Sets, Relations and Functions

5 solved problems from JEE previous year papers.

Logarithms

If x^((log₂x)² − 6log₂x + 1) = 64, Then x Is Equal To

Solve x^((log₂x)²−6log₂x+1)=64 by taking log base 2 of both sides and substituting t=log₂x, reducing it to a factorable cubic in…
Sets and Relations

Let A and B Be Two Finite Sets With m and n Elements. The Total Number of Subsets of A Is 56 More Than the Total Number of Subsets of B. Then the Distance of the Point P(m, n) From Q(−2, −3) Is

Sets A, B have m, n elements, with A’s subset count 56 more than B’s. Find m and n via prime factorisation of…
Sets and Relations

Two Sets A and B Are as Under: A = {(a,b) ∈ R×R : |a−5| < 1 and |b−5| < 1}, B = {(a,b) ∈ R×R : 4(a−6)² + 9(b−5)² ≤ 36}. Then

Set A is an open square defined by |a−5|
Sets and Relations

Sets A, B With 2 and 4 Elements — Subsets of A×B With 3+ Elements

A has 2 elements, B has 4 elements. Find the number of subsets of A×B having 3 or more elements, using the complement of small…
Sets and Relations

Let S Be a Set of 10 Distinct Primes and A the Set of Products of Two or More Elements of S. If P = {(x,y): x ∈ S and y ∈ A and y Is Divisible by x}, Then n(P) Is Equal To

S is a set of 10 distinct primes and A is the set of products of two or more elements of S. Find n(P) where P={(x,y): x∈S, y∈A, x…