ASSIGNMENT
CLASS: X
CH 3 (LINEAR EQUATIONS IN TWO VARIABLES)
MCQ’S (1 MARK)
1. The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:
(a) Unique solution
(b) Exactly two solutions
(c) Infinitely many solutions
(d) No solution
2. If a pair of linear equations is consistent, then the lines are:
(a) Parallel
(b) Always coincident
(c) Always intersecting
(d) Intersecting or coincident
3. If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?
(a) 4/15
(b) 15/4
(c) ⅘
(d) 5/4
4. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have
infinitely many solutions is
(a) 3
(b) -3
(c) -12
(d) No value
5. The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15
will be
(a) Parallel lines
(b) Coincident lines
(c) Intersecting lines
(d) Perpendicular lines
6. If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is
(a) -10/3
(b) 10/3
(c) - 13
(d) – 7
Two marks questions:
1. Find the value of p for which the given pair of equations has a unique solution:
2x + 3y – 5 = 0; px – 6y – 8 =0.
2. Two numbers are in the ratio 5:6.If 8 is subtracted from each of the numbers, the ratio
becomes 4:5.Find the numbers.
3. Find the value of x + y, if equations are:
43x + 67y = -24 and 67x + 43y = 24.
Three marks questions:
1. Two years ago a father was five times as old as his son. Two years later, his age will be 8
years more than three times the age of his son. Find the present ages of father and son.
2. Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c and lx + my = n.
3. Seven times a given two digit number is equal to four times the number obtained by
interchanging the digits and the difference of the digits is 3.Find the number.
CASE STUDY QUESTIONS (4 MARKS EACH)
CASE STUDY-1:
A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer
while ¼ marks is deducted for every wrong answer. A student knew answers to some of the
questions. Rest of the questions he attempted by guessing. He answered 120 questions and
got 90 marks.
Type of
Marks given for
Marks deducted
Question
correct answer
for wrong answer
True/False
1
0.25
1. If answer to all questions he attempted by guessing were wrong, then how many questions
did he answer correctly?
2. How many questions did he guess?
3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly,
then how many marks he got?
4. If answer to all questions he attempted by guessing were wrong, then how many questions
answered correctly to score 95 marks?
CASE STUDY-2:
Amit is planning to buy a house and the layout is given below. The design and the
measurement have been made such that areas of two bedrooms and kitchen together is 95
sq.m.
Based on the above information, answer the following questions:
1. Form the pair of linear equations in two variables from this situation.
2. Find the length of the outer boundary of the layout.
3. Find the area of each bedroom and kitchen in the layout.
4. Find the area of living room in the layout.
5. Find the cost of laying tiles in kitchen at the rate of Rs. 50 per sq.m.
Five marks questions:
1. Graphically, solve the following pair of equations:
2x + y = 6; 2x – y +2 = 0
Find the ratio of the areas of the two triangles formed by the lines representing these
equations with the x-axis and the lines with the y-axis.
2. Solve for x and y: mx –ny = m2 +n2 : x + y = 2m.Use method of Elimination.
3. A man starts his job with a certain monthly salary and earns a fixed increment every year.
If his salary was Rs.1500 after 4 years of service and Rs.1800 after 10 years of service, what
was his starting salary and what is the annual increment?