Below is given the distribution of money (in Rs. ) Collected by students for flood relief fund. [Ans. Rs. 23.80]

Money (In Rs.)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of Students	5	7	5	2	6

Find mean of money (in Rs. ) collected by a student using ‘Direct Method’.

(v) The number of hours, spent by a school boy in different activities in a day is given below. [Ans. The measure of the θ for ∷ Sleep = School = 105⁰ ; Play = 30⁰ ; Homework = Others = 60⁰  ]

Activity	Sleep	School	Play	Homework	Others	Total
Number of Hours	7	7	2	4	4	24

Represent the above information using pie diagram.