ALGEBRA SAMPLE PAPER FOR PRACTICE

PAPER 4

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


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







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]


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



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



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





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


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.]

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