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Class 11 · Mathematics · Medium
→If A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, and R = {(a,b): b/a ∈ N}, what is |R|?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5}) and (B={1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (\gcd(a,b)=1) and (a+b) even?
Class 11 · Mathematics · Expert
→If (A={0,1,2,3}), (B={0,1,2,3,4}), and (R={(a,b):b\ge a^2-1}), what is (|R|)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4}), (B={1,2,3,4}), and (S={(a,b):a+b\text{ is even}}), how many pairs are in the complement of (S) relative to (A\times B)?
Class 11 · Mathematics · Expert
→If \(A=\{1,2,3,4,5\}\) and \(B=\{2,3,4,5,6,7\}\), how many ordered pairs \((a,b)\) in \(A\times B\) satisfy both conditions: \(a+b\) is prime and \(a<b\)?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4,5,6}) and (B={1,2,3,4,5,6}), how many pairs ((a,b)) in (A\times B) satisfy both (a\mid b) and (a<b)?
Class 11 · Mathematics · Expert
→If (A={0,1,2,3,4,5}) and (B={0,1,2,3,4,5}), how many pairs ((a,b)) in (A\times B) satisfy (a^2+b^2=25)?
Class 11 · Mathematics · Expert
→If (A={2,3,4,5,6,7,8}), (B={1,2,3,4,5}), and (R={(a,b):a+3b=17}), what is (|R|)?
Class 11 · Mathematics · Expert
→If (|A|=2) and (|B|=5), what is the number of subsets of (A\times B) having exactly (5) elements?
Class 11 · Mathematics · Expert
→If (A={1,2,3,4}) and (B={5,6,7}), how many subsets of (A\times B) contain ((1,5)) and ((4,7)) but do not contain ((2,6))?
Class 11 · Mathematics · Medium
→If |A × B| = 24, |A| = 4, and |C| = 7, what is |B × C|?
Class 10 · Mathematics · Medium
→If the roots of the equation \(x^2+px+42=0\) are \(-6\) and \(-7\), what is the value of \(p\)?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4}), (B={2,3,4,5,6}), and (S={(a,b):b>a+2}), how many elements are in (S\subseteq A\times B)?
Class 11 · Mathematics · Hard
→If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,3,4,5\}\), how many ordered pairs \((a,b)\) in \(A\times B\) have \(a+b\) divisible by 2?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4,5}) and (B={1,2,3,4,5}), how many pairs in (A\times B) are other than the diagonal pairs ((a,a))?
Class 11 · Mathematics · Hard
→If (A={1,2}), (B={3,4,5}), and (C={6,7,8}), what is (|(A\times B)\times C|)?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4,5}) and (B={1,2,3,4,5,6}), how many pairs ((a,b)) in (A\times B) satisfy (ab\le10)?
Class 11 · Mathematics · Hard
→If (A={2,3,5}) and (B={4,6,10,12,15}), how many pairs ((a,b)) in (A\times B) have (b) divisible by (a)?
Class 11 · Mathematics · Hard
→If (A={1,2,3,4}), (B={1,2,3,4}), and (R={(a,b):a\le b}), how many elements are in (R)?
Class 11 · Mathematics · Medium
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