Relations and Functions

JEE Main Mathematics · 8 questions

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• Consider the relation R on the set {-2,-1,0,1,2} defined by (a, b) ∈ R if and only if 1+ab>0. Then, among the statements: I. The…20268 April, Shift 2 · Q1
• Let f be a polynomial function such that log_2(f(x))=( log_2(2+2/3+2/9+… … ∞)) · log_3(1+(f(x))/(f(1 / x))), x>0 and f(6)=37.…20268 April, Shift 2 · Q25
• Let f: R → R be defined as f(x)=(2 x^2-3 x+2)/(3 x^2+x+3). Then f is:20266 April, Shift 2 · Q1
• Let R={(x, y) ∈ N × N: log_e(x+y) ≤ 2}. Then the minimum number of elements, required to be added in R to make it a transitive…20266 April, Shift 2 · Q21
• Let A={1,4,7} and B={2,3,8}. Then the number of elements, in the relation R={((a_1, b_1),(a_2, b_2)) ∈((A × B) ×(A × B)):…20265 April, Shift 2 · Q21
• For the function f:[1, ∞) →[1, ∞) defined by f(x)=(x-1)^4+1, among the two statements: (I) The set S={x ∈[1, ∞): f(x)=f^-1(x)}…20264 April, Shift 2 · Q1
• Let for some α ∈ R, f: R → R be a function satisfying f(x+y)=f(x)+2 y^2+y+α x y for all x, y ∈ R. If f(0)=-1 and f(1)=2, then the…20264 April, Shift 2 · Q16
• Let A={2,3,4,5,6}. Let R be a relation on the set A × A given by (x, y) R(z, w) if and only if x divides z and y ≤ w. Then the…20262 April, Shift 2 · Q21