MTH101 Midterm Solved Subjective 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 = , 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