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Class 12 · Mathematics
→If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^2+2x+3), which statement about the range of (f) is correct?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), relation (R) has classes ({1,6}), ({2,3,5}), and ({4}). Which pair definitely will not be in (R)?
Class 12 · Mathematics
→On (A=\mathbb{R}), (xRy) if (\sin x=\sin y). What type of relation is this?
Class 12 · Mathematics
→If (A) has (5) elements and (R=A\times A), how many equivalence classes will (R) have?
Class 12 · Mathematics
→If (A) has (5) elements and (R) is the equality relation, how many pairs are in (R)?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if (a) and (b) have the same remainder on division by (2). Which pair will not be in (R)?
Class 12 · Mathematics
→On (A=\mathbb{Z}), (aRb) if (a-b) is even. What is true about ([1]) and ([2])?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8}), (aRb) if (a) and (b) lie in the same block among ({1,2}), ({3,4,5}), ({6,7,8}). How many pairs are in the relation?
Class 12 · Mathematics
→On natural numbers, (aRb) if (a) and (b) have the same sum of digits. What type of relation is this?
Class 12 · Mathematics
→If two equivalence classes ([a]) and ([b]) of an equivalence relation are distinct, what is true about their intersection?
Class 12 · Mathematics
→On (A={1,2,3,4}), an equivalence relation has the single class ({1,2,3,4}). Which relation is it?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if (a+b) is divisible by (3). Why is this not an equivalence relation?
Class 12 · Mathematics
→On (A=\mathbb{R}), (xRy) if (x-y\geq 0). Why is this not an equivalence relation?
Class 12 · Mathematics
→On real numbers, (xRy) if (x^3=y^3). What is the correct conclusion about this relation?
Class 12 · Mathematics
→An equivalence relation (R) on a set (A) has classes ({a,b}), ({c}), and ({d,e,f}). How many pairs are in (R)?
Class 12 · Mathematics
→On (A=\mathbb{Z}), (aRb) if (a-b) is divisible by (4). How many distinct equivalence classes does this relation have?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if (a) and (b) leave the same remainder on division by (3). What is ([2])?
Class 12 · Mathematics
→If an equivalence relation on (A={1,2,3}) contains ((1,2)) and ((2,3)), what is the minimum number of pairs in (R)?
Class 12 · Mathematics
→On (A=\mathbb{R}), (xRy) if (x-y=0). Which relation is this?
Class 12 · Mathematics
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