Class XI XII JEE Engineering Entrance Relations Functions Unit 2

Mathematics - Relations & Functions (Unit 2)
For Class XI, XII, JEE, BITSAT, Engineering Entrance.
For students from Class 11 to Class 12.
𝐼𝑛 𝑡ℎ𝑖𝑠 𝑐ℎ𝑎𝑝𝑡𝑒𝑟 𝑤𝑒 𝑤𝑖𝑙𝑙 𝑙𝑒𝑎𝑟𝑛 ℎ𝑜𝑤 𝑡𝑜 𝑙𝑖𝑛𝑘 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑒𝑛𝑡𝑖𝑡𝑖𝑒𝑠 𝑜𝑟 𝑠𝑒𝑡𝑠 𝑜𝑓 𝑑𝑎𝑡𝑎.
𝐶𝑎𝑟𝑡𝑒𝑠𝑖𝑎𝑛 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑆𝑒𝑡𝑠
𝑅𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠
𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠
𝑁𝐶𝐸𝑅𝑇 𝐶ℎ𝑎𝑝𝑡𝑒𝑟 2 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 𝑠𝑜𝑙𝑣𝑖𝑛𝑔
𝑻𝒐𝒖𝒈𝒉 𝒒𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒇𝒓𝒐𝒎 𝑱𝑬𝑬 𝒐𝒏 𝑹𝒆𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝒂𝒏𝒅 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏𝒔
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑓(𝑥) = √(𝑥^2−25𝑥+144)
𝐿𝑒𝑡 𝑓: 𝑁→𝑅𝑖𝑠 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑓(1)=1 𝑎𝑛𝑑 𝑓(1)+2𝑓(2)+…+𝑛𝑓(𝑛)=𝑛(𝑛+1)𝑓(𝑛) ∀𝑛≥2
𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓(2025)?
𝐿𝑒𝑡 𝐴 = {1,2,3,…,10} 𝑎𝑛𝑑 𝑓:𝐴→𝐴 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠 𝑓(𝑘)=𝑘+1 (𝑓𝑜𝑟 𝑜𝑑𝑑 𝑘) 𝑎𝑛𝑑 𝑓(𝑘)=𝑘 (𝑓𝑜𝑟 𝑒𝑣𝑒𝑛 𝑘)
𝑡ℎ𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝑔:𝐴→𝐴 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑔𝑂𝑓=𝑓 𝑖𝑠 [𝐽𝐸𝐸 𝑀𝐴𝐼𝑁𝑆]
[𝐽𝐸𝐸 𝑀𝑎𝑖𝑛𝑠] 𝑇ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑜𝑓 𝑓(𝑥)= sin^(−1)⁡((|𝑥|+5)/(𝑥^2+1)) 𝑖𝑠 (−∞,−𝑎]∪[𝑎,∞) Then value of a is
[𝑱𝑬𝑬 𝑴𝒂𝒊𝒏𝒔] Let A={2,3,6,7} and B={4,5,6,8}.
Let R be a relation defined on A×B by (a1,b1)R(a2,b2) if and only if a1+a2=b1+b2. Then the number of elements in R is __________.
[𝐽𝐸𝐸 𝑀𝑎𝑖𝑛𝑠] 𝐿𝑒𝑡 𝐴={1,2,3,…,20}. 𝐿𝑒𝑡 𝑅1 𝑎𝑛𝑑 𝑅2 𝑡𝑤𝑜 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑛 𝐴 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡
𝑅1={(𝑎,𝑏):𝑏 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 𝑎} 𝑅2={(𝑎,𝑏):𝑎 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 𝑏}.
𝑇ℎ𝑒𝑛, 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑖𝑛 𝑅1−𝑅2 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 _____________.