MTH101 Solved Practice Questions Lectures 1-22

MTH101 Practice Questions/ Solutions · Lecture No. 1 to 22 · Lecture No. 1: Coordinates, Graphs, Lines

Q1. Solve the inequality

x

x

Solution:

x

x

x

x

x x

x

x

x

Now there are two possibilities. Either 2 0 and x x or 2 0 and x x

Consider,

0 and

1 ,

( 1,

Takingintersectionof bothintervals,wehave

1 ,

...............(1) x x

x and x

Similarly, if we consider,

0 and

, 1)

Takingintersectionof bothintervals,wehave

, 1) ...............(2) x x

x and x

Combining (1) and (2), we have the required solution set. That is:

1 ,

, 1)

Q2. Solve the inequality and find the solution set of

x

Solution:

x

x x x x

So, solution set = x i.e. 0, 5

Q3. List the elements in the following sets:

(i)

0} x x x (ii) { : is an integer satisfying 5} x x x

Solution:

(i) Consider x x

x x x

(x 2) 2( 2) x x

(x 2)( 2) x

(x 2)

x 2

x

Solution set: 

(ii) Solution set:  0,1,2,3,4

Q4. Find the solution set for the inequality: 9

x x

Solution:

x x

3x x 2x x or x 

Hence,

Solution set: , 2

Q5. Solve the inequality 2

x

Solution:

x

x

x

x x

Lecture No. 2: Absolute Value

Q1. Solve for

8. x

x

x

Solution:

x

x

x x

or

x x

x x or x x

x x or x x

x x or x x

x or x

x or x

Q2. Is the equality

b b valid for all values of b ? Justify your answer with appropriate

reasoning.

Solution:

As we know that

if is positive or zero i.e 0,

but is always positive , because if 0 then is always positive.

So the given equality always holds. x x x x

b b

b b

b b b