SECTION-4 (Maximum Marks : 12)
• This section contains TWO (02) paragraphs.
• Based on each paragraph, there are TWO (02) questions.
• The answer to each question is a NUMERICAL VALUE.
• For each question, enter the correct numerical value of the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.
• If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct numerical value is entered in the designated place;
Zero Marks : 0 In all other cases.
PARAGRAPH- I
Let 
and 
be the set of all relations 
from 
to 
that satisfy both the following properties:
i. 
has exactly 6 elements.
ii. For each 
, we have 
.
Let 
: The range of 
has exactly one element 
and 
is a function from 
to 
.
Let 
denote the number of elements in a set 
. (There are two questions based on PARAGRAPH "I", the question given below is one of them)
(i) If , then the value of
is .
(ii) If the value of 
is , then
is ………..
Text Solution
Verified by Experts(i) (20); (ii) (36)
(i) (20) (ii) (36)
(i)
Number of elements in 
and for each 
set of all relation 
(ii)
Number of elements in 
and for each 
set of all relation 
If
Total number of ordered pairs 
s. t. 
number of elements in 
: The range of
has exactly one element 
From above, if range of 
has exactly one element, then maximum number of elements in 
will be 4 .
is a function from to
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