JEE Q1 to Q10 (PYQs)

Question 1

Let A and B be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B. Then the distance of the point $P(m,n)$ from the point $Q(-2,-3)$ is:

(a) 10 (b) 6 (c) 4 (d) 8

Solution

Step 1: Number of subsets of a set with $k$ elements is $2^k.$

Given: $2^m=2^n+56$

Step 2: Try small values of $n$.

Try $n=3$, then $2^3=8$
$2^m=8+56=64$
So, $2^m=2^6\Rightarrow$
m=6

Step 3: Use distance formula:

$d=\sqrt{(6-(-2\left)\right){²}^{}+(3-(-3\left)\right){²}^{}}=\sqrt{8{²}^{}+6{²}^{}}=\sqrt{100}=10$

✅ Final Answer: (a) 10