ALGEBRA 2 MARKS IMPORTANT QUESTION FOR MARCH 2016 BOARD PAPER

SET ONE

i. State whether the following sequence is an A.P. or not: 1, 3, 6, 10, ……… [Ans]

ii. Solve the following quadratic equation by factorization method: 9x² – 25 = 0. [Ans]

iii. If the point (3,2) lies on the graph of the equation 5x + ay = 19, then find a. [Ans]

iv. If 12x + 13y = 29 and 13x + 12y = 21, find x + y. [Ans]

v. A die is thrown then write the sample space (S) and number of sample points n(S) and also write events A of getting even umber on the upper surface and write n(A). [Ans.]

vi. For a certain frequency distribution, the value of mean is 20 and mode is 11. Find the value of median. [Ans]

SET TWO

(i) Find the first four terms in an A.P. when a = 10 and d = 3. [Ans. 10, 13, 16, 19]

(ii) Prepare the cumulative frequency (less than type) table from the following distribution table: [Ans. C.F. : 2, 5, 12, 20, 25]

Class	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency	2	3	7	8	5

(iii) Form the quadratic equation if the roots are 6 and 7. [Ans. x² – 13x + 42 = 0 ]

(iv) Find the value of determinant [Ans. 6 ]

5	2
7	4

(v) Find t_n for the A.P. 3, 8, 13, 18, ……[Ans.  5n – 2 ]

(vi) Three coins are tossed simultaneously, find S and n(S) [Ans. S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} n(S) = 8]

SET THREE

Q1. Attempt any five of the following sub – questions:  (5)

i.             Find the first four terms of the sequence, whose n^th term is t_n = n² – 2n(Click for answer)

ii.           Solve x² – 17 x + 60 = 0 by factorisation method. (Click for answer)

iii.         Find D_x and D_y of the given simultaneous equations. 3x – 2y = 3 and 2x + y = 16. (Click for answer)

iv.         Form two digit number using the digits 0, 1, 2, 3 without repeating the digits. Write sample space ‘S’, n(S), event P and n(P) where P is the event that the number so formed is divisible by 3. (Click for answer)

v.           A die is thrown, find the probability of the events

a.  Getting a number less than 3,     b. Getting a prime number. (click for answer )

vi.         State whether the given equation is quadratic or not: y + 1/y = 3. (Click  for answer)

SET FOUR

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

i. State whether the following sequence is an A.P. or not 1³, 2³, 3³, 4³, .... (Ans)

ii. Solve the given quadratic equation by factorization method. x² -13 x – 30 = 0. (Ans)

iii. Find D_x  and D_y  of the given simultaneous equations. 3x – 2y = 3 and 2x + y = 16.(Ans)

iv. A die is thrown. Find the probability of obtaining a perfect square on its upper surface.(Ans.)

v. For a certain frequency distribution, the values of Median and Mode are 95.75 and 95.5 respectively, Find the value of Mean. (Ans.)

vi. State whether the given equation is a quadratic or not. y + 1/y = 3   (Ans.)

SET FIVE

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

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]

SET SIX

i. There are 3 red, 3 white and 3 green balls in a bag. One ball is drawn at random from a bag :

P is the event that ball is red.

Q is the event that ball is not green.

R is the event that ball is red or white. [Ans.]

ii.           Solve the following simultaneous equations using Cramer’s rule : 3x + y = 1; 2x = 11y + 3   [Ans.]

iii.       In the example given below determine whether the values given against each of the quadratic equation are the roots of the equation or not: x² + 5x – 14 = 0, x = √2 , –7, 3    [Ans]

iv.         Find the sum of the first n odd natural numbers.

Hence find 1 + 3 + 5 +... + 101.

v.           The marks scored by students in mathematics in a certain examination are given below: [Ans.]

Marks scored	1 – 20	21 – 40	41 – 60	61 – 80	81 – 100
Number of students	3	8	19	18	6

vi.         Solve by factorization method : 6x² – 5x – 25 = 0