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Question

If the points (α,α2) and (1,2) lie in the same angular region between the lines 3x+4y1=0 and 2x+y3=0, then the range of α is:

A
α<3orα>1
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B
3a1
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C
α<12orα>1
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D
none of these
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Solution

The correct option is A α<3orα>1
The Given Lines are 3x+4y1=0 and 2x+y3=0

Putting point (1,2) in both lines we get,

3(1)+4(2)1=10>0 and 2(1)+(2)3=1>0

Hence Point (1,2) is same side of both the lines, opposite to origin.

If the point (α,α2) also lies in same angular region as of (1,2), then it must give positive values out of both the equations.

Hence, 3α+4α21>0 ...(1)

2α+α23>0 ...(2)

From equation (1) we get,

(α+1)(4α1)>0

(α+3)(α1)>0

On combining the result we get, α<3 or α>1

Hence correct option is A.

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