NIMCET 2025 — Mathematics PYQ

Solution

Step 1: Understand the Constraints

For an element $(x,y)$ to be in the relation $R$, both $x$ and $y$ must belong to the set $A$.

The relation is defined by the equation:

Step 2: Find the Lower Bound for $x$

Since $y\ge 1$ (the smallest element in $A$):

Step 3: Find the Upper Bound for $x$

Since $y\le 20$ (the largest element in $A$):

Since $x$ must be an integer, $x\le 13$.

Step 4: List the Possible Values of $x$ and $y$

The valid values for $x$ are integers from $4$ to $13$. Let's verify:

• If $x=4,y=2(4)-7=1\in A$

• If $x=5,y=2(5)-7=3\in A$

• If $x=6,y=2(6)-7=5\in A$

• ...

• If $x=13,y=2(13)-7=19\in A$

(Note: If $x=14,y=2(14)-7=21$, which is not in $A$.)

Step 5: Count the Elements

The set of possible values for $x$ is $\{4,5,6,7,8,9,10,11,12,13\}$.

Number of elements $=13-4+1=10$.

Final Answer:

The number of elements in $R$ is 10.