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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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On R, the set of real numbers, a relation $$\rho $$ is defined as 'a$$\rho $$b if and only if 1 + ab > 0'. Then,
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MCQ (Single Correct Answer)
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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 $$...
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Let R be the real line. Let the relations S and T or R be defined by $$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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Let S, T, U be three non-void sets and f : S $$ \to $$ T, g : T $$ \to $$ U be so that gof : s $$ \to $$ U is surjective...
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Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)
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Let the relation $$\rho $$ be defined on R as a$$\rho $$b if 1 + ab > 0. Then,
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Let $$\rho $$ be a relation defined on N, the set of natural numbers, as$$\rho $$ = {(x, y) $$ \in $$ N $$ \times $$ N :...
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On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.
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On R, a relation $$\rho $$ is defined by x$$\rho $$y if and only if x $$-$$ y is zero or irrational. Then,
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On set A = {1, 2, 3}, relations R and S are given byR = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},S = {(1, 1), (2, 2), (3...
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On R, the relation $$\rho$$ be defined by 'x$$\rho$$y holds if and only if x $$-$$ y is zero or irrational'. Then,
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On the set R of real numbers we define xPy if and only if xy $$ \ge $$ 0. Then, the relation P is
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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 $$\for...
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Let R be the set of real numbers and the mapping f : R $$\to$$ R and g : R $$\to$$ R be defined by f(x) = 5 $$-$$ x2 and...
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The domain of definition of the function $$f(x) = \sqrt {1 + {{\log }_e}(1 - x)} $$ is
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A mapping from IN to IN is defined as follows: $$f:IN \to IN$$ $$f(n) = {(n + 5)^2},\,n \in IN$$ (IN is the set of natur...
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For any two sets A and B, A $$-$$ (A $$-$$ B) equals
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Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B?
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A function f : A $$\to$$ B, where A = {x/$$-$$1 $$\le$$ x $$\le$$ 1} and B = {y/1 $$\le$$ y $$\le$$ 2} is defined by the...
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The mapping f : N $$\to$$ N given by f(n) = 1 + n2, n $$\in$$ N where N is the set of natural numbers, is...
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A mapping f : N $$\to$$ N where N is the set of natural numbers is defined as f(n) = n2 for n odd f(n) = 2n + 1 for n ev...
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Three sets A, B, C are such that A = B $$\cap$$ C and B = C $$\cap$$ A, then
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