UGC-NET January 2017 Paper-2 Discrete Maths Questions Solved

3. Q:: 3  The functions mapping R into R are defined as: f(x) =  and h(x) = .

Then find the value of the following composite functions: hog(x) and hogof(x)

(1)        and     
(2)        and     
(3)      and    
(4)      and   

Answer:: (4)

Explanation::

hog(x) = h(g(x)) = (1/(x^2+1))^4 = (x^2 + 1)^-4

hogof(x) = ho(g(f(x))) = 

Now g(f(x)) = 1/((x^3-4x)^2 + 1)

h(g(f(x))) = h(1/((x^3-4x)^2 + 1)) = (1/((x^3-4x)^2 + 1))^4 

= ((x^3-4x)^2 + 1)^-4

Hence  hog(x) = (x^2 + 1)^-4 and hogof(x) =  ((x^3-4x)^2 + 1)^-4

So correct answer is (D)

UGC-NET January 2017 Paper-2 discrete maths questions with solution

UGC-NET January 2017 Paper-2 Solved UGC-NET January 2017 Paper-2 UGC-NET January 2017 Paper-2 questions with solution UGC-NET January 2017 Paper-2 question 3 solved complete solution UGC-NET January 2017 Paper-2 

cbse-NET January 2017 Paper-2 Solved cbse-NET January 2017 Paper-2 cbse-NET January 2017 Paper-2 questions with solution cbse-NET January 2017 Paper-2 question 3 solved complete solution cbse-NET January 2017 Paper-2 

UGC-NET January 2017 Paper-2 Discrete Maths Question Solved

Q::1 Consider a sequence  defined as:

 

 for n ≥ 2

Then what shall be the set of values of the sequence ?

(1)   (1, 110, 1200)                                   (2)   (1, 110, 600, 1200) 
(3)   (1, 2, 55, 110, 600, 1200)             (4)  (1, 55, 110, 600, 1200)

Answer:: (1)

Explanation::

The sequence can be estimated by recursive solutions  let us calculate the resul produce by F00(5)

F00(5) = (10*F00(4)+100)/F00(3)

Now, calculate F00(4)

F00(4) = (10*F00(3)+100)/F00(2)

F00(3) = (10*F00(2)+100)/F00(1)

F00(2) = (10*F00(1)+100)/F00(0)

Now substituting values of F00(0) = 1, F00(1) = 1

We get ,

F00(2) = (10*1+100)/1 = 110

Substituting F00(1)=1, F00(2)=110

We get,  

F00(3) = (10*110+100)/1 = 1200

Substituting F00(2)=110, F00(3)=1200

We get,

F00(4) = (10*1200+100)/110 = 110

Substituting F00(3)=1200, F00(4)=110

We get, 

F00(5) = (10*110+100)/1200 = 1

So the sequence is like F00(0) = 1,  F00(1) = 1,  F00(2) = 110, F00(3) = 1200, 

F00(4) = 110, F00(5) = 1 and So on...(1,1,110,1200,110,1,1...)

So option A includes 1,110,1200 So it is correct.

UGC-NET January 2017 Paper-2 Discrete Maths Question Solved

cbse-NET January 2017 Paper-2 Discrete Maths Question Solved

UGC-NET January 2017 Paper-2 Solved UGC-NET January 2017 Paper-2 UGC-NET January 2017 Paper-2 questions with solution UGC-NET January 2017 Paper-2 question 1 solved complete solution UGC-NET January 2017 Paper-2 

cbse-NET January 2017 Paper-2 Solved cbse-NET January 2017 Paper-2 cbse-NET January 2017 Paper-2 questions with solution cbse-NET January 2017 Paper-2 question 1 solved complete solution cbse-NET January 2017 Paper-2