ALGEBRA SAMPLE PAPER FOR PRACTICE

PAPER 4

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

 i. Find the next four terms of the sequence: 2, 4, 8, 16, ...

ii. Find whether it is a quadratic equation or not:  ^{(q2 – 4)}/_q2 = - 3  [Ans.]

iii. Find the value of the following determinant.    [Ans]

-4/7	-6/35
5	-2/5

iv. Is the sequence is an A.P. ? 3m – 1, 3m – 3, 3m – 5 , .......

v.  Two coins are tossed. Find the probability of the events head appears on both the coins.

vi.  For a certain frequency distribution the value of Mean is 101 and Median is 100. Find the value of Mode.

Q2. Attempt any FOUR of the following sub – questions: (8)

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

Q3. Attempt any THREE of the following sub – questions (9)

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.

Q4. Attempt any TWO of the following sub – questions: (8)

i. Represent the following data using frequency curve: [Ans]

Electricity bill in  a month (in Rs.)	200 – 400	400 – 600	600  - 800	800 – 1000
No. of Families	362	490	185	63

ii. The weight of coffee (in gms) in 70 packets is given below: Determine the modal weight of coffee in a packet.

iii. Find the probability that a leap year selected at random will have 53 Fridays.

Q5. Attempt any TWO of the following sub questions. (10)

i.  In a flower garden, there are 23 rose plants in the first row, 21 in the second row, 19 in the third row and so on. There are 5 rose plants in the last row. How many rows are there in the flower garden?

ii.  The following table gives information about the monetary investment by some residents in a city:

Mode of Investment	Shares	Mutual funds	Real estate	Gold	Government bonds
Percentage of residents	10	20	35	30	5

Draw a pie diagram to represent the data.    [Ans]   

iii.         In a school, a plantation program was arranged on the occasion of world environment day, on a ground of triangular shape. The trees are to be planted as shown in the figure. One plant in the first row, two in the second row, three in the third row and so on. If there are 25 rows then find the total number of plants to be planted. [Ans.]