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)3
ii. Total number of functions that can be defined from A to B is equal to:
a) 5! b) 5! .4! c) 4
5 d) 5
4
iii. ( × ) is equal to:
a) 20! b) 202
c) 2
20! d) ℎ
iv. If ( ) exceeds ( ) by , then is equal to:
a) 4 b) 16 c) 32 d)8
v. From the following which one is true?
a) ⊆ b) ⊆ c) = d) ℎ
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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
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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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