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17.Let = : ≤ 5, ∈ ,= : = − 2 , 5 ≤ < 9, where . is the greatest integer function .Based on the above information, answer the followings.i. ( ∪ ) is equal to :a) 9 b) 0 c) 6 d)3ii. Total number of functions that can be defined from A to B is equal to:a) 5! b) 5! .4! c) 45 d) 54iii. ( × ) is equal to:a) 20! b) 202c) 220! d) ℎiv. If ( ) exceeds ( ) by , then is equal to:a) 4 b) 16 c) 32 d)8v. From the following which one is true?a) ⊆ b) ⊆ c) = d) ℎ |
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Answer» Answer: 11th Maths Relations and FUNCTIONS Some Functions and their Graphs Let [a] denotes the greates... MATHS Let [a] denotes the greatest integer LESS than or equal to a. GIVEN that the quadratic EQUATION x 2 +[a 2 −5a+b+4]x+b=0 has roots −5 and 1, which of the following is true This question has multiple correct options
HARD Share Study later ANSWER Since −5 and 1 are the roots of the equation x 2 +[a 2 −5a+b+4]x+b=0 ∴−5+1=−[a 2 −5a+b+4]and−5×1=b ⇒[a 2 −5a+b+4]=4andb=−5 ⇒[a 2 −5a−5+4]=4 ⇒[a 2 −5a−1]=4⇒4≤a 2 −5a−1<5 ⇒a 2 −5a−1≥4anda 2 −5a−1<5 ⇒a 2 −5a−5≥0anda 2 −5a−6<0 ⇒a≤ 2 5−3 5
ora≥ 2 5+3 5
and−1,6 ∴aϵ(−1, 2 5−3 5
)∪( 2 5+3 5
,6) |
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