Ques 1.

Eliminating z from  and  gives 

Ques 2.

The roots of  are given by 

Ques 3.

Ques 4.

Given any n positive numbers in R , the product of their harmonic mean and their arithmetic mean is 1.

Ques 5.

If A and B are two sets such that  is empty, then either A or =  B . = 

Ques 6.

For any 

Ques 7.

The geometrical representation of the set  is a point.

Ques 8.

Any finite set is a subset of 

Ques 9.

Every biquadratic equation has at least one real root

Ques 10.

The converse of the statement, ‘Every student of MTE-04 has completed FST-01’, is ‘Every student of FST-01 has completed MTE-04’.

Ques 11.

Show that 

Ques 12.

Let 1 ,a b > a,0 + b = ,1 n > . Show that  .

Ques 13.

Using the discriminant, give the nature of the roots of . Also solve the equation.

Ques 14.

Find the cubic equation whose roots are the cubes of the roots of 

Ques 15.

Obtain the resolvent cubics, by Descartes’ method and by Ferrari’s method, of the equation  . Are the cubics the same? Further, use either method to obtain the roots of this equation.

Ques 16.

If A and B are the set of even integers and set of odd integers, respectively, find A ∪ B and 

Ques 17.

i) Find A× B, and the number of elements in it, where
  and
 
 ii) Given any two sets C and D , under what conditions on them will C× D and D×C have the same number of elements? Give reasons for your answer. 

Ques 18.

Express the following situation in a Venn diagram:
In a survey of 60 women, it is found that 25 have studied upto Class 12 only, 10 have studied till Class 10 only, 26 got scholarships, 9 of those studying till Class 12 got scholarships, 8 of those studying till Class 10 got scholarships, and 11 had completed their BA degree. 

Ques 19.

In the context of your IGNOU studies, give the following:

i) an example of an implication;
 ii) the converse of your statement in (i) above;
iii) the contrapositive of your statement in (i) above;
iv) a statement using ∀ ;
v) a statement using ∃ . 

Ques 20.

Give the following:i) a 2× 4 matrix;
 ii) the transpose of the matrix in (i) above;
 iii) a system of linear equations represented by AX = B, where A is the matrix in (ii) above. 

Ques 21.

Consider the linear system

Give the two reasons for Cramer’s Rule being applicable for solving this system. Also use the rule to solve the linear system.

Ques 22.

Find the values of a ∈R for which ia is a solution of . Also find all the roots of this equation.

Ques 23.

Find all the 8^th roots of . Also show any one of them in an Argand diagram.

Ques 24.

Using the method of substitution, obtain the solution set in , of the following:

i) x − π = 5

ii) 
 iii) 

Ques 25.

Give a real life situation problem, which is mathematically translated into

 Also, explain how this linear system models your problem.