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MCQ (More than One Correct Answer)

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Let R and S be two equivalence relations on a non-void set A. Then
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For the mapping $$f:R - \{ 1\} \to R - \{ 2\}$$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is c...
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Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defi...
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A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P $$... WB JEE 2022 Let R be the real line. Let the relations S and T or R be defined by$$S = \{ (x,y):y = x + 1,0 ...
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Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote t...
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Let p1 and p2 be two equivalence relations defined on a non-void set S. Then
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Let $$A = \{ x \in R: - 1 \le x \le 1\}$$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then ...
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Let the relation p be defined on R by a p b holds if and only if a $$-$$ b is zero or irrational, then
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The domain of the function $$f(x) = \sqrt {{{\cos }^{ - 1}}\left( {{{1 - |x|} \over 2}} \right)}$$ is
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The function $$f(x) = \sec \left[ {\log \left( {x + \sqrt {1 + {x^2}} } \right)} \right]$$ is
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If A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6} are two sets, and function f : A $$\to$$ B is defined by f(x) = x + 2 $$\for... WB JEE 2010 Let R be the set of real numbers and the mapping f : R$$\to$$R and g : R$$\to$$R be defined by f(x) = 5$$-$$x2 and... WB JEE 2010 The domain of definition of the function$$f(x) = \sqrt {1 + {{\log }_e}(1 - x)} $$is WB JEE 2009 A mapping from IN to IN is defined as follows:$$f:IN \to INf(n) = {(n + 5)^2},\,n \in IN$$(IN is the set of natur... WB JEE 2009 For any two sets A and B, A$$-$$(A$$-$$B) equals WB JEE 2009 Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B? WB JEE 2008 A function f : A$$\to$$B, where A = {x/$$-$$1$$\le$$x$$\le$$1} and B = {y/1$$\le$$y$$\le$$2} is defined by the... WB JEE 2008 The mapping f : N$$\to$$N given by f(n) = 1 + n2, n$$\in$$N where N is the set of natural numbers, is... WB JEE 2008 A mapping f : N$$\to$$N where N is the set of natural numbers is defined as f(n) = n2 for n odd f(n) = 2n + 1 for n ev... WB JEE 2008 Three sets A, B, C are such that A = B$$\cap$$C and B = C$$\cap A, then
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